yi ignatius is of waec and neco using partial credit ducation ...

PRACTICAL PHYSICS TESTS USING PARTIAL

ADONU, IFEANYI IGNATIUS

PG/Ph.D/08/49721

PSYCHOMETRIC ANALYSIS OF WAECPRACTICAL PHYSICS TESTS USING PARTIAL

MODEL

FACULTY OF EDUCATION

DEPARTMENT OF SCIENCE EDUCATION

Paul Okeke

Digitally Signed by: Content manager’s DN : CN = Webmaster’s name O= University of Nigeri OU = Innovation Centre

ADONU, IFEANYI IGNATIUS

PSYCHOMETRIC ANALYSIS OF WAEC AND NECO PRACTICAL PHYSICS TESTS USING PARTIAL CREDIT

EDUCATION

DEPARTMENT OF SCIENCE EDUCATION

: Content manager’s Name

Webmaster’s name

O= University of Nigeria, Nsukka

OU = Innovation Centre

PSYCHOMETRIC ANALYSIS OF WAEC AND NECO

PRACTICAL PHYSICS TESTS USING PARTIAL CREDIT MODEL

BY

ADONU, IFEANYI IGNATIUS PG/Ph.D/08/49721

DECEMBER, 2014

iii

PSYCHOMETRIC ANALYSIS OF WAEC AND NECO PRACTICAL PH YSICS TESTS USING PARTIAL CREDIT MODEL

A Ph.D THESIS SUBMITTED TO THE DEPARTMENT OF SCIENCE EDUCATION

UNIVERSITY OF NIGERIA, NSUKKA

BY

ADONU, IFEANYI IGNATIUS PG/Ph.D/08/49721

DECEMBER, 2014

iv

APPROVAL PAGE

This project has been approved for the Department of Science Education,

University of Nigeria, Nsukka.

____________________ ____________________ Professor B.G. Nworgu Professor Z.C. Njoku Supervisor Head of Department ______________________ ____________________ Professor Kalu, Iroha Mathias Dr. B. C. Madu External Examiner Internal Examiner

________________________ Professor Uju C. Umo

Dean, Faculty of Education

v

CERTIFICATION

This is to certify that ADONU, IFEANYI IGNATIUS, a postgraduate student in the

Department of Science Education with Registration Number PG/Ph.D/08/49721 has

satisfactorily completed the requirements for the award of the Degree of Doctor of

Philosophy in Measurement and Evaluation. The work embodied in this Thesis is original

and has not been submitted in part or full for any other diploma or degree of this or any

other university.

________________________ ____________________ Adonu, Ifeanyi Ignatius Prof. B. G. Nworgu Student Supervisor

vi

DEDICATION

To my dear wife Carolyn Ukamaka for her patience and empathetic compromise.

vii

ACKNOWLEDGEMENTS

The researcher is infinitely grateful to Almighty God for granting him good

health, protection, favour, strength and divine grace all through the span of this study.

The transform of this work to a reality today is just a prime grant of the Almighty God.

The researcher therefore promises and prescribes constant adoration to God for this

singular gesture.

The researcher remains forever grateful to Prof. B.G. Nworgu his supervisor for

the study. Through his innate and infinite professional virtues, -tolerance, empathy,

wealthy technical experiences, perseverance etc – he offered immeasurable and exquisite

assistance, advice, criticism and motivations in the course of this study. For his

magnanimity in the course of this work, I will prevail on the Almighty God to bless him

beyond bounds and limits of his passionate expectations.

The immense gratitude of the researcher is also indelibly registered for Dr. B.C.

Madu, Dr. (Mrs.) F.O. Ezeudu, Prof. Z.C. Njoku, Prof. K.O. Usman, Mr Chris Ugwuanyi

and other lecturers in Department of Science Education, University of Nigeria. Their

painstaking efforts in reading through the manuscript, their criticisms and scholarly

inputs, contributed significantly to the grand success of this exercise. To all of you I say

bravo and let God multiply your blessings a million times, thank you so much.

It will be absolutely unfair if the researcher concludes this acknowledgement

without the recognition of prime role played by Dr. J.J. Agah of Department of Science

Education, University of Nigeria, Nsukka in procuring the WINSTEP Computer software

program used for the analysis of the data obtained in this study. Additionally, his roles in

providing directions and criticisms, reading of the manuscripts etc knew no bounds.

The researcher’s joy and thanks also go to Mr. C.E. Urama, former Dean, school

of Sciences, Federal College of Education, Eha-Amufu, Mr. Emmanuel Eze of National

Orientation Agency Enugu and Mr. Emmanuel Uroko of National Orthopedic Hospital,

Enugu. These close allys of mine were divinely inspired to ensure that the study did not

get extinguished when I was at the “Cross road”. The good God that inspired them to

propel the study forward cannot afford not to uplift them one by one in the nearest future.

Equally, appreciated are the following lecturers, Mr. Onyishi S.O., Mrs. Omeke

N.E., Miss Nwoke, C.M., Engr.Ugwu, H.C. (of Department of Physics Fed. College of

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Education Eha-Amufu), Mr. Adegoke Nathan, Mr. Odo Friday, of Integrated Science

FCE Eha-Amufu, Mr Eze Celestine Onyebuchi of College Library FCE Eha-Amufu (and

Sister Chika Sylvanus who typed most of the work). Their indispensable roles as able and

committed research assistants throughout the conduct of the study and marking are

hereby fully acknowledged. I cannot thank them well enough but I pray that God will

elevate all of them in the nearest future.

The prayers of Pastor and Pastor (Mrs.) Celestine Ugwuja and other brethren

provoked the requisite spiritual empowerment and psychological equanimity for the

success of this study. I thank them in a special way.

Finally, the researcher thanks in a special way his wife – Carolyn Ukamaka, and

his children – Ifeanyi Henry, Favour Chiamaka, Gold Abumchi and Divine Chimere for

their love, understanding, prayers and support were immeasurable during this study. I

remain forever grateful to them for tolerating and coping with my absence in the course

of this study.

To all of you I say more blessings.

Adonu Ifeanyi Ignatius

x

TABLE OF CONTENTS

Title Page i

Approval Page ii

Certification iii

Dedication iv

Acknowledgement v

Table of Contents vii

List of Appendices x

List of Tables xii

List of figures xiii

Abstract xiv

CHAPTER ONE: INTRODUCTION

Background of the Study 1

Statement of the Problem 12

Purpose of the Study 13

Significance of the Study 14

Scope of the Study 15

Research Questions 15

Hypotheses 16

CHAPTER TWO: LITERATURE REVIEW

Conceptual Framework 18

Achievement Testing 20

Item Analysis 21

Validity and Reliability of Measurement Instrument 25

Reliability and Standard Error of Measurements 31

Theoretical Framework

Classical Test Theory 32

Item Response Theory 34

− Historical Background of Item Response Theory (IRT) 34

− Conceptual Background of Item Response Theory 35

− Models of Item Response Theory 43

xi

The Partial Credit Model 45

Some IRT Methods in Estimating Item Parameters 50

Statistical Fit Tests 51

Empirical Studies 52

Summary of Literature Reviewed 61

CHAPTER THREE: RESEARCH METHODS

Research Design 63

Area of Study 63

Population of the Study 63

Sample and Sampling Techniques 64

Instrument for Data Collection 65

Validity of the Instrument 65

Reliability of the instrument 65

Method of Data Collection 66

Method of Data Analyses 66

CHAPTER FOUR: RESULTS

Research Question 1 69








Hypothesis 1 83

Hypothesis 2 83

Hypothesis 3 84

Hypothesis 4 84

Hypothesis 5 85

Hypothesis 6 85

xii

Hypothesis 7 86

Hypothesis 8 87

Hypothesis 9 87

Summary of the Findings of the Study 88

CHAPTER FIVE: DISCUSSION, CONCLUSION AND SUMMARY

Discussion of the Findings 90

Conclusion Reached from the Findings of the Study 98

Implications of the Study 99

Limitations of the Study 100

Recommendations 101

Suggestion for Further Studies 101

Summary of the Study 102

References 109

Appendices 115

A: List of Public secondary schools in Enugu State 115

B: Letter to principal / physics teachers for administration of the instrument 118

C: Practical physics Questions of NECO 2011 (PPQN 1) 119

D: Practical physics questions of NECO 2012 (PPQN 2) 124

E: Practical physics questions of WAEC 2011 (PPQW 1) 127

F: Practical physics questions of WAEC 2012 (PPQW 2) 131

G: Marking scheme of PPQN 2 134

H: Marking scheme of PPQN 1 142

I: Marking scheme of PPQW 1 150

J: Marking scheme of PPQW 2 154

K: Item statistics of Partial Credit analysis showing SEM, fit statistics and ZSTD, difficulty estimates for PPQN 1 158

L: Item fit order of Partial Credit analysis showing observed, expected, residual and STD residual for PPQN 1 159

M: Summary statistics of PCM analysis showing the test reliability for PPQN1 160

xiii

N: Item statistics of Partial Credit analysis showing SEM, fit statistics and ZSTD, difficulty estimates for PPQN 2 161

O: Item fit order of Partial Credit analysis showing observed,

expected, residual and STD residual for PPQN 2 162

P: Summary statistics of PCM analysis showing the test reliability for PPQN2 163

Q: Item statistics of Partial Credit analysis showing SEM, fit statistics and ZSTD, difficulty estimates for PPQW 1 164

R: Item fit order of Partial Credit analysis showing observed, expected,

residual and STD residual for PPQW 1 165 S: Summary statistics of PCM analysis showing the test reliability

for PPQW1 166

T: Item statistics of Partial Credit analysis showing SEM, fit statistics and ZSTD, difficulty estimates for PPQW 2 167

U: Item fit order of Partial Credit analysis showing observed, expected, residual and STD residual for PPQW 2 168

V: Summary statistics of PCM analysis showing the test reliability

for PPQW2 169

W: Education Zones, local government areas and the number of sampled Schools 170 X: Summary of sample size used for data collection as distributed in schools and education zones, local government 171

Appendix

AA: Paired sample t-test analysis of SEM for NECO 2011 and NECO 2012 172

AB: Paired sample t-test analysis of SEM for WAEC 2011 and WAEC 2012 173

AC: Paired sample t-test analysis of SEM for NECO 2011 and WAEC 2011 174

AD: Paired sample t-test analysis of SEM for NECO 2012 and WAEC 2012 175

AE: Paired sample t-test analysis of fit (validity) of NECO 2011 and NECO 2012

176

AF: Paired sample t-test analysis of fit (validity) of WAEC 2011 and WAEC 2012

177

AG: Paired sample t-test analysis of fit (validity) of NECO 2011 and WAEC 2011

178

xiv

AH: Paired sample t-test analysis of fit (validity) of NECO 2012 and WAEC 2012

179

AI: Paired sample t-test for item difficulty (b) of NECO 2011 and NECO 2012

180

AJ: Paired sample t-test for item difficulty (b) of WAEC 2011 and WAEC 2012

181

AK: Paired sample t-test for item difficulty (b) of NECO 2011 and WAEC 2011

182

AL: Paired sample t-test for item difficulty (b) of NECO 2012 and WAEC 2012

183

AM: Squared standardized Residual (fit analysis) of NECO 2011and NECO 2012

184

AN: Squared standardized Residual (fit analysis) of WAEC 2011and WAEC 2012

185

AO: Squared standardized Residual (fit analysis) of NECO 2011and WAEC 2011

186

AP: Squared standardized Residual (fit analysis) of WAEC 2011and NECO 2012

187

xv

LIST OF TABLES

Table pgs

1: SEM of practical physics exam conducted by NECO 2011 and NECO 2012 69

2: SEM of practical physics exam conducted by WAEC 2011 and WAEC 2012 70

3: Validity (Fit statistics) of practical physics exam by NECO 2011 and NECO 2012 72

4: Validity (Fit statistics) of practical physics exam by W AEC 2011 and

WAEC 2012 74

5: Item difficulty measures (b) of NECO practical physics questions conducted in NECO 2011 and NECO 2012 76

6: Item difficulty measures (b) of NECO practical physics questions conducted in WAEC 2011 and WAEC 2012 78

7: The infit, outfit and their ZSTD of NECO 2011 and NECO 2012 practical

physics exam 80

8: The infit, outfit and their ZSTD of WAEC 2011 and WAEC 2012 practical

physics exam 82

9: T test of SEM of NECO 2011 and NECO 2012 83

10: T test of SEM of WAEC 2011 and WAEC 2012 83

11: T test of SEM of NECO 2011 and WAEC2011 84

12: T test of SEM of NECO 2012 and WAEC 2012 84

13: T test of fit statistics (validity) of NECO 2011 and NECO 2012 84

14: T test of fit statistics (validity) of WAEC 2011 and WAEC 2012 85

15: T test of fit statistics (validity) of NECO 2011 and WAEC 2011 85

16: T test of fit statistics (validity) of NECO 2012 and WAEC 2012 86

17: T test of item difficulty estimates for NECO 2011 and NECO 2012 86

18: T test of item difficulty estimates for WAEC 2011 and WAEC 2012 87

19: T test of item difficulty estimates for NECO 2011 and WAEC 2011 87

20: T test of item difficulty estimates for NECO 2012 and WAEC 2012 88

xvi

LIST OF FIGURES

1. Item Characteristics curve for One Parameter Partial Credit Model of IRT.

10

2. Schematic Diagram of Conceptual and Theoretical Framework.

19

3. Adaptation of Rasch ICC for One Parameter PCM.

38

4. The Item Trace Line for Underlying Latent Variable.

39

5. Test Characteristics Curve.

40

6. Item Information Function.

41

7. Test Information Function with approximeter

42

xvii

ABSTRACT

The purpose of the study was to analyse the psychometric qualities of practical physics questions of West African Examination Council and National Examinations Council using the Partial Credit Model (PCM). The objectives of the study were specifically to evaluate the Standard Error of Measurement (SEM), the fit statistics and item difficulty estimates of WAEC and NECO practical physics items and also to test for significance difference of NECO, WAEC and NECO-WAEC psychometric qualities in various years. The apparent difference in the public image of WAEC and NECO examinations, the neglect of psychometric analsyis of polytomously scored physics items and the absolute importance of psychomotor assessments in physics, motivated the researcher to carry out this study. The design of the study was instrumentation research design and the area of the study was Enugu State of Nigeria. The population of the study was all SS III physics students of 2012/2013 academic session in Enugu State. A sample of 668 physics students was drawn through multi stage sampling procedure. The instrument for the study consisted of four different tests viz; two practical physics questions of NECO 2011 and 2012 (PPQN, 1 and 2) and two practical physics questions of WAEC 2011 and 2012 (PPQW, 1 and 2). Eight research questions and nine hypotheses guided the study. The research questions were answered using the descriptive statistics of Winstep software maximum likelihood ratio. The hypotheses were tested at 0.05 level of significance using the SPSS independent sample t-test statistics, and the chi square goodness of fit test using WINSTEP PCM analysis and SPSS. The major findings of the study indicated that: The standard error of measurement (SEM) of items of WAEC and NECO practical physics in 2011 and 2012 were very low- below 0.18 for all items. The fit statistic indicated that nearly all the items of both exams NECO and WAEC were valid and thus sufficiently demonstrated unidimensionality; The item difficulty estimates (b) for both examinations for the two years studied showed that all the items have difficulty estimates that range between -1.53 to +1.94 which show that their difficulty are moderate for all items. All the four different tests that constituted the instrument had very high proportion of their item fit to PCM with all the four parts having 0.92 proportion of fit. Other findings of the study include; There was significant difference in NECO 2011and NECO 2012, SEM. There was no significant difference between WAEC 2011 and WAEC 2012; NECO 2011 and WAEC 2011; NECO 2012 and WAEC 2012, SEM; NECO 2011 and NECO 2012; WAEC 2011 and WAEC 2012; NECO 2011 and WAEC 2011; NECO 2012and WAEC 2012 fit (validity) analysis; and in the difficulty estimates of NECO 2011 and NECO 2012; WAEC 2011 and WAEC 2012; NECO 2011 and WAEC 2011; NECO 2012 and WAEC 2012 tests. Based on the close resemblance of the psychometric qualities of these two examination bodies as revealed by these findings it is recommended that the confidence and recognition accorded to these two examination bodies by the public and educational institutions continues to be the same.

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CHAPTER ONE

INTRODUCTION

Background of the Study

Societal development and break through in any nation are predicated on education

sector of such a nation. New researches prove the long held expectation that human

capital formation (the population education) plays a significant role in country’s

economic development. Quality education leads not only to higher individual output but

is also a necessary precondition for long term economic growth. Rigorous analysis of

data provides policy makers with proof that education is a necessary precondition for

long term economic development.

It is for the above reason that Nigeria in her National Policy in Education adopted

education as an instrument “par excellence” for effecting national development and

harnessing the potentials of the citizens (Federal Republic of Nigeria, FRN 2008).

Akindogu and Bamjoko (2010) pointed out that the country’s vision is for a complete

transformation of all aspects of the nations life over time and that education should be

able to effect inter and intra generational transmission of our cherished heritages and life

inventions and should reposition Nigeria global status in science and technology in all

spheres of life.

While commenting on the role of education in national development, Blogspot

(2009) noted that education is a milestone for all types of development and provides all

knowledge to do any work in a systematic way. According to this author, with education

any country can develop her economy and society, develop the personality of youths of

the nation; make the citizens more productive by providing large number of skills to

make them self reliant.

The major challenge for education in the twenty first century for our country

Nigeria according to Maduagwu (2008) is designing an educational system that will be

stable and global in outlook, and maintaining high standard of education. A cardinal

challenge for Nigeria, if she is to use education to achieve the objective of overall

development, is maintaining high standard of education through high quality assessment.

And to achieve high quality assessment, in order to realize the goal of overall

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2

development, all the dimensions of educational objectives must be adequately measured

and assessed.

Educational objectives according to Onwuka (1981) are expressed in terms of

knowledge (cognitive domain), attitude (affective domain) and practical/motor skills

(psychomotor domain). Hence education is said to be balanced when it satisfies the

demands of the three major domains of educational objectives. Behaviour under the three

domains of objective should form the bases for teaching and learning process and

subsequently assessment. Bandele (2002) noted that the three domains should be taught

and assessed critically to mould individual in totality and make the recipient of education

to live a fulfilled life and contribute meaningfully to the society in which he lives.

The cognitive objectives refer to the intellectual results of schooling, the

improvement in the child’s intellectual structure, his increase in knowledge and his

ability to reason rather than just to remember. The affective objectives refer to the

emotional education, and the learners’ acquisition of certain desirable attitudes, interest

and appreciation; while psychomotor objectives refer to physical and practical

manipulative skills learnt at school (Nwana, 1979).

The three domains of educational objectives according to Oyesola (1986) are

inter-related. In general psychomotor domain deals with practical activities and some

examples of practical and motor activities include writing legibly, drawing maps

accurately, ability to manipulate laboratory equipment and use them effectively,

maintaining farm tools, weave and make baskets etc (Osunde, 1997). This author posited

that practical skill assessment requires some form of performance testing under a

controlled condition.

The National Policy on Education (FRN, 2008) considers the acquisition of

appropriate skills, abilities and competences as equipment for the individual to live and

contribute to the development of the society as one of the cardinal national educational

goals (FRN, 2008). The national policy was explicit on developing the manipulative

skills of students in the schools and de-emphasizing the memorization and regurgitation

of facts while encouraging practical, exploratory and experimental methods of

developing motor skills. Also, for secondary and tertiary institutions, the national policy

has vividly emphasized the acquisition of manual and practical skills that will enable us

3

to live and keep pace in the modern age of technology. The various policies of national

government as stated above can readily be realized by emphasizing qualitative

assessment of the aspect of curriculum that teach practical skills. Therefore, for the

objectives of national policy on technological advancement to be realized through the

school system, a greater emphasis has to be given to the psychomotor assessment of

practical aspect of various courses.

Since the instructional objective include psychomotor domains (practical skills),

this domain should be assessed and stressed like the cognitive assessment. Generally, in

sciences, WAEC and NECO place more emphasis on cognitive domain than on other

domains of educational objectives. At secondary school level, most often than not

assessment is concentrated on cognitive achievement to the detriment of psychomotor

and affective development of the learners. This is not unconnected with Nigeria societal

quest for paper qualification. Thus, a child with pass mark in his or her subject receives a

certificate at the end of the course no matter how bad his/her manners are or how

unskilled he/she may be (Idowu and Esere, 2009). In other words, psychomotor and

affective traits do not fully count towards obtaining a certificate. Educational evaluators

like Miller, Frank, Frank and Eheltor (1989), have prescribed a departure from excessive

emphasis on only cognitive domain to make room for a more comprehensive picture in

the development of the learners in the school system.

Test of practical skills in physics is measurement of psychomotor domain of

behaviour. Different instruments exist for the assessment of psychomotor domains of our

educational enterprise. To evaluate achievement in psychomotor domain, the procedures

are the same with that of cognitive domain, although the objectives differ. The procedure

for assessing the psychomotor domain includes among others practical work and projects

(Harbor Peters, 1999). Test of practical skills are of importance because like every other

reliable and valid test performances, they are utilized for selection of candidates, for

further studies, for employment etc. Several experts such as Yoloye (2004), Harbor-Peter

(1999), Nworgu (1992), and Gronlund (1975) have noted that achievement test in

psychomotor domains of educational objectives serve the purpose of evaluating students

progress and giving students, parents, family, school and society feedback on the students

progress. Also, achievement tests in psychomotor motivate students to learn more; giving

4

feedback on teaching effectiveness; predicting future performances; providing methods

of selection, etc.

Achievement test in physics practicals is inevitable because the practice of

physics equips us with the knowledge of underlying principle for the majority of our

technological products. According to Egbugara (1989), “physics is the most fundamental

science subject which act as the basic index to all courses in technological development

and myriad of other scientific development necessary to mankind”. WAEC (2009) stated

that the objectives of practical physics among others are to inculcate in students the spirit

of scientific investigation, to establish some basic principles of physics using experiment,

to understand the use of certain equipment, to develop the ability of conducting

experiment according to specification while using same for analysis.

Also, Kirschner and Meester (1988) suggested the students’ centered objective for

practical work to include (i) to formulate hypotheses (ii) to solve problems (iii) to use

knowledge and skill in unfamiliar situation (iv) to design simple experiment for testing

hypothesis (v) to use laboratory skills in performing experiment, interpret the data and

draw inference. In the same vein, Carduff and Reid (2003) provided many possible

reasons for inclusion of practical work in various subjects to include, illustrating key

concepts, training in specific practical skills, developing observational skills, deduction

and interpretation skills, developing problem solving skills, showing that theory arises

from practical and developing the scientific bases for some products etc. Practical physics

as a matter of fact is indispensable as they improve our disposition towards the scientific

bases of technology. Adequate practical activities in physics correlate with good school

results in physics. Practical, project and examinations, test achievement in psychomotor

domain.

Test is only one technique of measuring educational outcomes and other

techniques include questionnaire, interview, practicals, observations etc. Test connotes a

structured situation comprising a set of questions which an individual is expected to

respond to, on which bases his behaviour, and/or performance is quantified ( Habor

Peters, 1999; Nworgu, 1992; Gronlund, 1976)

Gronlund (1976) hinted that the validity of information provided by the test (of

practical skills) however, depends on the care with which the test are planned and

5

developed. Also, measurement of practical skills in education is the quantitative

description of pupils change in behavior and measurement instruments are tests, class

work, projects, assignment etc (Habor Peters, 1999; Nworgu, 1992;). Nenty (2004) and

Kerlinger and Lee, (2000), have suggested that for measurement in education to be

meaningful, the objectives to be measured, the number to be assigned and the rules of the

assignment of the number must be well defined. Yoloye (2004) stated that responses to

tests and other measuring instruments enable the examiner to assign the testees numeral

or set of numerals from which inferences could be made about the testees performance on

whatever the test is supposed to measure. This means that a good instrument for testing of

psychomotor ability should have some psychometric properties

In the first instance psychometric analysis is the science of measuring latent traits

or constructs in our subjects of interests. The psychometric analysis of a test would imply

analyzing such constituents of psychometrics as (i) Validity- whether a test measures

what it is intended to measure (ii) Reliability – the consistency in measuring what it

intends to measure (iii) Difficulty index or conversely easiness index ( iv) Discrimination

index –how sharply does the test distinguish between low and high ability students. The

psychometric analysis of a psychomotor test in physics therefore implies analysis of

practical test in physics to obtain the validity, reliability, difficulty and discrimination

indices.

In practice, the relevance of practical test is largely dependent on the levels of

reliability, validity, difficulty and discrimination indices. All these constitute

psychometric properties of a test. The psychometric analysis of a test is a multi step

process that can follow more than one measurement theory frame work. These

frameworks are usually classical test theory (CTT) and item response theory (IRT).

The teacher, the school and various assessment agencies such as West African

Examination Council (WAEC) and National Examination Council (NECO), etc are

saddled with the responsibility of implementing the objectives as stated in national policy

on education. In WAEC and NECO the analysis of psychometric qualities of their

polytomously scored items are mostly done with classical test theory (Korashy, 1995).

Thereafter the qualities of these items are kept as classified information and can be hardly

accessed by the public, researchers or other educational agencies. Since the practical

6

aspect of physics curriculum is a sine-qua-non to technological advancement and

realization of objectives of national policy on education, it is therefore pertinent that the

psychometric properties of practical tests by the examination bodies such as WAEC and

NECO should be determined. This will indicate the overall quality of assessment/ test

conducted by the examination bodies in practicals. This will go a long way towards

enlisting confidence or otherwise in the examining bodies.

The ultimate examining bodies in secondary schools such as WAEC and NECO

assess /test the psychomotor aspects of objectives through practical examinations in the

sciences. WAEC, NECO and National Business and Technical Education Board

(NABTEB) are the three bodies in Nigeria today that have the responsibility of awarding

ordinary level certificate.

The origin of WAEC dates back to 1949, when the British Council of states for

colonies invited Jeffry to visit West Africa to study and come up with a proposal for West

African Examination Council (WAEC, 2002). The report was submitted and adopted in

1950 by four West African governments (Nigeria, Ghana, Sierra Leone and Gambia).

These governments came up with an ordinance that established WAEC as a cooperate

body. WAEC in these countries conduct both national and international examination at

both ordinary and advanced levels.

Also, in 1999, the Federal government of Nigeria established the National

Examination council (NECO). The aim of this is for Nigeria to have an independent and

national examination body that has the same standard with WAEC. The cooperate

headquarters of NECO is Minna and they conduct national examinations such as

examination into unity schools i.e. entrance examination into Federal government

secondary schools, entrance examinations into schools for the gifted children and

ordinary level school certificate examinations (NECO, 2001).

The WAEC physics O’level examinations are made up of three parts: paper 1

(practical – 50 marks); paper 2 (objective – 50 marks); and paper 3 (essay – 60

marks)(WAEC,2009).Exactly the same allocation of marks to various papers apply to

NECO. For this study, only the practical questions will be used for analyses. This is

because many studies like Obinne (2011, 2008) have dwelt on psychometric properties of

objective test items in various subjects. Up to now no study could be assessed in literature

7

that has attempted the analyses of psychometric properties of practical aspects of physics

(polytomously scored with varied category) in WAEC and NECO O’level examinations.

The West African Examination Council and the National Examination Council

base the analyses of psychometric properties of items on classical test theory framework

(Obinne, 2008). On the premise of having weak theoretical assumptions and the item and

person circular dependency statistics, the classical test theory has been seen as not precise

as item response theory for ensuring objectivity in psychometric analyses (Ndalichako

and Rogers, 1997; Smith, 1996; Korashy, 1995).

Despite the importance of practical physics, the various analysis of psychometric

properties of questions (in research studies) have not attempted psychometric analysis of

practicals (Korashy, 1995). Such studies as Obinne (2011), Obinne (2008), Nworgu

(1985), Agwagah (1985), Obioma (1985) went variously into psychometric analyses of

questions that are dichotomously scored. Moreover, most psychometric analyses so far

used classical test theory (CTT) model. The classical test theory is no longer considered

fully or 100% valid enough for ensuring objectivity in measurement (Smith, 1996;

Korashy, 1995).

The classical test theory (that is mostly being used for test analysis) has many

limitations such as circular dependency, weak theoretical assumptions etc which cast

doubts when psychometric properties of tests are obtained using the CTT model. There is

therefore, the need to change the method of analysis of psychometric properties of tests

from CTT to a theory that will further attenuate the shortcomings of CTT model. In

particular, there is the need to study the psychometric properties of physics practical in

WAEC and NECO practical physics as many has been done for objective physics and

virtually none for practical examinations and both are of equal weight in these exams ie

they carry equal marks.

Almost every, if not all instruments used in Nigeria currently for assessment of

achievements in our educational processes rely on classical test theory. This CTT model

produces scale that yield different results across different population i.e. item and person

parameter are sample dependent; there is weak theoretical assumption to meet with test

data such as the assumption that error scores in high and low ability students are equal –

in other words student error of measurement is consistent across the entire population and

8

the sample size for the item parameter estimation is small. [Embretson and Reise, 2000;

Fan, 1998; Hambleton and Jones, 1993; Lord and Norvick, 1968; and Lord, 1952; 1953].

The major limitation of CTT can be summarized as circular dependency (a) the person

statistics (i.e. observed score) is item sample dependent and (b) the item statistics (i.e.

item difficulty and item discrimination) are examinee sample dependent. This circular

dependence poses some theoretical difficulty in CTT application in some measurement

situations (Fan, 1998).

Due to the inherent advantages of item response theory, it becomes absolutely

compelling that emphases are to shift from classical test theory to item response theory in

test analyses. Theoretically IRT overcomes the major weakness of CTT, that is the

circular dependency of CTT item/ person statistics. As a result IRT models produce item

statistics independent of examinees samples and person statistics which are independent

of the particular set of items administered. This invariance property of item and person

statistics of IRT has been illustrated theoretically (Hambleton and Swaminathan, 1985);

Hambleton, Swaminathan and Rogers, 1991) and these have been widely accepted by the

global measurement community: This invariance property of IRT model parameters

makes it theoretically possible to solve some measurement problems that have been

difficult to handle within the CTT framework such as computerized adaptive testing

(Hambleton et al., 1991). The importance of invariance property of IRT model parameter

cannot be overstated. Without this crucial property however, the complexity of IRT

models can hardly be justified on either theoretical or practical grounds (Fan, 1998).

Item Response Theory (IRT) is an attempt to model the relationship between an

unobserved variable - the examinees ability and the probability of the examinee correctly

responding to any particular test item. IRT models are therefore mathematical functions

which relate the probability of success on a task to the underlying proficiency measured

by the task. IRT avails us of the opportunity of attaining invariant item parameters such

as difficulty index (b-parameter), discrimination index (a-parameter), guessing index, (c-

parameter) in the cases of dichotomously scored responses. IRT on the whole is a

statistical framework for addressing measurement problems such as test development,

test score equating and identification of biased test items (Hambleton and Jones, 1991).

With IRT, it is possible to construct trait line for exact measurement of a particular trait

9

possessed by an individual. The foregoing merits of IRT made possible by invariant

property of Item Response Theory (IRT) makes IRT a plausible alternative to classical

test theory in an attempt to enthrone better objectivity in measurement.

Item response theory can be divided into two families – uni-dimensional and

multi-dimensional models. While uni-dimensional model require a single trait or ability

dimension, multi dimensional IRT models response data (instrument data) arising from

multiple traits. Most item response theory researchers and applications make use of uni-

dimensional IRT models. IRT models are also categorized on the bases of scored

responses. The typical multiple choice items are dichotomously scored. Even if there are

four or five options they are still being scored as correct or incorrect, right or wrong. A

different class of models apply to polytomous outcomes where each response has

different score values. An example of polytomously scored items are those rated on a

scale of 1-5 or a situation where some number of steps are required to complete a

particular assignment.

The relationship between examinees performance and the set of traits underlying

the item performance can be explained by a monotonically increasing function known as

Item Characteristic Curve (ICC) or Item Characteristic Function (ICF) (Hambleton,

Swaminathan and Rogers, 1991). For items that are dichotomously scored, the ICF can be

verified using the one parameter, two parameter and three parameter logistic models.

Using these models the item statistics,- the item difficulty (b-parameter), item

discrimination (a-parameter) and pseudo guessing, (c- parameter) can be verified for

items that are dichotomously scored. The one parameter model (Rasch model) can only

verify b, the two parameter model or Birnbaun model can verify b and a; while the three

parameter model or Lords models can verify b, a and c.

For items that are polytomously scored various models for studying the item

statistics exist. Some of these models are: Graded Response model, Nominal Model,

Partial Credit model and Rating Scale Model. The various models provide mathematical

equations for the relationship that exists between the probability of correct response (θ) to

the ability level of the student. Each of the models has one or more parameter –(b, a or c

defined above) that describes a particular item characteristic curve along with other

10

technical properties of the item. In each IRT model, a mathematical function is used to

estimate the probability of correct response at several ability levels (-3 to +3).

In IRT, the Item Characteristics Curve (ICC) is described by (i) the difficulty

parameter b which is the location on the ability axis at which the probability of correct

response P(θ) = 0.5 (ii) the discrimination parameter (a) which is the slope of ICC at a

particular ability level; the higher the value of a, the steeper the slope (iii) the guessing

parameter c is the vulnerability to guessing which makes ICC asymptotic and always

positive along vertical axis.

The assessment of psychomotor/practical skills in any area will be better studied

if the examinees responses are polytomously scored rather than dichotomously scored.

Cognitive outcomes may be simply studied using dichotomous scoring but for

psychomotor outcomes they are better done with polytomous scoring. This makes partial

credit scoring indispensable in many assessment situations. The usual motive for partial

credit scoring as stated in Masters (1982) is the hope that it will lead to a more precise

estimate of person’s ability than a simple pass/fail score. This author noted that certain

type of data should come from an observation format which requires the prior

identification of several other levels of performance on each item and thereby award

partial credit for partial success on each item.

The item item characteristics curve for Rasch (one parameter) Partial Credit

Model of IRT is illustrated below:

1.000

0.800

0.600

0.400

0.200

0.000 -3 -2 -1 0 b 1 2 3

Pro

bab

ility

of c

orr

et r

esp

ons

e P

(θ)

Ability ( θ) in Standard Scores

Fig. 1-Item Characteristics Curve for One Parameter / Rasch (One Parameter) Partial Credit Model of IRT

11

The polytomous Rasch model which is a generalization of the dichotomous model

can be applied in contexts in which successive integer scores represent categories of

increasing level of magnitude of a latent trait such as increasing ability, motor function

and so forth. The PCM is an appealing model for many applications because unlike the

Graded Response model, Generalized partial credit model, etc it does not contain a

discrimination parameter and thus can be used with sample sizes that are smaller than

those required for models containing a discrimination parameter. Furthermore, because

the PCM belongs to Rasch family of models it brings with it the advantageous properties

known to exist for all Rasch models including separation of person and item parameters

(Andrich, 1988; Michell, 1990; Fischer, 1995).

Hypothetically, an examinee could take the test a great many times and obtain a

variety of test scores. One would anticipate that these scores would cluster themselves

around some average value. In measurement theory, this value is known as true score and

its definition depends upon the particular measurement theory. In item response theory,

the definition of true score according to Lawley, in Baker (2001) is given by

∑=

=N

jij PTs11

)(θ

where Tsj is the true score for examinee with ability level θj

i denotes an item and Pι jθ depends on the item characteristics curve

model employed.

Just like other IRT models, the PCM is characterized by specific objectivity and

uni-dimensionality. Mellember (1994) stated that specific objectivity means that

comparison of two items difficulty are assumed to be independent of any group of

subjects being studied and does not depend on any subset of item being administered.

And uni-dimensionality means that a single latent variable fully explains task

performance (Carlson, 1993).

Latent characteristics of examinees cannot be measured with physical implements

or instruments like measurements in the physical sciences. But objective measurements

of latent traits can be achieved using the item response approach. The sample free nature

of the results provided by the IRT models are technically known as Invariance of item

parameters. With this invariance of item parameters a uniform scale of measurement is

12

provided for use in different populations. Latent traits are behaviours that can be

indirectly observed. To measure these traits we need to provoke the examinees to act

while trying to capture the intensity of such a trait in the individual by putting up a

related graded task (known as item) for the examinees. Through this we can elicit the

behaviour that describes the trait under study (Nenty, 2005).

All examinations conducted in Nigeria have been based on classical Test Theory

framework CTT for years (Obinne, 2008). Examination bodies have as well relied on

CTT for testing their candidates. Psychometric analyses done on instruments by Nworgu

(1985), Agwagah (1985), Obioma (1985) all relied on classical test theory. There is

nearly no psychometric analysis of practical physics yet as revealed by literature. Even

though practical physics in WAEC and NECO have the same weight with their objective

tests, studies that have so far been done have mostly dwelt in objective aspect. There is

therefore the need to study the psychometric qualities of our practical questions in these

two examinations using item response theory Format-Partial Credit, model. This will help

attenuate the shortcomings of CTT model that is presently used for analysis by the exam

bodies. There is also the need for more concise, objective and pragmatic method of

constructing, scoring and analyzing psychometric properties of practical physics. This

will go a long way to convince the public that the standard of the two examinations

WAEC and NECO are about the same thereby removing bias and doubt against any of

their standard as is sometimes the case.

Statement of the Problem

West African Examination Council Ordinary level examinations in Physics are

made up of three parts, namely paper 1(practical -50 marks); Paper 2 (objective-50

marks) and paper 3 (essay-60 marks) (WAEC 2009). Exactly the same mark allocation is

applicable to the respective patterns of assessment in National Examination Council

O’level physics examination. Studies on psychometric properties of WAEC and NECO

examination have dwelt on the objective component of these examinations (i.e. paper 2)

to the exclusion of the practical, component (i.e. paper 1) and the essay component (i.e.

paper 3). The polytomously scored components i.e. practical (paper 1) and essay (paper3)

of these examination (practical and essay) contribute more than two thirds of the total

score on both WAEC and NECO O’level physics. Yet there is no study that has gone into

13

psychometric analyses of polytomously scored components of WAEC and NECO physics

examinations. This situation creates an obvious gap, part of which this study was able to

address.

Furthermore, these studies on psychometric properties of WAEC and NECO

mostly utilized the classical test theory (CTT) approach in their analyses. The modern

measurement theory – item response theory (IRT) has not been fully explored with

respect to analyses of psychometric properties of our tests in WAEC and NECO.

Considering the obvious advantages in the underlying assumption and basic tenets of the

framework- IRT, would the scenario be different if we utilize IRT for analyses of

psychometric properties of WAEC and NECO examinations in Nigeria?

Purpose of the Study

The purpose of the study was to investigate some psychometric properties of

WAEC and NECO practical physics questions using the partial credit model of item

response theory.

Specifically, the study did:

1. Estimate the standard error of measurement of the practical physics test items set

by the National Examination Council (NECO) of Nigeria.

2. Estimate the standard error of measurement of the practical physics test items set

by the West African Examination Council WAEC.

3. Investigate the validity of the practical physics test items produced by NECO.

4. Investigate the validity of the test items of practical physics test items produced

by WAEC.

5. Estimate the item parameter (item difficulty) of NECO practical physics

test items using the Partial Credit Model.

6. Estimate the item parameter (item difficulty) of WAEC practical

physics test items using Partial Credit Model.

7. Determine the proportion of fit of NECO practical physics questions using Partial

Credit Model of IRT.

8. Determine the proportion of fit of WAEC practical physics questions using Partial

Credit Model of IRT.

14

Significance of the Study

The following could benefit from the findings of the study- test devevelopers, the

classroom teacher, the society, and examination bodies.

The results of the study would make input into the present state of test

construction. This would help test developer and examination bodies to determine the

existence or otherwise of Item Differential Functioning (DIF). Item bias or Differential

Functioning is readily and more reasonably possible in item response theory model due to

its invariant sample properties. And so, the results from this study will encourage test

developers to undertake rigorous item analysis before and after test administrations.

The results of the study will be useful to classroom teachers, as they gets

informed on the possibility of use of partial credit model for the analysis of their

polytomously scored items. To the guidance counselors it exposes the students’

performance item by item and the possible reason for such performance for each item.

And for educational establishments it offers some explanation of examinees results

through person by item response pattern for large scale testing purposes. The results of

the study would serve as a tool for diagnosis of student’s strengths and weaknesses by

teachers and guidance counselors. The method of this study would involve identification

of errors and factors/misconceptions leading to such errors. Hence, it will ensure

improvement in the teacher’s instructional strategies, coverage and practices. The study

will arm the guidance counselor with the weapon, necessary information and data to

diagnose students’ strength and weaknesses since the study will have the data on their

performance item by item.

The results of this study would help to establish the quality of examination

conducted by WAEC and NECO. It will confirm the reliability and validity of the

examination conducted by NECO and WAEC. This will go a long way to establish to the

society public trust and acceptability of results from these examination bodies. The

results of this study would probably convince the public that the exams conducted by

WAEC and NECO are of comparable standard.

Presently, the examination bodies such as WAEC, NECO and others are largely

dependent on classical test theory for their test development and analyses. The use of the

CTT in test analysis conceals some of the characteristics of both the examinees and the

15

items at the same time. For the purpose of more objective and comprehensive verdict to

be taken on the performance of students by these examination bodies (WAEC and

NECO), the psychometric properties of the test items need to be determined using a more

precise model of test theory - the IRT. These examination bodies need the psychometric

properties of test items in expressing the performance of the examinees. This will enable

them to further improve upon test construction practices, administration and analysis. For

these two examination bodies, this study would accentuate clearer understanding of their

performance in test construction, adoption and acceptance of IRT framework in analysis

of practical examinations using Partial Credit Model (PCM).

Scope of the Study

The study covered all the secondary school in the six education zones of Enugu

state Nigeria because the state has all demographic attributes

(urban, semi-urban and rural etc schools) to produce good psychometric analysis. The

study was limited to May June WAEC 2011 – 2012 practical physics tests and the June /

July 2011 – 2012 NECO practical physics tests.These content scope were the most

recently concluded practical tests by the two examination bodies as at the time of the

conduct of the study. The study was limited to the partial credit model (Rasch Option) for

the analysis. This is because this is the IRT option for the analysis of polytomously

scored responses when the response categories are free to vary i.e not uniformly gradeded

and not at nominal scale level.

Research Questions

The following research questions guided this study

1. What are the standard errors of measurement of the 2011 and 2012 practical

physics test items produced by NECO?

2. What are the standard errors of measurement of the 2011 and 2012 practical

physics test items produced by WAEC?

3. How valid are the practical physics test items of NECO 2011 and NECO 2012?

4. How valid are the practical physics test items of WAEC 2011 and WAEC 2012?

5. What are the item parameter estimates of NECO 2011 and NECO 2012 practical

physics questions using partial credit model?

16

6. What are the item parameter estimates of WAEC 2011 and WAEC 2012 practical

physics questions using partial credit model?

7. What proportion of NECO 2011 and NECO 2012 practical physics test items fit

the partial credit model of IRT?

8. What proportion of WAEC 2011and WAEC 2012 practical physics test items fit

the partial credit model of IRT?

Hypotheses

1. There is no significant difference (P<.05) in the Standard Error of Measurement

(SEM) between NECO 2011 and NECO 2012 practical physics tests items.

2. There is no significant difference (P<.05) in the Standard Error of Measurement

(SEM) between WAEC 2011 and WAEC 2012 practical physics test items.

3. (a) There is no significant difference (P<.05) in the Standard Error or

Measurement (SEM) between (NECO 2011 and WAEC 2011); practical physics

tests items.

(b) There is no significant difference (P<.05) in the Standard Error or

Measurement (SEM) between (WAEC 2012 and NECO 2012) practical physics

tests items.

4. There is no significant difference (P<.05) in the validity (fit statistic) of NECO

2011 and NECO 2012 practical physics tests items.

5. There is no significant difference (P<.05) in the validity (fit statistics) of WAEC

2011 and WAEC 2012 practical physics test items.

6. (a)There is no significant difference (P<.05) between the validity (fit statistics) of

(NECO 2011 and WAEC 2011) practical physics test items.

(b) There is no significant difference (P<.05) between the validity (fit statistics) of

(NECO 2012 and WAEC 2012) practical physics test items.

7. There is no significant difference (P<.05) in the item difficulty estimates (b) of

NECO 2011 and NECO 2012 practical physics test items using PCM.

8. There is no significant difference (P<.05) in the item difficulty estimate (b) of

WAEC 2011 and WAEC2012 practical physics test items using PCM.

9. (a)There is no significant difference (P<.05) between the item difficulty estimates

(b) of (NECO 2011 and WAEC 2011) practical physics test items using PCM.

17

(b) There is no significant difference (P<.05) between the item difficulty estimates

(b) of (NECO 2012 and WAEC 2012) practical physics test items using PCM.

18

CHAPTER TWO

LITERATURE REVIEW

The relevant literature on the psychometric analysis of practical physics question

given by WAEC and NECO using Partial Credit Model (PCM) of Item Response Theory

(IRT) was done under the following subheadings:

Conceptual Framework

• Achievement Testing

• Item Analyses

• Validity and Reliability of Measurement Instruments

Reliability and Standard Error of Measurement

Theoretical Framework

Classical Test Theory

Item Response theory

Some IRT methods in estimating item parameters

Empirical Studies

Summary of Literature Reviewed

18

19

18

Test Developer Examination bodies

Guidance conusellors

Teachers

Achievement Testing

Test Theories

Classical Test theories

Item characteristics curve Test characteristic curve Item Information function

Item Response Theory Model

Dichotomously Scored dd

Polytomously Scored dd

1PLM dd

2PLM dd

3PLM dd

Partial Credit Model

Graded response Model

dd

Rating scale Model

Correlation Method

Regression Method

Approximation Method

Maximum Likelihood Procedure Method

Ability Estimate

Parameter Estimate

Validity Reliability /Standard

error of measurement

Testing

Nominal scale model

Fig. 2-Schematic Diagram of Conceptual and Theoretical Framework

20

In achievement testing two major test theories are mostly utilized for assessment

of psychometric properties of the items. These theories are Classical Test Theory and

Item Response Theory. Item Response Theory Models utilize Item Characteristcs Curve

(ICC), Test characteristics Curve (TCC), and Item Information Function (ICF),

differently for Dichotomously scored and Polytomously scored responses. In both

dichotomously and polytomously scored reponses, four methods are used in estimating

item parameters - correlation method, regression method, approximation method and

maximum likelihood procedure method. These methods are used to estimate the ability

estimates, Parameter estimates, validity and Reliability of the items under item response

theory. These item characteristics are useful for Test developers, examination bodies,

guidance counselors, and classroom teachers.

Achievement Testing

An achievement test according to Nworgu (2003) is an instrument designed to

measure the outcome of the level of accomplishment in a specified programme of

instruction in a subject area or occupation which a student has undertaken in the recent

past. Ali (1996) also defined achievement test as an instrument administered to an

individual as a stimuli to elicit certain desired and expected responses as demanded in the

instrument, performance on which the individual is assigned a score representing his

achievement. According to the author, this score baring other unforeseen circumstances is

a measure of his possession of the characteristics being measured by the test taken.

Essentially if a test has to measure achievement very well, it has to be valid, reliable and

manifestly objective. The use of test can be greatly improved and substantiated if it has a

clear and usable marking scheme and direction for administration, scoring and

interpretation of the test. For proper analyses of achievement test, the researcher has to

prepare instructional objectives on the topic of instruction of the test. Nworgu (2003)

specifically noted that since tests are designed to aid in determining the extent of

attainment of objectives, assessment measure can therefore be classified into three on the

basis of corresponding objectives as follows: Measures of cognitive ability, measures of

affective ability and measures of psychomotor ability.

An achievement test is a measure of maximum performance and is classified into

general and diagnostic achievement test. Gronlund (1976) defined diagnostic evaluation

21

to connote a test designed to reveal a persons strengths and weakness in one or more

areas of the field being tested. It is mainly used to identify source of difficulty in a

curriculum area, while the general achievement test sample the entire field of work being

tested and which yield a single score that indicate relative achievement in the area being

tested.

Achievement tests are designed to identify what a student has learned in a general

or specific area of knowledge that he has been exposed to. The achievement test dwell on

specified content area. The items of test have to be sampled for suitable statistical

properties. According to Ferguson in Nworgu (2003) "Such items are those which will

contribute positively in the differentiation of the individual or description of individual

differences" (p. 103). Hence in analyzing achievement tests, the emphasis is on ensuring

that the test posseses a fairly large variance in relation to the number of items of the test.

Since the total test variance is a function of the items variance and the inter items co-

variances, it therefore follows that items with large item variances will make more

contribution to total test variance. Items variance is largest and ideal when item facility is

0.50. Value of item facility is large if it is close to 0.50. However the ideal item facility of

0.50 is not readily practically possible. Therefore in test construction, we include items

within specified range of facilities equally spaced on both side of 0.5. For practical

purposes, the acceptable range, according to Harbor Peters (1999), Nworgu (2003) is 0.03

to 0.7,Q. Item facility could take values of 0 where nobody gets the answer correctly to 1

where everybody gets the answer correctly.

In this study, the researcher identified important psychometric qualities of a test

and used WAEC and NECO questions to determine the level of these qualities in these

questions. The study was undertaken using partial credit model of item response theory.

Item Analysis

Item analysis is a process which examines students’ responses to individual test

items (questions) in order to assess the quality of those items and of the test as a whole.

Item analysis is especially valuable in improving items which will be used again in later

test but it can also be used to eliminate ambiguous test items or misleading items in a

single test administration. Additionally, item analysis is valuable for increasing

22

instructor’s skill in test construction and identifying areas of the course content that need

greater emphasis or clarification.

Item analysis is a method of reviewing items on a test and that this review could

be both qualitative and statistical, to ensure that they all met minimum quality control

criteria. Qualitative review according to this author is essential during item development

when no data are available for quantitative or statistical analysis. Item analysis

(quantitative) is conducted after test administration and data is available for analysis. The

objectives of item analysis is to identify problematic items or bad or misfitting items.

Items may be problematic because (1) they are poorly written causing students to be

confused during response (2) graphs, diagrams, pictures etc are not clear (3) items do not

have a clear response and a distraction may potentially qualify as the correct answer (4)

items containing distractors that most students can see are obviously wrong, increasing

the chance of correct guessing (5) tyey represent a different content area than that

measured by the test. This is known as multi dimensionality.

In summary, Harbor-Peters (1999) stated that test item analysis deals with the

processes involved in determining the psychometric qualities of the tests and that since

the qualities of the test items determine the quality of the whole test, the assessment of

these qualities of items constitute item analysis. This could be qualitative or quantitative.

One may ask why is it important to review every item in a test. One may equally

speculate that as long as the majority of the test items are good, there may not be much

impact if a few items are problematic. However, based on statistical theory and previous

experience, we know that the presence of few problematic items reduces overall test

reliability and validity sometimes markedly. Measurement tools (test) are frequently

assessed based on reliability and validity.

Qualitative item analysis deals with the consideration of content validity – how

effective the items are in terms of their writing procedures. Content validity is the most

important validity consideration for an achievement test. Anastasi in Nworgu (2003)

noted that content validity involves systematic examination of the test content to

determine whether it covers a representative sample of the behaviour domain to be

measured. This implies analysis of a test to ascertain if the aspect of behaviour domain

23

under consideration are covered to reflect the relative importance of each section and if

the skills resulting from the behaviour is covered.

From the foregoing, it can be deduced that ordinary inspection of a test is not

enough to ensure its content validity and the behaviour domain to be sampled by a test

has to be well defined before it is developed. Consequently, a number of specific

procedures can be adopted in evaluating content validity of an achievement test. One of

such procedure involves in cooperating content validity into the test from the beginning

through the choice of appropriate item. For educational achievement tests this is done by

adoption of appropriate test blue prints. The test blue print is developed in the beginning

of the test construction based on close inspection of relevant course syllabus, textbooks

and consulting subject experts. In this way, the content area to be covered and the

objective to be tested and the relative importance of each area in the syllabus is given a

thorough survey hence ensuring content validity. The second procedure adopted in

ensuring content validity of an achievement test is supplementary and empirical in nature.

The total score on the test and performance are checked for grade progress. Items that

show large gains in the proportion of students passing them from lower to upper grade

are retained. This procedure is not applicable to all contents, like in a situation where the

syllabus is not sequenced according to class level. In this type of situation better

performance at lower level does not necessarily mean some defects in the items. It may

imply that the items represent content areas that the higher class was not exposed to.

Quantitative item analysis deals with analysis of statistical properties of the items

such as item facility and item validity. Izard (n.d) stated that two main indices are

obtained from a traditional analysis of students responses to test items. These are item

difficulty (or item facility) and an index of item discrimination. Item facility also known

as item easiness or item difficulty is defined as the index that describes the level of the

difficulty of test item (Harbour-Peters, 1999). The index of difficulty of item which is

reported for a particular test administered to a particular group is function of the skills

required by the questions and the skills achieved by those attempting the test. According

to Ross (n.d) item facility is the opposite of item difficulty and as the difficulty increases,

fewer candidates are able to give the correct responses; as the facility increases, more

candidates are able to give the correct response. Habor-Peter (1999) and various other

24

authors relate the item facility to the proportion of students answering each item

correctly. It helps in ensuring that items that are suitable are included in the final version

of the items in the parallel form of test and arranging such items of the test in an

approximate order of decreasing facility. Such deferential sequencing of test items has

been shown by Haliday and Patridge (1979) to produce superior performance than any

other ordering. The facility of the test items determines the test mean facility, the lowest

and the highest scores and the spread of the test scores. This implies that if the

distribution of the test scores deviates sufficiently from normality when a large sample

was used then the facility of the items included in the test may be considered unsuitable.

The item facility will need to be adjusted until the distribution of the test scores shows

normality (Nworgu, 2003).

Item validity indices are however, based on item criterion relationship. The

criterion may have been the one employed in the validation process of the test. Over fifty

of such indices have been developed and employed in test construction according to

Anastasi as reported in Nworgu (2003). These indices could be differentiated, some

applied to dichotomous while others apply to continuous measure, and some are

dependent on item facility while some are not. Those item validity indices that are

dependent on item facility yield high validities for item facilities near 0.50. Irrespective

of these differences, all the indices yield very close results even though their numerical

value varies a bit, the item selected or rejected through different validity indices are more

or less the same. On this basis the researcher for the purpose of item analysis should

choose the index that can be computed with ease.

Item discrimination is a procedure that investigates how each item distinguishes

between candidates with knowledge and skill and those lacking such knowledge and

skill; choosing items with an acceptable discrimination index will tend to provide new

version of test with greater homogeneity (Ross, nd) or simply put that the discrimination

is the measure of the extent to which a test item discriminates between high ability and

low ability students who got the item right divided by the number in either group (Harbor

Peters 1999).

Two item validity indices are worthy of mention because they are commonly used

25

(i) Discrimination Index: This is a measure of the proportion of testees passing each item

in the upper and lower criterion groups, Discrimination Index ranges from -1 to+1; items

with higher values are preferred. If the sample N is large (N>150 say) discrimination

index of 0.22 and above is recommended (Nworgu 2003). The criterion group is

frequently selected on the bases of total test score. Other criteria that may be employed

are cumulative grade point, job rating, course grade, teachers rating etc. The important

thing is the consideration of criterion measure vis-a-vis the ability being assessed by the

test. The extreme group has sharp differentiation but the reliability of the test result is

reduced.

The following characteristics are identified for discrimination index

• It is simple in calculating and in concord with most other measures of validity

indices

• The size of the sample from where it is obtained does not affect the interpretation

of the index

• There is relationship between mean discrimination index and the reliabilities of

the test. The higher the mean index the higher the reliability coefficient

• It is independent of item facility but biased in favour of intermediate values of

item facility

(ii) The Phi-Coefficient: This is a measure of the relationship between item and the

criterion. Its value ranges from -1 to +1. It is computed from a four fold table based on

proportion passing and failing each item in the upper and the lower group. This

coefficient assumes a genuine dichotomy in both variables. It is strictly applicable to

dichotomous condition under which it was obtained. This coefficient is biased towards

intermediate facility.

Validity and Reliability of Measurement Instrument

Cardinals among the proprieties of good research instrument are validity and

reliability

Validity: An instrument is deemed to be valid when it measures what it is supposed to

measure. This definition is in line with the View of Gronlund (1976) where he defined

validity in terms of the usefulness of the result of the test. According to Gronlund (1976)

validity is "The extent to which results of an evaluation procedure serves the particular

26

uses for which they are intended for" (p.79). In his view if test result is used to describe

achievement, it should represent specific achievement and nothing more. That is if test

result is used to predict success in future activity, the result should provide as accurate as

possible the estimate of the future success. To that extent therefore is the test valid.

Also Stanley (1964) views validity in terms of the result being a suitable measure.

According to Stanley (1964) "A test is valid if in the end it turns out to be a suitable

measure" (p. 160). Thousand and one authors such as Mehrens and Lehman (1978) have

consistently described an instrument to be valid when the instrument measures

specifically what it is supposed to measure.

In all, instrument validity differs according to the situation and the major criterion

for the instrument validity is the purpose for which the instrument was being established.

The validity of the instrument therefore has to be determined by the research objective. If

the objective of the instrument is in line with the research objective then the instrument is

valid. An instrument that is not valid is useless so to say. An instrument could be valid

for some purposes and invalid for others. Different interpretations for the use of a test

have different degrees of validity for each interpretation. Since no test is valid for all

purposes or in all situations for every pupil, there is nothing like the validity of a test.

Actually a test cannot just be said to be valid. A test is valid for a particular purpose and

for a particular group. For instance a valid test of intelligence is not likely to be a valid

test of personality

A test, which has high validity for a purpose may or may not have low or

moderate validity for another. A test no matter how well designed is valid for some

purpose and invalid for others. Precisely speaking we talk of validity of test scores and

not of the test. This view is also shared by Gronlund (1976) when he stated that “Validity

refers to the extent to which the results of an evaluation procedure serve the particular

uses for which they are intended” (P.79). Also Harbor Peters (1999) noted that validity

pertains to the results of the evaluation instrument not the instrument itself.

Three types of validity are known to exist. They are:

(1) Content validity

(2) Criterion related validity

(3) Construct validity

27

There exist a fourth type but in the technical sense strictly, it is not a type of

validity. This is face validity. Some authors like Harbor Peters (1999) regards all the four

mentioned as types of validity.

Face validity according to Harbor Peters (1999) confirms the extent a test -

represents what has been specified in the blueprint. Face validity is a crude method of

assessing (by measurement experts) the content validity of the specification on the test

blueprint. In general face validity has to do with appearance of the measuring instrument.

It confirms whether the instrument looks like a test and asseses whether the test is content

valid. In face validation, the validator considers (a) appropriateness of language for the

intended audience (b) Relevance of items with respect to research objectives (c) Extent of

Content coverage.

Content Validity: This according to Gronlund (1976) may be defined as "the extent, to

which a test measures a representative" sample of the subject matter content and the

behavioural change under consideration. The content validity is essentially concerned

with the adequacy of the sample with respect to the content this is the primary concern in

achievement testing. This form of validity is usually built into the instrument during its

process of development making use of test blue prints. Content validity is applicable

where the content domain is delineated e.g. Achievement in a given area. But if the

dependent variable is not delineated e.g. Interest, content validity is not applicable.

For the development of test blue print which we usually use as basis for

determining content validity we usually compose the table of specification on various

level of the taxonomy of the educational objective. The number of question at various

levels (the weighting) is determined by the curriculum area emphasis, the time of

teaching and the extent of material covered. The test blue print is therefore the

benchmark for assessing content validity. A consideration of test vis-a-vis the table of

specification tells whether the test is content valid.

Criterion Related Validity: This is the extent to which measures from a test is related to

an external criterion. The measure from the test or instrument is the predictor where the

external behaviour the test is predicting is known as the criterion. Criterion related

validity according to Harbor Peters (1999) “is the extent to which test performance is

28

accurate in predicting future performances or estimating some current performances” (p.

49).

There are two types of criterion related validity. These are predictive and

concurrent validity. The distinction between concurrent and predictive validity lies in the

time lag between when the predictor measure was collected and when the criterion

measure became available. If the two measures are available about the same time then it

is called concurrent validity. But when there is time lag of days, weeks or years then it is

predictive validity. The procedure for establishing criterion related validity is to correlate

the two measures, the predictor and criterion measure using appropriate correlation

technique. The resultant correlation coefficient is the concurrent or predictive validity as

the case may be.

Construct Validity: This deals with the extent to which a test performance can be

interpreted in terms of a given psychological construct. In researches where the

dependent variable is in form of construct (e.g. Intelligence, scientific attitude, critical

thinking, study habit etc) that do not have a defined content domain; construct validity is

the, most appropriate form of validity. Factor analysis is frequently used to establish

construct validity.

Reliability: According to Harbor Peters (1999) "the reliability of test scores refers TO

their relative freedom from unsystematic errors of measurement" Pg. 44. (Unsystematic

errors are errors that may emanate from administrative conditions -Physical and

psychological).

Reliability therefore refers to the ability of a test to measure consistently even

under varying conditions. It establishes the consistency or other wise of a particular

score. Reliability is intimately related to validity. In fact all valid tests are reliable but all

reliable tests are not necessarily valid. Gronlund (1976) noted that "reliability merely

provides consistency that makes validity possible" (p.107). He further observed that a test

that has high reliability may have little or no validity, but a test that has satisfactory

validity must essentially have satisfactory reliability. He went further to state that the

only difference between validity coefficient and reliability coefficient is that the former is

based on agreement with an outside criterion and the latter is based on agreement

between two sets of result from the same procedure.

29

If a test is not reliable, it may be due to influence of some sources of error with

the test subjects. In theory each source of error defines instability. In practice these types

of reliability estimates have been identified, by several authors such as Harbor Peters

(1999), Gronlund (1976), Stanley (1964) etc.

Types of Reliability

(i) Stability

(ii) Equivalence

(iii) Internal consistency

(iv) Scorer or Rater’s Reliability

i) Stability is the ability of the same test to produce the same results if the test is given

the same testees within short interval. The reliability coefficient of stability is

obtained through test - retest method. The result from the same test for the same

testees obtained twice is correlated using Pearsons product moment correlation

method. In this way the result obtained after correlation gives us reliability coefficient

of the test results for stability.

ii) In obtaining equivalence form of reliability we talk of two parallel tests. The two

parallel tests are given in short time interval or even in quick succession. The results

obtained from the same testees for the two parallel tests are then correlated using

Pearson's product moment correlation formula. This is the index of Equivalence for

the two tests.

iii) Internal consistency is concerned with the accuracy with which an instrument has

sampled a given content universe. The major source of error here is the content

coverage. The internal consistency can be established using:

(a) Split half method

(b) Kuder Richardson method

(c) Cronbach Alpha or Coefficient Alpha

(a) In split half method you administer the test once but in scoring you split the

scores into two (may be even and odd number scores). In this, each testee will

have two composite scores. The reliability coefficient for each half is obtained

30

and represented as r12.To get the reliability of the whole test from the correlation

between the two halves, we can use the Spearman-Brown prophecy fomula.

Thus

1

1

1

2

r

rrtt +

=

Where rtt = reliability of the whole test

ri = reliability of half of the test

(b) Kuder- Richardson method is used to estimate the internal consistency when the

items are dichotomously scored using the formula

K – R(20) rxx =

Σ−

− xS

pq

n

n2

11

K – R(21) rxx =

×−×−

− xnS

n

n

n2

(1

1

Where rxx = internal consistency reliability of the test result

pq = variance of single item

n = number of items in the test

S2x` = variance of total test

× = mean of the total test

K – R20 is used for dichotomously scored items

K – R21 is used for polytomously scored items

c) Cronback Alpha is used for continuously scored and essay type questions to

estimate the internal consistency.

(d) Scorer or Raters Reliability: When the same scripts are given to two scorers to mark,

we can obtain individual scorers consistency using Pearson's product moment

correlation. We can as well obtain the relationship between two different scorers

using the spearman's rank order correlation. But if the scorers are more than two we

31

can use Kendal Coefficient of concordance or any other appropriate technique to

obtain the scorers reliability.

Reliability Coefficient could vary depending on the method used to estimate the

index. Gronlund (1976) identified a number of factors that -can influence the reliability of

test result such as test length, speed of the test, the group homogeneity, difficulty level of

test, objectivity in scoring etc.

Reliability and Standard Error of Measurement

Psychometric instruments are valuable if and only if such instrument is a valid

and reliable measure. The first major task of a test developer is establishing the

instrument to be valid and sufficiently reliable. This reliability is characteristic of the

scores from the instrument. When the test is given to a specified group of testees under

designated conditions, it is standardized instrument. Since the reliability of a test

according to Thondike (1990) is intended to measure the degree of accuracy,

dependability and consistency, the concept is indispensable in test development and as a

result has been undergoing continuous redevelopment with increasing definition

clarification and applicability. As a result there are several perspectives of interpreting

reliability.

Lord and Norvick (1968), Allen and Wendy (1979), interpreted reliability in

several ways to include:

(a) The reliability of a test is equal to the correlation of its observed scores with

observed scores on a parallel test

(b) The reliability coefficient is the ratio of true score variance to observed score

variance i.e. reliability = VarianceScoreObserved

VarianceScoreTrue

(c) The reliability coefficient is one minus the squared correlation between the

observed and error score i.e. Reliability = 1 – r2 where r is the correlation between

observed and error score

(d) The reliability coefficient is the square of correlation r between observed and true

score i.e. Reliability = r2

32

(e) The reliability coefficient is one minus the ratio of error score variance VE to

observed score variance VX i.e. Reliability = 1 - X

E

V

V

(f) The reliability of the test refers to the relative freedom of test scores from errors

of measurement. The standard error of measurement (SEM) is given by

SEM = sd XXr−1

Where

Sd = Standard deviation of the observed scores rxx = the reliability of the test.

Therefore the SEM is dependent on reliability coefficient rxx and the standard

deviation of the test. While the rxx takes into consideration the measurement errors

present in the observed scores, the S.d takes into consideration the variability of the

observed scores. In conclusion, from this perspective, both standard error of measurement

and standard deviation are important in determining the reliability of a test.

B. Theoretical Framework

Classical Test Theory

Schumacker (2009), Embretson and Reise (2000), Fan (1998), Hambleton and

Jones (1993), etc were all consistent in stating that classical test theory was an emanation

of the early 20th century approach to measurement of individual differences. Classical

theory has three basic measurement concepts (a) Test Score or observed score (b) True

score and (c) Error score.

Classical Test Theory (CTT) postulates linking the observed score or test score X,

to the sum of true score (latent unobservable score) T and error score (E) as X = T + E.

The following assumptions are at the background of the CTT (1) That true score and

error score are uncorrelated (2) The average error score in a population of testes is zero

(3) Error scores in a parallel test are uncorrelated.

CTT utilizes item and sample dependent statistics. These include item difficulty,

item discrimination estimates, distractor analysis and other such related statistics. Most of

the psychometric analyses have focused on examinee assessment at the test score level

and not at the item level as in the case of item response theory. Analysis of test scores

using the CTT also includes a measure for the reliability of the scores, difficulty of test

etc.

33

The major advantage of CTT is its relatively weak theoretical assumption which

makes CTT easy to apply in many testing situations (Hambleton and Jones 1993).

Relatively weak assumption does not only characterize CTT but also its extensions such

as generalizability theory. Although CTT’s major focus is on test level information, item

statistics (item difficulty and item discrimination) are also important aspect of CTT

models.

The second advantage of CTT is that at item level the CTT model is relatively

simple. CTT does not invoke a complex theoretical model to relate an examinee’s ability

to success on a particular item. The CTT instead considers a pool of examinees and

empirically examines their success rate on an item. Another advantage of CTT is that the

analysis can be performed with smaller representative samples of examinees. This is

particularly important when field testing an instrument.

The major limitations of the classical test theory are (1) the two statistics that

form the cornerstone of most CTT i.e. item difficulty and item discrimination are both

sample dependent. Higher item difficulty values are obtained from examinee samples of

lower-average knowledge. And for the discrimination indices higher values tend to be

obtained from heterogenous sample of examinees and lower values from homogenous

samples. Such sample dependency relationships reduce the overall utility of these

statistics (Schumacker 2009). (2) Another limitation of CTT is that the person statistic

(observed score) is (item) sample dependent. The two limitations of CTT above can be

summarized as circular dependency i.e person statistic is item dependent; and item

statistics are (examinee) sample dependent. This circular dependency poses some

theoretical difficulties in CTT application in some measurement situations such as test

equating, computerized adaptive testing (Fan 1998).

Embretson and Reise (2000) reviews the ramifications or rules of CTT to include:

1) The standard error of measurement of a test is consistent across the entire

population i.e the standard error of measurement (SEM) does not differ from

person to person but instead is generated by large number of test takers and is

therefore generalized to the population of the test takers. Additionally regardless

of raw test scores the standard error for each score is the same.

34

2) Another ramification is that as the test become longer the test become

increasingly reliable. Statistics generated from large population is more stable

than that generated from small population. Larger number of items better sample

the universe of items and statistics generated by them such as mean test scores are

more stable if they are based on more items.

3) Multiple form of test are considered to be parallel only after much effort has been

expended on them to demonstrate their equality. Also their variances and

reliabilities as well have to be equal.

4) Another ramification is that the item statistics depend on the sample of the

respondents being representative of the population. The interpretation of

normative information should also be applicable to test scores in CTT so that the

sample characteristics can be conveniently generalized to the population.

Item Response Theory

Historical Background of Item Response Theory

The concept and methodology of IRT have been developed for over three quarters

of a century now (Reeve 1986). In effect the modern psychometric theory is no longer too

recent. Thurstone (1925) laid down the conceptual foundation of IRT in his paper titled:

A method of scaling Educational and Psychological Tests. In this paper he provided a

technique for placing items of Binet and Simon test of 1905 which is a test of childrens

mental development on an age graded scale.

Thurstone abandoned his work in measurement to pursue the development of

multiple factor analysis but his colleagues and students continued to refine the theoretical

bases of IRT (Steinberg and Thissen 1995). Normal orgive model was introduced as a

means to display the proportions correct for individual items as a function of normalized

scores. Lawley (1944) extended the statistical analysis of the properties of normal orgive

curve to describe the maximum likelihood estimation procedure for item parameters and

linear approximation to those estimates. Also Lord (1952) introduced the idea of latent

trait or ability and differentiated this construct from observed test score and Lazarsfeld

(1950) explained and established the unobserved variable as accounting for the observed

interrelationship within the item responses.

35

Embretson and Reise (2000) textbook titled “Item Response Theory for

Psychologist” is considered a landmark in IRT development while Lord and Novick

(1968) textbook titled “Statistical Theories of Mental Test Scores” provided a unified

treatment of the classical test theory. The remaining half of this textbook Statistical

Theory of mental Test Scores written by Allen Brinbaun also provided rigorous

description of the IRT models. Reeve (1986) noted that Bock; David Thissen; Muraki

Eiji; Robert Gibbons; Robert Mislevy, were among notable students of University of

Chicago contributed in no small measure in developing effective estimation methods and

computer program such as Bilog, multi log, par scale and Test fact. Also Bock and

Aitken (1981) developed the algorithm of maximum likelihood method to estimate item

parameters that are used in many item response theory programs.

Rasch (1960) explained the need for creating statistical models that exhibit the

property of specific objectivity, and the idea that people and item parameters be estimated

separately but comparable on similar metric. Rasch inspired Fischer (1968) to extend the

applicability of Rasch model into psychological measurement. Ben Wright was also

inspired to teach the same methods and to inspire other students for further development

of the Rasch model. Such students include David Andrich, Geoffrey Masters, Graham

Douglass etc who helped and pushed the methodology into education and behavioural

medicine (Wright 1997).

Conceptual Background of Item Response Theory

Item response Theory (IRT) just like CTT is a popular statistical frame work for

addressing measurement problems like test development, test score equating and

identification of a biased items (Hambleton and Jones 1993). IRT affords us of different

ways apart from CTT of constructing tests and at the heart of the IRT according to Nenty

(2005) is the characteristics of the individual items. In IRT the proportion of Individuals

getting a valid item correct is correlated with ability (θ). Using factor analysis,

undimensionality and local independence is established for each item. This enhances

additional validation issues for tests developed using IRT. In IRT each test item is

correlated with the ability assessed by the testee, if the result is negative or uncorrelated

then the item should be dropped. This will ensure the homogeneity of items developed.

36

IRT is a model for expressing the association between an individual’s response to

an item and the underlying latent variable (ability or trait) being measured by the

instrument (Reeve 1986). The latent variable expressed as theta (θ) is a continuous

unidimensional construct that explains the covariance among item responses (Steinberg

and Thissen 1995). Individuals at higher level of (θ) have higher probability of

responding or endorsing an item correctly.

IRT models use item responses to obtain scaled estimate of θ as well as to

calibrate the items and examine their properties (Mellenbergh 1994). Such item is

characterized by one or more model parameters. The item difficulty or threshold

parameter b is the point on the latent scale (θ) where a person has 50% chance of

responding positively to the scale item (question). Items with high threshold are less often

endorsed (Steinberg and Thissen 1995). The scope or discrimination parameter, a,

describes the strength of an item discrimination between people with trait level (θ) below

and above the threshold b. the a parameter may also be interpreted as describing how an

item may be related to trait measured by scale and is directly related, under the

assumption of normal (θ) distribution to the biseral item test correlations ρ (Linden and

Hambleton 1997). For item i the relationship is

a: = 21

.p

pi

−

the scope parameter is under some conditions linearly related to the variable

loading in factor analysis. Some IRT models in educational research may include a lower

asymptote parameter or guessing parameter c to possibly explain why people of low

levels of the trait (θ) are responding positively to an item.

The probability P(θ) of correct response to an item is modeled depending or

conditional on the latent variable (θ) or ability being measured. The item trace line for

each item estimated from corresponding item parameter is plotted as in the figure below.

The partial credit model is a simple adaptation of Rasch model for the

dichotomies (Reeve, 1986). The Rasch model (one parameter logistic model), assumes

that all items are equal in discrimination and that chance or guessing does not influence

the responses of the individual. Thissen, Nelson, Buileaud and McLeod (2001) noted that

37

partial credit model is constrained to have the same slope (discrimination) for all items.

The partial credit model contains two set of location parameters; one for person and one

for items in an underlying trait (Masters and Wright, 1997).

The equation for Rasch model is given as:

P(θ) = )(7.11

1be −−+ θ

This model for dichotomous responses has only the difficulty parameter b. This

can have various values for various steps, but the discrimination (a) is constant and the

guessing index c is assumed not to exist. The item difficulty parameter/index (b),

corresponds to the location on the ability axis at which the probability of correct response

P(θ) is 0.50.

It is this Rasch model which was adapted to obtain the partial credit model

(Reeve, 1986). The partial credit model (PCM) which is generally written as:

P(θ) = ).(exp1

)(exp

ix

ixj

δθδθ−+

−

Where P(θ) is probability of correct response for a given ability level of person

j,` ixδ is an item parameter governing the probability of scoring x rather than x-1. The

ixδ parameter can be thought of as item step difficulty associated with the location on

the underlying trait where categories x-1 and x intersect for a given item i.

38

Fig. 3-Adaptation of Rasch Item Characteristics Curve for one

parameter Partial Credit Model.

Most IRT models in research assume that normal orgive or logistic function

described the relationship between the P(θ) and θ and fits the data perfectly well. The

logistic model is similar to orgive model and is mathematically simpler to use and is

more often used in researches.

The trace line also called the item characteristics curve (ICC) can be vviewed as

the regression of item score on the under lying variable θ (Lord, 1980). The graph below

models the probability of endorsing an item conditional on the level of underlying trait.

Ability ( θθθθ) in Standard Scores

P( θθ θθ

)

39

Fig. 4- The item trace line for Underlying Latent Variable.

The higher the persons trait level moving from left to right along the θ scale, the

greater the probability that the person will endorse the item.

The collection of the item trace lines forms a scale. Hence the sum of the

probabilities of correct response of the item trace lines yields the test characteristics curve

(TCC) the TCC describes the expected number of scale items endorsed as a function of

the underlying latent variable.

40

Fig. 5- The Test Characteristics Curve (TCC)

The graph above represents a TCC curve for 30 items. When the sum of the

probabilities is divided by the number of items, the TCC gives the average probability or

expected proportion correct as a function of the underlying trait (Weiss 1995).

Another essential feature of IRT models is the information function, an index

indicating the range of trait level θ over which an item or test is most useful for

distinguishing among individuals. Impliedly the information function characterizes the

precision of measurement for persons at different levels of underlying latent construct

with higher information, denoting more precision. The graph of information function

place persons trait level on the horizontal axis and amount of information on vertical

axes.

41

Fig. 6- Item Information Function.

The shape of the item information function depends actually on the item

parameters. High item discrimination implies more peaked information function. Higher

discrimination parameters provide more information about individuals whose trait level θ

lie near the item’s threshold value. The item difficulty parameter (s) determines where the

item information function is situated (Flannery, Reise and Widaman 1995). With the

assumption of local independence, the item information values can be summed across all

of the items in the scale to form the test information curve (Lord 1980).

In each level of the underlying trait θ the information function is approximately

equal to the expected value of the inverse squared standard errors of the θ estimate (Lord

1980). The smaller standard error of measurement (SEM), more information or precision

the scale that has information value of 16 at θ = 2.0; then the examinees score at trait

level of 2 have SEM of 25.016

1 = indicating a good precision (reliability approximately

= 0.94) at the level of theta (Flannery et al.,l 1995).

42

Fig. 7- Test information curve with approximater

Precision in measurement is contained within the middle of the scale (-1 <θ<1.5) with

reliability r for the various latent trait.

IRT has a major advantage over CTT .In CTT the summed score scale is

dependent on the difficulty level of the items used in the score scale and therefore not an

accurate measure of the trait level. The procedure in CTT assumes that equal rating on

each item of the scale represents equal level of the underlying trait (Cookie and Michie,

1997). But IRT estimates individual latent trait level scores based on all information in a

participant response pattern. IRT takes into consideration which items were answered

correctly and which ones were answered incorrectly and utilizes the difficulty and

difficulty parameters of the items when estimating trait levels (Weiss 1995). Individuals

with the same summed scores but different response pattern may end up having different

IRT estimated latent score. One may answer more of the highly discriminating and

difficult items and receive higher latent score than one who answers the same number of

items with lower discrimination or difficulty. IRT level estimation utilizes item response

curves associated with the individual response pattern. IRT models focus on

43

measurement of change in trait level which connotes the level of positive behavioural

change and is therefore indispensable in education.

(C) Models of Item Response Theory

There exist two approaches to model building in IRT. The first is to develop a

well fitting model to reflect the response data and the second is to obtain measurement

properties (defined by the model) to which the item response data must fit (Thissen and

Orlando 2001). The case where the data fits the model, offers a simple interpretation for

scale scoring and item analysis.

Educational research measurement is about describing behaviours behind the

response pattern. For this purpose in education we use the most applicable IRT model

such as one, two, three parameter logistic models, partial credit, graded response models,

etc, to fit the data. The choice of the IRT model to employ in a study is data dependent.

Rasch family models are suggested to be used when each item carries equal

weight and is equally important in defining underlying variable and when specific

objectivity and simple sufficiency are needed. But if there is the need of an IRT model to

fit already existing data or highly accurate parameter estimates required, then a more

complex model such as 2 or 3 parameter logistic model or partial credit model or graded

model etc is to be used (Embretson and Reise 2000).

Specifically for dichotomously scored responses in Item Response Theory

Models, the Item characteristics curve (ICC) is described by one, two or three parameters.

First is the difficulty parameter (b) which is the location on the ability axis when the

probability of correct response P(θ) = 0.5. Second is the discrimination parameter (a)

which is the slope of the ICC curve. The higher the value of a, the steeper the slope and

the lower the value of a, the more gentle the slope. The third parameter C is the

vulnerability to guessing which makes ICC asymptotic and to have positive value along

the vertical axis. The equation for Rasch Model i.e. One Parameter logistic Model

(IPLM) is given by

Pθ = 11 + e.(θ )

44

For one PLM only the difficulty parameter (bi) varies. This model assumes the ai

is constant at value of one and the c, is zero for each item in the test. The bi is the location

in ability axis when P(θ) = 0.5.

The equation for Birnbaun model, ie the 2-PLM, is given by

P(θ) = = . (θ )

The 2-PLM contains values for each item difficulty b and the discrimination index

ai but assumes the vulnerability to guessing c, is zero. In 2PLM, b is still location on

ability θ axis when P(θ) = 0.5 and a is the slope of the ICC curve.

The equation for Lord’s model or three Parameter Logistic Model (3PLM) is given by

P(θ) = C + ( ). (θ )

In 3PLM each ICC is described by three parameters

bi = location in ability axis when P(θ) is a bit > 0.5

ai = slope of ICC and

C = vulnerability of the item to guessing.

In the 1-3 PLM e is base of natural logarithm = 2.7 while 1.7 is the scaling factor.

From dichotomously scored items to polytomously scored items, IRT adapts to

the transition more easily than CTT by needing only to make changes to the trace line

model themselves (Thissen, Nelson, Bulleand and McLeod, 2001).But for polytomously

scored responses, the ICC is described by Graded Response Model (GRM), Nominal

Model, Partial Credit Model (PCM) Rating Scale Model (RSM). In all, the 1 PLM, PCM

and RSM belong to Rasch family.

For questions with three or more response categories, Samejina (1969) proposed a

model for graded response or ordered response. This model is based on the logistic

function giving the probability that item response will be observed in category K or

higher.

() = 11 + exp(−( − !)) − 1

1 + exp(−( − !))

45

Bock (1972) proposed the Nominal Model as an alternative to GRM for

polytomously scored item not requiring any prior specification of exclusive response

category as:

() = exp("( + #")∑ exp(!( + #!)%

!&

The Rating Scale Model (RSM) is derived from the partial credit model with

constant a-parameter across all items (Andrich, 1978). The RSM differs from PCM in

that the distance between difficulty steps from category to category within each item is

same across all items. The RSM includes an additional parameter λI which locates where

item i is on the construct being measured by the scale. The probability of person j scoring

x on the possible outcome 0,1,2… m of item i is

() = '( ∑ ()*(+*,-)).-/0

∑ '( ∑1-/2 3)4(5*,-)674

1/2

Another model for polytomously scored items when the response categories vary

is the partial credit Model.

The Partial Credit Model

For items with two or more ordered responses, Masters (1982) created the partial

credit model within the Rasch model and thus, the model shares the desirable

characteristics of the Rasch family discussed above. i.e. simple sum as sufficient statistics

for trait level measurement and separate persons and item parameter estimation allowing

specifically objective comparisons. The partial credit model contains two sets of location

parameters, one for person and one for items on an underlying unidimensional construct

(Masters and Wright, 1997).

According to Reeve (1986), the partial credit model is a simple adaptation of

Rasch model for the Dichotomies. The model follows that from intended order 0 < 1 <

2,…, < m of a set of categories the conditional probability of scoring x rather than x -1 on

an item should increase monotonically throughout the latent variable range for the partial

credit model, the expectation for persons j scoring in category x over x-1 is modeled.

P(θ )j = )(exp1

)exp(

ixj

ixj

δθδθ−+

−

where

46

ixδ is an item parameter governing the probability of scoring x rather than x-1.

The ixδ parameter can be thought of as item step difficulty associated with the location

on the underlying trait where categories x -1 and x intersect.

The response function (from this model) for the probability of person j scoring x

on the possible outcome 0,1,2,3… m of item i can be written as:

( )

( )ikj

m

h

h

ok

x

ok ik

ji j

xUTδθ

δθθι

−

−=

=∑ ∑

∑

= =

=

0exp

exp

where x = 0, 1, 2 … mi

Thus, the probability of respondent j endorsing category x for item i is a function

of the difference between their level on the underlying trait step difficulty (θ - δ )

Thissen et al. (2001) noted that partial credit model is constrained to have the

same slope (discrimination) for all items.

The partial credit model has been applied to wide range of item types, (Wu and

Adams, 2007). For example

i. Likert type questionnaire items such as strongly agree, agree, disagree, and

strongly disagree.

ii. Essay rating for example on a scale 0-5

iii. Item requiring multiple steps such as a problem solving item requiring students to

perform different steps

iv. Items where some answers are more correct than others.

v. A testlet or item bundle consisting of a number of questions.

vi. Test items where the response categories vary.

The Generalized Partial Credit Model

The Generalized Partial Credit Model is a generalization of the partial credit

model that allows discrimination parameter to vary among the items.

According to Tang (1996), the major difference between the partial credit model

and the generalized partial credit model is that the partial credit model assumes that the

item discrimination is a constant for all the items in a test. The generalized partial credit

model on the other hand assumes that item discrimination can be different across items

and has a parameter to model this. The difference between these two models is similar to

47

the difference between Rasch model and the two parameter logistic model in the

dichotomous case.

Muraki (1992) extended Master’s partial credit model by relaxing the assumption

of discrimination power of test items based on the two parameter logistic model. In

Muraki’s formulation, the probability of choosing k over category k-l is given by the

conditional probability

)()(1

)(

)(.1/

θθθ

θ

jkjk

jk

jjk

pkp

p

kkkpC

+−=

−≡

=

where k = 1, 2 … mj

The above equation can be written as:

After normalizing each Pjk(ϑ ) so that )(θjkPΣ = 1 then the Generalized partial credit

model can be written as:

[ ][ ])(exp

(exp)(

υ

υ

θ

θθ

jjaj

c

ov

)jjaj

k

ovjk

dbD

dbDP

+−

+−=

∑∑

=

=

Where D is a scaling constant set to 1.7 to approximate the normal orgive model, a is a

slope parameter, b is an item location parameter and djv is a category parameter. The

slope parameter indicates the degree to which categorical responses vary among the items

as θ level changes with mj categories; only mj-1 category can be identified.

Indeterminacies in the parameters in the Generalized partial credit model are resolved by

setting.

OdandOd jk

m

ojj

k== ∑ −

−

1

1.

Muraki (1992) pointed out that bj – djk is the point on the θ scale at which the plot of Pj,k-1

ad Pjk θ intersect and so characterizes the point on θ scale at which the responses to item j

[ ][ ])(exp1

)(exp

jkj

jkj

ba

ba

−+−

θθ

[ ] )()(exp)(1

)( 11 θθθθ −− −=−

= jkjkjjkjk

jkjk PbaP

C

CP

48

has equal probability of falling in response category k-1 and falling in response category

of k.

Tang (1996) noted the following while discussing parameter interpretation in GPCM

that both the partial credit model and GPCM

(i) Assume that each of the two adjacent categories (k and k-1) in a polytomously

scored item can be seen as dichotomous categories and therefore, the

likelihood of a person with certain ability level reaching the score category of

k rather than k-1 can be described by a dichotomous IRT model.

(ii) The models IRT were thus generalized from dichotomous IRT model to

describe the probability of selecting a particular score category from all

possible score categories for an examinee.

(iii) For a polytomously scored item that has m score categories, based on GPCM,

the item has one item discrimination parameter, one location parameter and a

set of m-1 threshold parameters. That is to say that in GPCM we have only

one b, one a, and m score cathegory minus one threshold parameters

The item discrimination parameter describes how well the item can distinguish

between individual of different ability levels. The location parameter indicates the item

difficulty.

Assumptions of Partial Credit Model

Unidimensionality means that a single latent variable fully explains task

performance. This is one of the major assumptions for the polytomous item response

theory models. Carlson (1993), has shown that even if the cognitive processes required to

answer constructed items are inherently complex, data from these items meet the

unidimensionality assumptions essentially before applying partial credit model to data,

the data should be investigated, whether it conforms to the unidimensionality assumption,

that is to say that the data must be assesing only one latent ability . Hugh and Ferrara

(1994) investigated whether the test for Maryland school performance assessment

programme met the unidimensionality assumption. All the task in this programme

required brief or extended responses to performance task designed to elicit students

ability to apply knowledge, skills and thinking processes. The conclusion was that the

49

responses to the polytomously scored items were dominated by one major factor or the

data was unidimensional.

The second assumption for polytomously scored items is local independence. This

means that items even if they are based on a common passage should be mutually

independent or exclusive. The response to one question is independent of response to

other questions. However, items within each cluster could show minimal level of

dependency. Yen (1993) showed that performance assessments tend to produce more

local item dependence (LID) than multiple choice items and suggested some strategies

for reducing local item dependence to avert negative measurement implications.

Advantages of Partial Credit Model

The following are advantages of Partial Credit Model as identified by Hancook

(2006)

1) All items independent of type are placed on the same common score scale.

2) The Partial Credit Model (PCM) provides the same score scale for which

students’ achievement results are placed. Thus, direct comparison of items

and achievement level can be made. This is enormously helpful in

describing results of assessments to students and parents.

3) The PCM allows for the pre-equating of future test forms which is a

valuable component of test construction process.

4) The PCM supports post equating of the test items. There is a link established

between previous forms and current administration

5) The PCM allows for direct comparison of performance level standards

established against future test forms.

Some IRT Methods in Estimating Item Parameters

The estimation procedures for item parameters in IRT include (i) correlation

method (ii) regression method (iii) approximation (PROX) method (iv) maximum

likelihood procedure.

Correlation method was used by Lord (1968) for estimation of item

discrimination indices for all items in the test at the same time using the factor analysis of

the matrix of inter item correlation. The parameter estimating the item difficulty is

evaluated by the normal deviate that matched the proportion of subjects in the total group

50

that answered the item correctly. Also the discrimination index was estimated by the item

loading in the factor analysis. A direct conversion method for estimation of item

parameter in latent trait models is possible from item parameters of classical test model

through the test point biserial (Urry, 1974).

According to Baker (1977), the regression method involves the regression of an

item on the latent trait based on the item characteristics curve. In this the discrimination

index of an item is the scope of the item characteristic curve while the item difficulty is

the value of the ability θ at which the probability of correct responses to an item is 0.5 or

50%.

Izard and White (1980) had an approximation (PROX) procedure for item

analysis of the latent trait models. In PROX analysis, the answers given by examinees are

listed in students by item matrix. The analyses are based on marginal totals of correct and

incorrect responses (frequency counts) for each items and subjects. The procedures

estimate any testee with perfect or zero scores. Items not attempted by any testee are

deleted from the matrix before calculation. This facilitates validation of the whole items.

If N is the number of examinees that attempted an item,

S is the total score on an item ie total no. of correct responses for an item.

b = Ln ( )

S

SN −

Also if Y is the number of correct respondents to an item

N is the number of examinees that attended the item Izard and White (1980)

established that the ability θ estimate is

θ = Ln YN

Y

−

Lord (1968) also employed estimation procedure in statistics known as maximum

likelihood estimation. In this procedure there is conditional and unconditional maximum

likelihood. For conditional likelihood the data for item parameter are estimated based on

the students ability scores and the item difficulty indices. But for unconditional likelihood

the students ability score is removed from the estimation equation and so the item

parameters are estimated with no respect to students latent ability. On the whole

maximum likelihood estimation is a statistical procedure that finds the maximum

likelihood function created from the product of a population distribution with the

51

individual trace curve associated with each items right or wrong response. The pattern of

the subjects score, 1 if correct 0 if wrong is the basic data for the item analysis in this

approach. Amidst other procedural steps, the indices of item parameters and estimate of

individual latent ability scores are obtained.

Out of the methods described above, that are used in IRT to estimate parameters

the use of maximum likelihood procedure is more frequent and preferred. This is because

the maximum likelihood procedure yields comprehensively the item parameters and

ability estimated for all examinees (Baker, 1977).

Statistical Fit Tests

The statistics usually utilized when assessing the validity of a test in classical test

theory are the item bi serials. But the magnitude of this item statistics in CTT depend on

the ability distribution of the samples and it has the disadvantage of being sample

dependent.

In item Response Theory, the validity of a test is assessed in terms of the

statistical fit of each item to the model of IRT used. The analysis of fit is a check on the

validity when the fit statistics of an item is susceptible, then it is valid and if a given set

of item fit the model, it is an evidence that they refer to unidimensinoal ability (Korashy,

1995). Also, fit to the model implies that the items’ discrimination are uniform and

substantial and hence little or no error in scoring. A measure of fit statistic commonly

employed is the Chi square goodness of fit. A large positive fit statistics indicate no

fitting, a low fit statistic nearer one (1) indicates better fit (Bryce, 1981). This criterion of

fit to the model enables the test developers to identify and delete bad or misfitting items.

Specifically, for Partial Credit model, the infit and outfit mean square statistics

has goodness of fit when the infit and outfit of the item has the range (0.7 – 1.5) and has

the mean statistics that approximate 1 (one); with mean square (MNSQ), standardized in

z-score (Z STD) which approximate a theoretical distribution with mean O (Opsomer,

Jenson, Nusser, Drignei and Amemiya; 2002)

In an attempt to assess the model data fit to PCM, we use the Residual Based

measures (Ostini and Nering, 2006). Fit measures can be classified in terms of the level

of generality of their application. Fit can be assessed globally in terms of the fit of an

entire data set from a complete measurement instrument. Fit can also be assessed in terms

52

of the fit of specific groups of items from a test if specific hypotheses about fit are to be

tested (Ostini and Nering, 2006).

In direct residual based measure, a simple response residual comprises the

difference between observed and expected item response. This can be standardized by

dividing the residual by the standard deviation of the observed score (Masters and

Wright, 1997).

Response residuals can be summed over respondents to obtain an item fir measure

and generally the accumulation is done with squared standardized residuals, which are

then divided by the total number of respondents to obtain the fit statistic (mean chi

square). In this form, the statistic is highly sensitive to outlier responses (Masters and

Wright, 1997; Ostini and Nering, 2006)

Empirical Studies

Nkpone (2001) utilized one and two parameter logistic models of IRT and also

CTT in the development and standardization of physics achievement test for senior

secondary students. The sample of the study was 2215 students who sat for SSCE of

May/June 1999 in River State of Nigeria. The instrument of the study was 60 multiple

choice item, physics achievement test. The result of the study was analysed. The

reliability and validity of each of the items and whole test, item parameter estimation (b

and a), the person parameter estimation (the ability estimates) each item S.E.M, and

analyses of fit test were carried out by the researcher. The item parameters (b and a) of

CTT and IRT were compared by the study.

The data analyses were done using PROX and regression techniques of Microsoft

Excel Visual Basic Computer programme. The chi square goodness of fit test as used and

factor analysis was used to establish the unidmensionality (validity) of 0.89 (using K-R

20) for the instrument and the items showed a good fit to the model. There was also no

significant difference among item parameter obtained using 1 PLM, 2 PLM and CTT in

analysing the dichotomously scored physics achievement test.

Lian and Idris (2006) assessed the algebraic solving ability of form four students.

The purpose of the study was to use the SOLO model (Unistructural, multistructural,

relational and extended abstract) as a theoretical framework for assessing the form four

algebraic solving ability in using linear equation. The content domain in the framework

53

were linear pattern, direct variation, concept of functions and arithmetic sequence. The

test composed eight super items of four items each. The sample of the study was 40 form

iv student in a secondary school in Malaysia. This study used qualitative and quantitative

approach to assess the students algebraic solving ability based on SOLO model. The

rationale of the researcher in choosing quantitative method was to assess the students

level of algebraic solving ability. The data set was subjected to partial credit analysis and

later quantitative method was used to seek clarification of the students algebraic solving

processes. Each of the four items for each super item, represented four levels of reasoning

defined by SOLO model. The data analysis was done based on the finding from the

pencil and paper test and interview.

The test paper results were analyzed by using partial credit model. Partial credit

model (Wright and Masters, 1982) is a statistical model that specifically incorporates the

possibility of having different number of steps or levels for each item in a test (Bond and

Fox, 2001). In this study the ordered values 0,1,2,3,4… was applied to super items as

follows 0 = Totally wrong or no response, 1 = Unistructural level, 2 = Multistructural

level, 3 = Lower relational level, 4 = Relational level, 5 = Higher relational level, and 6 =

Extended abstract level i.e. codes 0-6 covered all the response possibilities in the test.

Winstep software programme was used to run the analysis. It computed the

probability of each response pattern to obtain the ability of the each learner and difficulty

of each item. The purpose of this computer analysis was to estimate the value of the

validity, the reliability index, difficulty of items, and the levels achieved by the students

on each content domain. The partial credit model of this study estimated reliability both

for person and items. The item reliability index indicated the replicability of items if they

are given to another samples with comparable ability levels and persons reliability index

and indicated the persons replicability of person ordering if the sample are given another

set of item measuring the same construct. In this study the partial credit model revealed

the item and person reliability indices were 0.91 and 0.73. According to this study

validity is dependent on reliability and success of evaluation to fit statistics (infit and

outfit). The expected value of mean square was between 0.7 and 1.3. Also the infit (mean

for infit mean square) was 1.06 and out fit (mean for outfit mean square was 0.98. In the

analysis the infit and outfit mean square for each super item fall within the acceptable

54

range. Generally the result of the study indicated that 62% of the students have less than

50% probability of success at relational level. This result also provided evidence on the

significance of SOLO model in assessing algebraic solving ability in upper secondary

school level.

Justice, Bowles and Skibbe (2006) measured pre school attainment of print

concept knowledge; a study of typical and at risk 3-5 year old children using item

response theory. This study determined, the psychometric quality of a criterion –

referenced measure that was thought to measure pre schoolers Print Concept Knowledge

(PCK). The total sample of the study consisted of 128, 3-5 year old children from urban,

sub-urban and rural regions of southeast Ohio made up of 65 boys and 63 girls with a

mean age of 53 months. The measure titled Pre-school Word and Print Awareness

(PWPA) was analysed using the Partial Credit Model (PCM) to determine its suitability

for use by clinicians, educators and researchers. The study also investigated the extent to

which PWPA differentiated estimates of PCK for at risk population on the basis of Socio

Economic Status (SES) and language ability. The sample varied in SES (middle, low)

and language ability (typical and impaired language). The result of the partial credit

model fit analyses showed good fit between the overall data and the PCM indicating that

PWPA provided a valid estimate of the latent PCK trait. Socio-economic status and

language ability were found to be significant predictors in the study when age was used

as a covariate. These results showed PWPA to be suitable for measuring Pre school age

print concept knowledge to be sensitive differences among children as a function of risk

status. According to this result Pre School Print Word and Print Awareness PWPA is an

appropriate instrument for clinical and educational use in pre school children.

Wallace, Prather and Ducan (2012) performed an item response approach to the

study of General Education Astronomy Students’ Understanding of Cosmology Part III in

which they evaluated four cosmology surveys. In this work they developed cosmology

survey and analysed student’s responses to three out of the four cosmology survey they

developed. Partial Credit Model of IRT was specifically used for the analysis of the

students responses to assess the reliabilities of the survey forms and to determine the

probabilities of students achieving different scores on the survey items. The sample of the

study was 4359 students that responded to the four forms in semesters of 2009 and 2010

55

academic session in University of Arizona. For a given semester the students and item

parameters using pre and post instruction responses. This is acceptable because IRT

unlike CTT attempts to disentangle item difficulty parameters from the students abilities.

They therefore estimated difficulty parameters using students of low and high abilities

by, using pre and post-instruction responses in the estimation. The researchers used only

forms A, B and C leaving form D since form D exhibited item chaining- a situation

where each item builds off the previous item such that knowing the answer for one

increases the probability of correctly answering the next (Yen 1993). This study

compared the item step parameters b and the Thurstone threshold parameters step

difficulty β for all the items in forms A,B,C for all the students in the two sessions under

studied. The aim of this study was to present IRT analysis of students responses to for A-

C of conceptual cosmology survey, to provide insight to conceptual knowledge and

reasoning abilities of their students.

The analysis of step difficulties b and thurstone thresholds β for each item

revealed which levels of understanding that were obtainable or well beyond the abilities

of the students. The data presented in the study indicated that interpreting Hubble Spot

(Form A) is much more difficult than understanding the Big Bang and evolution of the

universe (Form B and C). The evidence for the reliabilities of forms A-C was obtained

using Wright maps which showed that the items adequately span the students abilities.

Finally the study established foundation for their research methodology and the reliability

and validity of the survey instrument they used to assess students understanding of

cosmology.

Opsomer, Jenson, Nusser, Drignei and Amemiya (2002) carried out statistical

consideration for the United States Department of Agriculture (ASDA) food insecurity

index. This work reviewed the statistical properties of the model used to obtain the

estimates of the prevalence and severity of poverty linked food insecurity and hunger in

the United States. The assessment of household food insecurity was based on a one

parameter logistic model of item response theory also called the Rasch partial Credit

Model and applied to a series of eighteen question reported in the population survey Food

Security Module. According to the authors, the partial credit model as a technique is of

interest to them since PCM can answer the questions that are polytomously scored and as

56

well collapse some questions to fit PCM without making them dichotomous. The

researchers fitted PCM on a set of 1995 current population survey (CPS) food insecurity

questions used in the original scale.

The item parameter estimates and goodness of fit statistics computed by BIGSTEP

software following the procedural steps explained in Hamilton ,Cook,Thompson, Buron,

Olson, Frongillo, and Welher (1997b) . Also the same estimates and statistics for PCM

fitted with BIGSTEPS. Both item parameters and goodness of fit for the dichotomous

case as described in Hamilton et al. (1997b) and PCM fitted with BIGSTEPS for

polytomous responses, their columns had the following interpretations:

(i) Entry Number: The sequence number of the question

(ii) Raw Score: The number of ‘yes’ answers to the question

(iii) Count: the total number of valid responses for that questions

(iv) Measure: the estimate of the severity parameter (Difficulty estimates)

(v) Error: The standard error of the estimate

(vi) Infit/Outfit: BIGSTEPS goodness of fit statistics. NMSQ is the mean square

statistics with expectation = 1; ZSTD is the mean square statistic with

standardized to approximate theoretical distribution with mean = 0 and variance =

1.

In Hamilton et al(1997b) items with both infit and outfit MNSQ – mean square

statistics larger than 1.2 indicate a poor fit, and are targeted for removal from the scale.

Items that have infit and outfit MNSQ smaller than 0.8 are redundant with respect to

information they share with other items in the scale. In this study the goodness of fit as

measured by the infit and outfit statistics is degraded for some items since the changes in

the PCM model are aimed at improving the model of fit and removing assumption

violations. Using the technique of this study it could also be evaluated whether this PCM

model would hold for subgroups of American population. This work was used as the

basis for discussions concerning future directions of research on food insecurity measure.

Siasang and Nenty (2012) studied the differential functioning of 2007 Trends in

International Mathematics and science study (TIMSS) examination items. In this work

there was a comparative consideration of students performance in Botswana, Singapore

and United States of America using TIMSS examination items. The study was

57

necessitated by the import of educational decisions made by many countries and

international organizations based on comparative countries. The purpose of the study,

was to investigate differential item functioning (DIF) in test items of 2007 TIMSS for

16184 students from Botswana, Singapore and USA. The sample of the study were 4208,

4599 and 7377 eight grade students from Botswana, Singapore and USA respectively

generated using random sampling done by TIMSS headquarters. A comparative DIF

analysis of data was done using two statistical method; the Scheuneman modified chi

square (SSX2) and Mantel Haenszel (M.H) analysis. The findings of the study reflected

that most of the TIMSS items functioned significantly differently among students from

Botswana, Singapore and USA and therefore showed the existence of significant bias

across learners in the three nations. The recommendation of the study was that future DIF

studies in TIMSS should investigate the causes of DIF and the subject curriculum

developers in the three nations should review their curriculum.

Nworgu and Agah (2012) applied three parameter logistic model (3PLM) in the

calibration of a mathematics achievement test. The purpose of the study was to use 3PLM

of item response theory in the caliberation of a mathematics achievement test. The

sample of the study was 1514 SS III students from Rivers and Cross river states of

Nigeria and the instrument for the study was a 40 items multiple choice test developed

by the researchers. The data analysis was done using BILOG-MG an IRT computer

software that estimated the item parameter and their corresponding standard error of

measurement. Three research question and three hypotheses guided the study. The chi

square goodness of fit was used to determine the goodness of fit of the items of the

instrument to three parameter logistic model. The study also generated item

characteristics curve to determine if the items in the tests are good enough for the

assessment of the students’ ability. The result showed the empirical reliability coefficient

of 0.79. The item parameter indices obtained indicated that the discrimination parameter

(a) ranges from 0.29 to 2.05; item difficulty form -0.40 to 1.79; the probability of

guessing in the test correctly ranged from 0.02 to 0.50 for all the ability levels.

Ojerinde and Onyeneho (2012) conducted a comparison between classical test

theory and item response theory from 2011 pre test in the use of English of the unified

tertiary matriculation examination (UTME) in Nigeria. The aim of the study was to

58

evaluate the use of English pre-test data so as to compare the indices obtained using 3-

parameter model of IRT with those of the classical test theory (CTT) and hence verify

their degree of comparability. The sample of the study was 1075 test takers that took one

version of the pretest use of English. The instrument was a 100 item use of English items

developed by UTME and the data was analyzed by using Microsoft excel programme for

the CTT analysis. For the IRT model the data was analyzed using XCALIBRE software.

The findings of the study showed that the 3PLM was found to be more suitable in

multiple choice ability test. Overall, the indices obtained from both approaches gave

valuable information with comparable and almost interchangeable results. It was

recommended that both IRT and CTT parameters should be used in empirical

determination of validities of dichotomously scored items to ensure common bases of test

analysis, enhance interpretability and objectivity of test agencies in Africa.

Pido (2012) also compared item analysis results obtained using item response

theory (IRT) and classical test theory CTT approaches. The aim of the study was to

analyze, determine and compare the item parameters of multiple choice questions of

Uganda certificate of education (UCE) the sample of the study, selected though multi

stage procedure was 480 students scripts in dichotomously scored, physics, chemistry,

Biology and Geography part of the UCE. The data analysis was done suing XCALIBRE

4.1.7.1 software to determine items parameters based on the CTT and IRT approaches.

The output included the item characteristics curve (ICC), item difficulty indices (b) item

discrimination indices (a) and differential item functioning with respect to gender. Two

methods of correlation coefficent were used to compare the b and a indices based on CTT

and IRT approaches. The result revealed that there is a high correlation between b and a

in IRT and CTT approaches. The study therefore recommended that both CTT and IRT

should be used for item analysis since they produce similar results.

Odili (2010) investigated the effect of manipulating the language test items on

differential item functioning of test items in Biology in a multicultural setting. The

purpose of the study was to manipulate by simplifying the language of biology multiple

choice items and evaluate the effect on DIF index and to investigate the effect of such

manipulation on index of DIF for testees from high and low Socio-economic status SES.

The sample of the study was 1, 025 SSIII students from Delta State composed using

59

random and proportionate sampling technique. The instrument of the study was SES

questionnaire and Biology multiple choice achievement test (in two forms). Four research

questions and four hypothesis guided the study. The data was analyzed using

Scheuneman modified Chi-square statistic and the hypotheses were tested using

dependent t-test. The results of the study showed that manipulation of test items to

simplify their language reduce the index of DIF among testers in a multicultural setting.

The study recommended that for test validity in a multicultural setting, the language of

the test items should be simplified to reduce DIF.

Ugodulunwa and Muttsapha (2011) used differential Item Functioning (DIF)

analysis for studying the improvement of quality in State Wide examination in Nigeria.

The problem of threat to validity of JSCE as a result of low correlations between results

of JSCE and SSCE in Mathematics that is replete in literature necessitated this study.

Cluster sampling was used to select eleven local government areas and 77% of all the

scripts used for JSCE examination in mathematics in the years 2007 and 2008. A total of

27038 scripts formed the sample for the study. Six hypotheses guided this study. The data

analysis was done using Scheuneman modified Chi-square statistics to identity the

presence or otherwise of DIF in the mathematics items that were dichotomously scored.

The findings of the study were that the examination items contained items that

differentially functioned for candidates described by gender, school type and school

location. The study recommended that to ensure quality in a state wide examination such

as JSCE, DIF analysis should form part of the test process and in fact in other nation wide

examinations in Nigeria.

Akindele (2004) worked on development of prototype of items for selection tests

into universities in Nigeria. Using computer progamme he randomly generated a sample

of a thousand students who entered for 1998 university entry examination-made up of

626 males and 374 females-in English Language. The data analysis was done using SPSS

and BILOG MG software. The SPSS accomplished the classical item statistics, while the

BILOG MG software was used to calibrate the test to determine the item parameters and

ability estimates. On testing the hypothesis, the study indicated significant differences in

the item parameter estimates of test items using IRT and CTT; but the scaled scores for

the three subparts of the test (grammar, lexis and structure, comprehension) did not show

60

any significant difference in the mean and standard deviations as computed using CTT

and IRT procedures. Three different ability estimation procedure used in the study did not

reveal any significant difference in estimated abilities of the students. Gender was noted

in the study as a moderating variable in the student academic performance as it

established differential item functioning. The values of item statistics a,b and c as

estimated using 1,2 and 3 parameter logistic models of IRT showed significant

difference. The item developed and stored in this study’s item bank was calibrated with

3-PL model because the study deemed it (3-PLm) to be more robust given the sample

size and the length of the test.

Obinne (2008) did a comparison of psychometric properties of WAEC and NECO

Biology examinations under item response theory. The purpose of the study was to

investigate the psychometric properties (reliability, validity, difficulty index etc) of the

items of biology examinations conducted by WAEC and NECO using the item response

theory (IRT). The study was necessitated by public persistent out cry that NECO is too

cheap to pass. Fourteen research questions and seven hypotheses guided this study. The

sample of the study was 1800 SS III students from 36 secondary schools in urban and

rural areas of Benue State. Multistage stratified sampling technique was used. WAEC and

NECO biology examination questions (objective) from year 2000 – 2002 were the

instruments for data collection. The research questions were answered using maximum

likelihood estimation technique of BI LOG MG computer programme according to IRT

procedure. The SPSS was used to test the hypotheses.

The results of the study were that biology examination items from WAEC and

NECO were equally reliable and valid; and that biology items of NECO examination

were more difficult than those of WAEC of the same year. The study concluded that

NECO questions were really not cheap to pass. The study also discovered that WAEC

items were more prone to guessing than those of NECO items. This study finally

recommended that IRT procedures should be adopted by all examination bodies in

Nigeria so that most measurement problems will be put to test.

Obinne (2011) performed a psychometric analysis of two major examinations in

Nigeria, WAEC and NECO:- Standard error of measurement. This work dealt with the

psychometric analysis of two major examinations in Nigeria conducted by NECO and

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WAEC. The aim of this study was to compare the standard error of measurement (SEM)

of biology examination conducted between year 2000 to 2002 using one parameter

logistic model of IRT. Instrumentation research design was used for the study; the area of

study was Benue State of Nigeria. The population of the study was all year three (SS III)

who registered for May/June 2006 biology examination in WAEC and NECO in Benue

State. The sample of the study was 1800 students selected using multistage stratified

random sampling technique. The instrument of this study was 2000-2002 objective

Biology questions. Maximum likelihood estimation techniques of the BILOG MG

computer software programme and SPSS were used for data analyses. The result

indicated significant difference in the SEM of NECO and WAEC Biology in the years

understudied. The result showed that Biology examination conducted by NECO had

smaller SEM than those of WAEC and noted that NECO Biology has higher reliability

than that of WAEC. The recommendation of the study is that IRT analysis should be

employed for test development and examination bodies in Nigeria for increased

precision.

Summary of Literature Reviewed

The reviewed literature in this study has among other things looked at theoretical

and conceptual background of item response theory. In these the historical development

and progress made in IRT over time, explanation of basic concepts in IRT etc were made.

Also explored is how item analyses were conducted using some latent trait models and

their procedures for item selection. Various methods of determining the standard error of

measurements were also reviewed. The need for enhanced precision in measurement was

continually highlighted in this review. Presently most studies that have been done in test

analyses made use of classical test theory. This is attributable to ease of computation in

CTT; but tests analyzed using CTT are highly questionable due to the circular

dependency of item parameters on population and person parameters on items. Owing to

these inherent defects in the CTT there is the need for analyzing our tests using item

response theory models.

Extensive and diligent search during this review for researches done using partial

credit model (PCM) of item response theory revealed that this model (PCM) has been in

use in overseas, and even then none of them went into test analyses in physics. Given the

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indispensable nature of partial credit scoring in some areas such a performance in music,

dance, describing a work of art, technical drawing and in fact in all psychomotor

activities that require completion of a number of steps, there is the need for analyses of

tests in psychomotor aspects of physics using the PCM as this will increase precision in

this area.

During the review, no study could be accessed that was conducted in Nigeria that

used PCM. The studies that have been attempted in Nigeria using Item Response Theory

used 1PL, 2PL and 3PL (either one or more) in their test analyses. Their use of these

logistic models, are actually appropriate. But there is the need to analyze test using PCM

in Nigeria in a situation where series of steps are needed (Polytomously scored).

Locally in Africa, some studies used 1, 2 and 3 parameter logistical models for

test analysis. In Nigeria only one study used 1PLM and 2PLM in development and

standardization of dichotomously scored physics achievement tests. No research has been

carried out in Nigeria using IRT model in practical physics or any polytomously scored

aspect of physics. This research stands out as it analysed practical physics of WAEC and

NECO in Nigeria using the IRT model called Partial Credit Model PCM to investigate

the psychometric qualities. From the literature, it was also revealed that WAEC and

NECO always use classical test theory in their psychometric analysis. It is high time

another measurement framework is utilized for psychometric analysis of their

examination to see if the precision will change.

Since no study has been conducted in Nigeria using Partial Credit Model and

many studies that have been done in Nigeria, and in Africa as a whole dwelt on

psychometric analysis of objective questions, then there is the need for such analysis in

practical aspects of the physics. Practical physics is of equal weight with objectives in

both WAEC and NECO, while some studies have attempted psychometric analyses of

objective aspects of sciences as revealed by literature, none has attempted psychometric

analysis of practical physics. Then there is every need for psychometric analyses of

practical physics questions given by our examination bodies – WAEC and NECO.

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CHAPTER THREE

RESEARCH METHOD

This chapter basically discusses the general framework on which this study was

carried out. This general framework includes: The research design, The Area of Study,

Population of the Study, Sample and Sampling techniques, Instrument for Data

Collection, Validity of the Instrument, Reliability of the Instrument, Method of Data

Collection, and Method of Data Analyses.

Research Design

This study is an instrumentation research. Instrumentation research design was

therefore appropriate for this study. Instrumentation research is that study which is geared

towards the development and validation of instrument in education (Ali, 1996). And

according to international Centre for Educational Evaluation (ICEE) (1982),

instrumentation research is a study aimed at introduction of new or modified content,

procedure, technological or instruments of educational practice. In this present study,

WAEC and NECO in practical physics questions were analysed with respect to some

psychometric properties of the questions.

Area of the Study

The area of study was Enugu state of Nigeria. Enugu state is located at South

Eastern part of Nigeria. This state is made up of seventeen local government areas. The

state is entirely an Igbo speaking tribe. The area of this study is made up of six

educational zones. Three education zones (Nsukka, Enugu and Obollo-Afor) made up of

nine local government areas were used for the study. There are public and private

secondary schools in the state. The public secondary school (state owned) is 272 in

number. The 83 government approved private secondary schools were ignored in the

study because only very few of them have physics laboratory.

Population of the Study

The population of this study comprised all senior secondary year three physics

students, who enrolled for May/June/July 2013 physics senior secondary certificate

examination of WAEC and NECO in state owned secondary schools (public) in the six

educational zones of Enugu state. The research subjects (2013 SS three physics

candidates) would have covered the WAEC and NECO physics syllabuses. The number

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of candidates of 2013 SSCE level physics examination in WAEC and NECO in state

owned (public) schools is 12,067 (WAEC and NECO sources respectively).

Sample and Sampling Techniques

Six hundred and sixty eight (668) respondents formed the sample for this study.

Multistage sampling technique was used in selecting the sample for the study. Firstly,

three educational zones out of six educational zones of Enugu state were selected using

simple random sampling.

Enugu state has about 272 public (state owned secondary schools) and they are

distributed in the six educational zones of the state (Appendix A). The three sampled

zones were Enugu, Nsukka and Obollo-Afor education zones. (See appendix W)

In each sampled educational zone the schools were stratified into various local

governments. From various strata of schools in various local governments, purposive

random sampling were used to select two schools from each local government where the

number of SS3 physics candidates were up to thirty. Purposive sampling was used to

select all schools that had up to thirty physics students in the local government. This was

done in order to enable the researcher sample only schools that can give reasonable

number of respondents four the four different sections of the instrument at the same time.

From this random sampling was again used to select two schools finally used per local

government area. Between thirty to forty physics (SS3) candidates were randomly

selected for the study in each sampled school. This gave a sample of sixty to seventy

candidates in every local government and about two hundred candidates in every sampled

education zone. This gave a total of six hundred and sixty eight candidates used for the

study (Appendix X). From this between 164-172 respondents used for analysis of each of

the four sets of questions were generated. This is because the number of respondents

required in Rasch model for polytomusly scored items for 95% confidence level is from

64-144, and higher numbers are acceptable. (Linacre 1994; 1999; 2002; 2007) Eckes

(2011). From the total of eighteen sampled schools, a total of 668 respondents that

registered for 2012 / 2013 WAEC and NECO May/June/July emerged as the sample for

the study (See appendix X, p. 171).

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Instrument for Data Collection

The instrument for this study consisted of WAEC and NECO 2011 – 2012

May/June/July practical physics examination questions. The instrument was made up of

four parts that were used for the study. They are (i) 2011 practical physics questions of

NECO (PPQN 1) – Appendix C, (ii) 2012 practical physics questions of NECO (PPQN

2) - Appendix D ,

(iii) 2011 practical physics questions of WAEC (PPQW 1) - Appendice E, (iv) 2012

practical physics questions of WAEC (PPQW 2) - Appendix F. Results from the

instrument consisted of performance of each student item by item in the practical

question set of questions attempted. These results were obtained using the appropriate

marking guide (to each part of the instrument) from the two examination bodies

(Appendices G, H, I, and J)

Validity of the instrument

The instrument is made up of WAEC and NECO practical physics questions for

May/June/July for years 2011 and 2012. These were validated by West African

Examination Council and National Examination Council.

Reliability of the Instrument

The reliabilities of the questions were as well obtained before administration to

the candidates who took the examination in those years by the two examination bodies.

The presumption therefore is that the questions are equivalent in content. Moreover the

validity and reliability of the practical physics questions are among the major thrusts of

the study.

In the response analysis of Item Response Theory, every estimate of item

difficulty measure comes with its standard error of measurement and the smaller the

standard error, the better the test item and the higher the reliability (Baumgartner,2002).

Also in IRT, validity connotes a fit to the model, that item discrimination is uniform.

(Nkpone, 2001). An item is valid or has a good fit to the model if it has fit statistics

between 0.7- 1.5. (Curtis and Boman, (2007); Opsomer et al (2002), Bryce, (1981)).

Eventually in the study the researcher analysed the validity of the items using fit

statistics (Results to research question 1and 2). And the reliability was analysed through

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the standard errors of measurement for the test items (Results to research question 3 and

4).

Method of Data Collection

The instrument for the study was administered to the respondents by the trained

research assistants and the sampled schools physics teachers under the supervision of the

researcher. The researcher ensured adequate supervision to avert cheating. The

invigilators of the examination ensured strict compliance of respondents to instruction.

Similar conditions of administration by WAEC and NECO were ensured. The study was

carried out in the second half of second term when the SS3 students fully were ready for

WAEC and NECO examinations.

The practical physics questions that were administered to the respondents were in

two sets for WAEC (PPQW1and2) and two sets for NECO (PPQN1and2). Each set was

made up of three different practical activities that the students were instructed to answer

all questions in the set he/she had. The four sets of practical physics question were

administered at the same time in the same class (See Appendix X p. 171). In each

sampled school the sampled students were randomly assigned to the four different sets of

practicals. This implies that each examinee had either NECO or WAEC practical physics

question for the year 2011 or 2012 May/ June/July examination. Each examinee was

required to answer one of the four sets of questions. The data of the students’ scores in

practical physics questions were collected. On the whole, 166, 172, 166, and 172

students responded to NECO 2011, NECO 2012, WAEC 2011 and WAEC 2012

respectively (appendix x).Their performance (scores) were used for data analysis and

subsequently to answer the research questions and test the hypotheses.

The marking guide for the questions were the marking scheme provided by the

examination bodies- WAEC and NECO (Appendices G, H, I and J). The marking scheme

therefore was supposed to offer the different score categories to the questions or sub

questions.

Method of Data Analysis

In this study, the data collected were analysed using maximum likelihood

estimation procedure of the CATS WINSTEP 3.80.1 computer programme of partial

credit model analysis. The research questions were answered using item response theory

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descriptive statistics estimation procedure such as mean, SEM, reliability, fit statistics

and difficulty measure.

To test the hypotheses, independent-test analysis was carried out at (0.05) level of

significance using the SPSS computer program.

Specifically the criteria on which basis the items psychometric qualities were

considered are as follows: –

(i)SEM: Any value less than 0.5 is acceptable.

(ii)Validity and Fit : The infit/outfit range is 0.7-1.5,

(iii) Item Difficulty parameter: Ranges from -3 to +3

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CHAPTER FOUR

RESULTS

The results obtained in this study are presented in this chapter. The data are

presented in tabular form and analysed according to the research questions and

hypotheses that formed the thrust of this study.

Research Question One

What are the Standard Errors of Measurement of the 2011 and 2012 practical

physics test items produced by NECO using the partial credit model of IRT

Table One: Standard Errors of Measurement of practical physics tests conducted by NECO for the years 2011 and 2012 using partial credit model

Item SE 2011 SE 2012 1. .10 .16 2. .11 .16 3. .07 .07 4. .09 .12 5. .11 .11 6. .10 .12 7. .10 .10 8. .10 .12 9. .08 .09 10. .09 .09 11. .07 .17 12. .10 .12 13. .13 .16 14. .10 .11 15. .10 .10 16. .09 .13 17. .06 .08 18. .07 .07 19. .06 .06 20. .08 .10 21. .09 .13 22. .10 .10 23. .09 .10 24. .11 .14

Mean .09 .11 S.D .02 .03

Recall that the recommended limit of SEM for a good item is 0.5. Table one

shows the standard errors of measurement of the test items of practical physics tests for

the years 2011 and 2012 based on partial credit model of item response theory. The range

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of standard error for NECO 2011 is from 0.06 for items 17 and 19 to 0.13 for item 13.

The standard errors for the year 2011 NECO practical physics examination is therefore

very low with all the item having standard error far below .5 the recommended limit of

SEM. This is an indication of very high reliability for NECO 2011 practical physics tests.

In the year 2012, practical physics tests had the standard error of measurement

ranging from 0.06 of item 19 to 0.16 of items 1,2 and 13. 100% of the items have low

standard error of measurement. This range of SEM 0.06 – 0.16 indicate very high

reliability as it is very much below 0.5 which is the recommended limit of good item

SEM.

On a general note, the items have the following statistics for practical physics

tests NECO 2011 and NECO 2012.

Year 2011, mean SE = 0.09, SD = 0.02

Year 2012, mean SE = 0.11, SD = 0.03

Therefore, the items of NECO practical physics have very high reliability i.e. very low

SEM with consistently low standard deviation for the years studied.

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Research Question Two:

What are the Standard Errors of Measurement of the 2011 and 2012 practical

physics test items produced by WAEC?

Table Two: Standard Errors of Measurement of practical physics tests produced by WAEC for the years 2011 and 2012.

Item SE 2011 SE 2012 1. .09 .10 2. .08 .10 3. .08 .07 4. .11 .12 5. .12 .13 6. .11 .12 7. .10 .10 8. .10 .11 9. .07 .10 10. .08 .11 11. .06 .07 12. .11 .11 13. .18 .10 14. .11 .10 15. .10 .10 16. .10 .10 17. .07 .07 18. .06 .07 19. .06 .06 20. .09 .10 21. .10 .13 22. .10 .10 23. .10 .10 24. .10 .10

Mean .09 .10 S.D .02 .02

Table two shows the standard error of measurement of the test of practical physics

conducted by WAEC in the year 2011 and 2012 using partial credit model of IRT. The

items of the test for the year 2011 have the standard error of measurement ranging from

.06 of items 11, 18 and 19 to 0.18 of item 13. The implication is that all the items of the

test of 2011 WAEC practical physics has all the construct measurement with low

standard error. Since the range is below S.E of 0.5, the reliability of the test is high.

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For the constructs/items measured by WAEC 2012 practical physics test, the

standard error of measurement ranges from 0.06 of item 19 to 0.13 of items 5 and 21.

Also, the S.E. for WAEC 2012 practical physics is sufficiently low for one to infer that

the reliability of this test is very high.

On a general level, the items have the following statstics for practical physics

WAEC tests.

Year 2011, mean S.E. = .09, S.D = .10

Year 2012, mean S.E = 0.02, S.D .02

It could therefore be said that the items of WAEC practical physics have perfectly high

reliability for the years under studied.

Research Question Three

How valid are the Practical Physics test items produced by NECO for year 2011

and 2012 based on Partial Credit Model of Item Response Theory?

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Table Three: Validity of test items of Practical Physics test conducted by NECO (Fit Statistic) for years 2011 and 2012 based on Partial Credit Model of IRT

Item Infit 2011 Outfit 2011 Infit 2012 Outfit 2012 1. 1.02 0.83 1.03 1.02 2. 1.08 1.00 1.04 1.05 3. 0.99 0.98 1.47 1.44 4. 1.11 1.28 0.85 0.78 5. 0.92 0.90 1.00 1.02 6. 0.81 0.78 1.10 1.12 7. 1.01 1.09 1.12 1.03 8. 0.99 0.90 1.32 1.85 9. 0.93 0.77 1.07 1.16 10. 0.97 0.99 1.01 1.01 11. 0.73 0.70 1.08 1.08 12. 0.82 0.84 0.88 0.83 13. 0.92 0.95 1.23 2.37 14. 0.88 0.83 0.95 0.92 15. 0.96 0.89 0.95 0.84 16. 1.31 1.28 1.02 1.15 17. 1.51 2.49 0.96 0.83 18. 1.50 1.73 0.87 0.93 19. 1.40 1.50 0.87 0.83 20. 1.07 1.09 0.80 0.75 21. 0.99 1.01 0.92 0.93 22. 1.05 1.00 0.85 0.84 23. 0.83 0.78 0.95 0.88 24. 0.91 0.89 0.90 0.78 Mean 1.03 1.06 1.01 1.06 S.D 0.20 0.38 0.15 0.36

Table three shows the result of the fit statistics of the test items for the years under

study using Partial Credit model of IRT. The result showed that the test item for the year

2011 had the infit and out fit statistic ranging from 0.82 to 1.51; and 0.83 to 2.49

respectively. It is only items 17 (that has infit of 1.51 and out fit of 2.49) and 18 (that has

outfit of1.73) beyond the accepted range of 0.7 – 1.5. The fit statistics of the NECO 2011

practical physics apart from item 17 and18 indicate that all the items are perfectly valid.

Since the mean of the infit and outfit are 1.03 and 1.06 respectively since they all fall

within the accepted range of infit/outfit i.e 0.7-1.5.

The test items for NECO 2012 practical physics has infit statistic range of 0.8 to

1.47; and outfit statistics range of 0.78 – 2.37. In the items of NECO 2012, it is only item

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numbers 8 and 13 outfit statistics of 1.85 and 2.37 that are outside the accepted range.

The rest of the NECO 2012 items have their infit and out fit within the acceptable range

of 0.7 – 1.5. The mean of the infit and outfit statistics is 1.01 and 1.06. The spread of the

outfit and infit and their mean indicate highly valid items (since their mean are

sufficiently close to one (1). All the items of NECO 2011, NECO 2012 show high

validity. This is also an expression of undimensionality - a situation where all the items

asses one latent ability, that is psychomotor skills achievement in physics .

Therefore, apart from items 8 and 13 of NECO 2012, item 17 and 18 of NECO

2011, all other items of NECO practical physics are valid and shows undimensionality

Research Question Four

How valid are the practical Physics test items produced by WAEC for year

2011and 2012 based on Partial Credit Model of Item Response Theory?

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Table Four: Validity of test items of practical Physics tests produced by WAEC (fit statistics) for years 2011 and 2012 based on Partial Credit Model of IRT

WAEC 2011 WAEC2012 Item In

fit Out fit

In fit

Out fit

1. 1.14 1.10 1.07 1.01 2. 1.01 0.95 1.02 1.00 3. 0.87 0.85 0.99 1.05 4. 0.93 0.83 0.86 0.82 5. 1.38 1.53 1.45 2.14 6. 1.03 1.02 1.06 1.02 7. 1.16 1.11 1.12 1.09 8. 1.12 1.04 1.12 1.38 9. 1.28 1.12 1.04 1.36 10. 0.97 1.12 1.04 1.36 11. 1.10 1.17 1.20 1.10 12. 0.86 0.87 0.90 0.87 13. 1.49 3.07 0.94 0.97 14. 0.87 0.83 0.98 0.99 15. 0.88 0.77 1.06 0.14 16. 1.10 0.99 1.17 1.41 17. 1.23 2.24 1.08 1.52 18. 0.76 0.57 0.76 0.70 19. 1.16 1.09 0.78 0.82 20. 0.93 0.90 0.78 0.82 21. 0.93 0.90 0.79 0.79 22. 0.76 0.65 0.83 0.77 23. 0.93 0.89 0.90 0.85 24. 0.93 0.85 1.08 1.10 Mean 1.03 1.05 1.00 1.08 S.D 0.18 0.46 0.15 0.31

In Table four, the results of fit statistic of test items for years 2011 and 2012 are

shown for practical physics tests of WAEC using Partial Credit model of IRT.

The results showed that the test items for the year 2011 had the infit and outfit

statistics ranging from 0.76-1.49 and 0.83-3.07 respectively. It is only items 13 and 17

that have out fit of 3.07 and 2.24 respectively beyond the accepted range of 0.7-1.5. The

fit statistic of WAEC 2011 apart from item 13 and17 indicate that all the items are perfect

and valid since they all fall within the range of fit regarded valid. Since the mean of the

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infit and outfit are 1.03 and 1.05 with generally low S.D of 0.18 and .46; 92% of the

items are valid and unidimensional.

For the test items of WAEC 2012 practical physics, the in fit statistics range of

.76 to 1.45 and outfit statistic range of 0.70 to 2.14. It is only items 5 and17 that have the

outfit of 2.14 and 1.52 respectively which are outside the accepted range. The fit statistics

of WAEC 2012 items (apart from the outfit statistic of items 5 and 17) indicate that the

items are valid since they fall into the range of 0.7-1.5. The mean of the infit and outfit

are 1.00 and 1.08 with standard deviations of 0.15 and .31 respectively. The percentage

of the fitting items is 92%. This implies high validity and almost all items are

unidimensional

It could therefore be said that apart from items 13 and 17 in WAEC 2011 and

items 5 and17 of WAEC 2012, all the items of WAEC practical physics are within the

accepted range and therefore valid and sufficiently demonstrates unidimensionality.

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Research Question Five

What are the item parameter estimates (difficulty index, b) of NECO practical

physics questions produced in the years 2011and 2012 using Partial Credit Model of

IRT?

Table Five: Item Difficulty Measures (Difficulty Estimates b) of practical Physics tests produced by NECO for years 2011 and 2012 based on Partial Credit Model of IRT

Item Difficulty Measure 2011

Difficulty Measure 2012

1. -0.89 0.33 2. 0.02 0.35 3. -0.36 -0.91 4. 1.18 -1.06 5. 0.52 -0.75 6. -0.09 -1.01 7. 0.64 0-.58 8. -0.48 1.94 9. -0.18 -1.26 10. -0.79 -1.31 11. 0.21 -0.75 12. -0.85 1.12 13. 0.45 1.63 14. -1.31 -0.27 15. -.59 -0.60 16. 1.47 1.25 17. -1.29 -0.17 18. 1.15 -0.80 19. 0.84 -0.32 20. -0.40 1.35 21. 0.89 0.70 22. 0.01 -0.08 23. -0.31 -0.21 24. 0.18 1.41 Mean 0.00 0.00 S.D 0.76 0.97

Table five shows the item difficulty estimates or difficulty measures of the test

items of practical physics questions conducted by NECO.

For items of NECO 2011 practical physics questions, the results show that items

ranged in difficulty from -1.31 of item 14 (the easiest item) to +1.47 of item 16 (the most

difficult item) for the year 2011 NECO questions. Twelve items were with negative index

and so were fairly easy and twelve items were with indices that are positive-fairly

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difficult. That means 50% of the questions were fairly easy and 50% fairly difficult,

striking a perfect balance at 0.00. That the mean of the difficult index distribution is also

0.00 with low S.D of 0.76.

On the analysis of NECO 2012 questions, the result showed that the range of item

difficulty is -1.26 of item 9 (the easiest item) to 1.94 of item 8 (the most difficult item).

Fifteen items had negative b estimates and so were fairly easy. But eleven b estimates

were positive and were fairly difficult. However, the mean of the difficulty estimate

distribution is 0.00 (SD of 0.77) and that connotes a balance between moderately difficult

and easy items.

Research Question Six

What are the item parameter estimates (difficulty index b) of WAEC practical

physics questions produced in the years 2011and 2012 based on Partial Credit Model of

IRT?

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Table Six: Item difficulty estimates b of practical physics tests produced by WAEC for years 2011 and 2012 based on Partial Credit Model of IRT

Item Difficulty Measure 2011

Difficulty Measure 2012

1. -1.24 -1.56 2. -1.07 -1.39 3. -0.94 0.19 4. 1.13 -0.81 5. 0.92 1.47 6. 0.01 -0.75 7. -0.39 -0.51 8. -0.24 0.77 9. -0.97 -0.57 10. -0.88 -0.57 11. -0.50 -0.69 12. -0.43 1.22 13. -0.98 0.10 14. -0.38 0.16 15. -0.56 0.81 16. 1.17 0.72 17. 0.24 -0.85 18. -0.63 -0.25 19. -0.06 0.63 20. 1.53 -0.11 21. 0.46 1.12 22. 0.16 0.03 23. 0.29 0.34 24. 0.40 0.49

Table six shows the item difficulty estimates b of the practical physics test items

of WAEC for years 2011 and 2012 using Partial Credit model of IRT.

The results show that items for the year 2011 had difficulty estimate that ranges

from -1.24 of item (1) (the easiest item) to 1.53 of item 20 (the most difficult item).

Within this range, fourteen items had negative difficulty estimate which means fourteen

fairly easy items. Also, ten items had positive difficulty estimate which implies fairly

difficult questions. The mean of the estimate distribution is 0.00 which suggest that fairly

easy items balances fairly difficult items. The difficulty indices are desirable since both

the positive and negative range, are close to 0.00 and the standard deviation is low 0.84.

The results of difficulty estimate b for 2012 WAEC items revealed that the range

of difficulty estimate is from -1.56 of item (1) one to 1.47 of item 20. In between this

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range there are eleven items with negative difficulty and 13 items with positive difficulty

moderately easy and difficult items respectively. The mean of 0.00 for the distribution

and S.D of the .80 suggest a fair balance between difficult and moderately easy questions.

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Research Question Seven

What proportion of NECO practical physics test items fit the Partial Credit Model

of IRT?

Table Seven: The Infit, Outfit and their ZSTD of NECO practical Physics questions for years 2011 and 2012 based on Partial Credit Model of IRT

Item 2011 NECO 2012 NECO Infit ZSTD Outfit ZSTD Infit ZSTD Outfit ZSTD 1. 1.02 0.20 0.83 -0.90 1.03 0.30 1.02 0.20 2. 1.08 0.40 1.00 0.10 1.04 0.30 1.05 0.30 3. 0.99 0.00 0.98 -0.10 1.47 2.90 1.44 2.60 4. 1.11 0.60 1.28 1.50 0.85 -1.40 0.78 -1.50 5. 0.92 -0.90 0.90 -1.00 1.00 0.00 1.02 0.20 6. 0.81 -2.60 0.78 -2.50 1.10 1.00 1.12 0.90 7. 1.01 0.20 1.09 1.00 1.12 1.30 1.03 0.20 8. 0.99 0.10 0.90 -0.70 1.32 2.70 1.85 4.30 9. 0.93 -0.40 0.77 -1.30 1.07 0.40 1.16 1.00 10. 0.97 -0.10 0.99 0.00 1.01 0.10 1.01 0.10 11. 0.73 -2.40 0.70 -2.60 1.08 0.70 1.08 0.70 12. 0.82 -1.30 0.84 -1.10 0.88 -1.30 0.83 -1.60 13. 0.92 -0.70 0.95 -0.40 1.23 1.10 2.37 1.90 14. 0.88 -1.6 0.83 -1.90 0.95 -0.60 0.92 -0.80 15. 0.96 -0.50 0.89 -0.70 0.95 -0.60 0.84 -1.00 16. 1.31 3.20 1.28 2.40 1.02 0.20 1.15 0.90 17. 1.51 3.40 2.49 6.40 0.96 -0.20 0.83 -0.80 18. 1.50 2.90 1.73 3.00 0.87 -1.10 0.93 -0.40 19. 1.40 3.30 1.50 4.30 0.87 -1.10 0.83 -1.40 20. 1.07 0.50 1.09 0.60 0.80 -2.40 0.75 -2.40 21. 0.99 0.00 1.01 0.10 0.92 -0.90 -0.93 -0.70 22. 1.05 -0.70 1.00 0.00 0.85 -1.80 0.84 -1.00 23. 0.83 -2.30 0.78 -2.40 0.95 -0.50 0.88 -1.00

24. Mean

0.91 1.03

-0.9 0.10

0.89 1.06

-0.70 0.10

0.88 1.01

-1.50 -0.10

0.82 1.06

-1.70 -0.10

S.D 0.02 1.70 0.38 2.10 0.15 1.30 0.36 0.15

Table seven shows the results of the goodness of fit statistics of the test

items for the years under study using partial credit model of IRT. The results show that

for NECO 2011, two items (17 and 18) had a poor fit. The rest of the item had their fit

within the range that fits PCM. Therefore, 22 items out of 24 had good fit i.e. 91.67% or

0.92 of the items of NECO 2011 items had good fit to the PCM and the mean of the Z

STD = 0.1 for both infit and outfit which conforms to theoretical view for good items.

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Also, for NECO 2012, two items (8 and 13) had a bad fit. So 22 out of 24 items

had a good fit to the PCM. This implies that 91.67% or 0.92 of the items of NECO 2012

items fitted the PCM and the mean of the Z STD = .1 for both infit and outfit goodness of

fit which is sufficiently close to zero and this agrees with theory for good item fit to

PCM.

Research Question Eight

What proportion of WAEC practical Physics test items fit the Partial Credit

Model of IRT?

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Table Eight: The infit, outfit and their ZSTD of WA EC practical Physics Examination for years 2011and 2012 based on PCM of IRT

Item 2011 WAEC 2012 WAEC Infit ZSTD Outfit ZSTD Infit ZSTD Outfit ZSTD 1. 1.14 0.90 1.10 0.60 1.07 0.60 1.01 0.10 2. 1.01 0.10 0.95 -0.30 1.02 0.20 1.00 0.00 3. 0.87 0.90 0.85 -0.90 0.99 -0.10 1.05 0.40 4. 0.93 0.60 0.83 -1.10 0.86 -1.50 0.82 -1.60 5. 1.38 3.30 1.53 3.50 1.45 3.00 2.14 4.80 6. 1.03 -0.40 1.02 0.20 1.06 0.60 1.02 0.30 7. 1.16 1.80 1.11 0.80 1.12 1.20 1.09 0.60 8. 1.12 1.50 1.04 0.30 1.12 1.30 1.38 2.60 9. 1.28 1.70 1.12 0.80 1.04 0.30 1.36 2.00 10. 0.97 -0.20 0.94 -0.40 0.90 -0.50 0.87 -1.00 11. 1.10 0.80 1.17 1.10 1.20 1.60 1.10 0.80 12. 0.86 -1.80 0.87 1.10 0.90 -1.10 0.87 -1.20 13. 1.49 -1.80 3.07 2.60 0.94 -0.80 0.97 -0.30 14. 0.87 -1.60 0.83 -1.60 0.98 -0.20 0.99 -0.10 15. 0.88 -1.30 0.77 -1.20 1.06 0.60 1.42 2.30 16. 1.10 -1.10 0.99 0.00 1.17 1.80 1.41 2.30 17. 1.23 1.40 2.24 1.00 1.08 0.60 1.52 2.30 18. 0.76 -2.00 0.57 -2.70 0.76 -1.80 0.70 -1.90 19. 1.16 1.40 1.09 0.60 0.89 -1.00 0.94 -0.50 20. 0.93 -0.50 0.90 -0.80 0.78 -1.30 0.82 -2.10 21. 0.93 -0.80 0.90 0.70 0.79 -2.40 0.79 -2.40 22. 0.76 -3.30 0.65 -3.20 0.83 -2.40 0.77 -2.50 23. 0.93 -0.80 0.89 -0.80 0.90 -1.30 0.85 -1.40 24. Mean

0.93 1.03

0.80 0.10

0.85 1.05

-1.20 -0.20

1.08 1.00

0.90 -1.00

1.10 1.08

1.00 0.20

S.D 0.18 1.50 0.46 1.40 0.15 1.50 0.31 1.80

Table eight shows results of the goodness of fit statistics of test items for the years

being studied using Partial Credit model of IRT. The results showed that for WAEC 2011

items; items 13 and 17 had the infit and/or out fit outside the good fit range; therefore, 22

out of 24 items had a good fit to PCM. This implies that 91.57% or 0.92 of the items of

WAEC 2011 items have a good fit to PCM of IRT. Also, the mean of ZSTD for the infit

and outfit are 0.1 and 0.2 respectively. These ZSTD means are close to zero and so agrees

with theory that most items have good fit for PCM.

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For WAEC 2012, items, items 5, and 17 had poor fit to PCM mostly due to their

outfit. Therefore WAEC 2012 questions had 22 items with good fit and two items with

poor fit. It means 91.57% or .92 of WAEC 2012 items fits or has a good fit to PCM.

Hypothesis One (H01)

There is no significant difference (P<.05) in the standard error of measuring

(SEM) of practical physics questions conducted by NECO 2011 and NECO 2012.

Table Nine: Standard error of measurement for NECO 2011 and NECO 2012

Variable K Mean 89 S.D Df t-value sig Decision

NECO 2011 24 .09 .02 23 2.50 .02 S

NECO 2012 24 .11 .03 23

α = 0.05, significant

The result on Table 9 shows that the t-value obtained was 2.50 with associated

probability value of 0.02. This probability value is less than the 0.05 level of significance.

Therefore, the null hypothesis which states that there is no significant difference in the

SEM of NECO 2011 and NECO 2012 practical physics questions was rejected. It was

concluded that there is a significant difference in the SEM of NECO 2011 and NECO

2012 practical physics questions.

Hypothesis Two (H02)

There is no significant difference (P<.05) in the standard error of measurement

SEM of practical physics tests conducted by WAEC 2011 and WAEC 2012

Table 10: Standard Error of measurement for WAEC 2011 and WAEC 2012 Variable K Mean 89 S.D df t-value sig Decision

WAEC 2011 24 .10 .03 23 0.59 .56 NS

WAEC 2012 24 .10 .02 23

α = 0.05, Not significant

The result on Table 10 revealed that the t-value obtained was 0.59 with associated

probability value of 0.56. This probability value is greater than the 0.05 level of

significance. Therefore, the researcher fails to reject the null hypothesis which states that

there is no significant difference in the SEM of WAEC 2011 and WAEC 2012 practical

physics questions. It was therefore concluded that there was no significant difference in

the SEM of WAEC 2011 and WAEC 2012 Practical physics tests

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Hypothesis Three (H03)

There is no significant difference (P<.05) in the SEM of practical physics tests

conducted by NECO and WAEC 2011-2012.

Table 11: Standard error of measurement for NECO 2011 and WAEC 2011 Variabe K Mean 89 S.D Df t-value sig Decision

NECO 2011 24 .09 .02 23 0.54 .59 NS

WAEC 2012 24 .10 .02 23

α = 0.05, Not Significant

In Table 11 the result showed that the t-value obtained was 0.54 with associated

probability of 0.59 . This probability value is greater than the level of significance 0.05.

Therefore, the researcher fails to reject Ho. That means that there is no significant

difference in the S.E.M of NECO 2011 and WAEC 2011 practical physics questions.

Table 12: Standard error of measurement for NECO 2012 and WAEC 2012

Variable K Mean 89 S.D Df t-value sig Decision

NECO 2012 24 .11 .03 23 -1.47 .16 NS

WAEC 2012 24 .10 .02 23

x = 0.05 Significant

The result in Table 12 showed that the t-value obtained was -1.47 with associated

probability of 0.16. This probability value is greater than the 0.05 level of significance.

Therefore, we fail to reject Ho. That implies that there is no significant difference in the

S.E.M of NECO 2012 and WAEC 2012 practical physics questions.

Hypothesis Four (H04)

There is no significant difference in the validity (fit statistics) of NECO 2011-

2012 practical physics questions

Table 13: Fit statistic (for partial credit model) for NECO 2011 and NECO 2012. ( Appendix AM)

Variable N Mean 89 S.D df t-value sig Decision

NECO 2011 50 18.78 12.40 49 1.11 .27 NS

NECO 2012 50 21.25 9.68 49

α = .05, Significant

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The result on Table 13 revealed that the t-value obtained was 1.11 with associated

probability of 0.27. This probability value is less than the level of significance 0.05.

Therefore we fail to reject the null hypothesis Ho. This implies that there is no significant

difference in the fit statistic (validity) of NECO 2011 and NECO 2012 practical physics

questions.

Hypothesis Five (H05)

There is no significant difference in the validity (fit statistics) of WAEC practical

physics questions

Table 14: Fit statistics for PCM for WAEC 2011 and WAEC 2012 (Appendix AN) Variable N Mean 89 S.D df t-value sig Decision

WAEC 2011 50 21.33 20.57 49 -.96 .34 NS

WAEC 2012 50 17.94 14.36 49


On Table 14 are the results of t test for the validity (fit statistic) of practical

physics items in questions conducted by WAEC in 2011 and 2012 based on PCM of IRT.

The result showed that the t-value obtained was .96 with associated with

associated probability of 0.34. This probability value is greater than the level of

confidence 0.05. The researcher therefore, fails to rejects the Ho. This means that there is

no significant difference between the validity (fit statistics) of practical physics items of

questions conducted by WAEC 2011 and WAEC2012.

Hypothesis Six (H06)

There is no significant difference (P<.05) in the validity (fit statistic) of practical

physics questions conducted by NECO 2011 and WAEC 2011.

Table 15: Validity (fit statistic) for PCM of NECO 2011 and WAEC 2011 Appendix AO)

Variable N Mean 89 S.D df t-value sig Decision

NECO2011 50 18.78 12.40 49 .75 .46 NS

WAEC 2011 50 21.32 20.57 49

α = .05,Not Significant

Table 15 is the result of fit statistic (validity) of practical physics items in

questions conducted by WAEC 2011 and NECO 2011 based on PCM.

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The result revealed that the t-value of 0.75 was obtained with associated

probability of 0.46. This probability value is greater than the level of confidence 0.05. We

therefore fail to reject Ho. This means that there is no significant difference between the

validity (fit statistic) of practical physics items of tests conducted in WAEC 2011 and

NECO 2011.

Table 16: Validity (fit statistic) for PCM of NECO 2012 and WAEC 2012 (Appendix AP) Variable N Mean 89 S.D df t-value sig Decision

NECO 2012 50 21.26 9.68 49 1.36 .18 NS

WAEC 2012 50 17.94 14.35 49


Table 16 shows the result of the t test for the validity (fit statistic) for practical

physics items in questions conducted by NECO 2012 and WAEC 2012 based on PCM of

IRT.

This result revealed that the value of significance 0.18 is greater than the level of

significance 0.05. Therefore Ho is upheld (fail to reject). This implies that there is no

significant difference between the validity (fit statistic) of practical physics items of tests

conducted in NECO 2012 and WAEC 2012.

Hypothesis Seven (H07)

There is no significant difference in the difficulty parameter estimates (b) of

NECO practical physics tests.

Table 17: Item Parameter estimates (difficulty) b for NECO 2011 and NECO 2012

Variable K Mean 89 S.D df t-value sig Decision

NECO 2011 24 .00 .78 23 0.003 0.997 NS

NECO 2012 24 .00 .99 23

α = 0.05,Not Significant

The result from Table 17 revealed that the t-value obtained is 0.003 with

associated probability of 0.997 .This probability value is greater than the significance

level of (0.05). Therefore, we fail to reject the Null hypothesis. There is therefore no

significant difference in the difficulty estimates of NECO 2011 and NECO 2012 practical

physics tests using PCM of IRT.

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Hypothesis Eight (H08)

There is no significant difference (P<.05) in the difficulty parameter estimates (b)

of WAEC 2011-2012 practical physics tests.

Table 18: WAEC 2011 and WAEC 2012 Item difficulty parameter estimates for practical physics questions.

Variable K 89 S.D df t-value sig Decision

WAEC 2011 24 -.12 .77 23 .54 .59 NS

WAEC 2012 24 .00 .81 23

α = .05,Not Significant

From Table 18, it can be seen that the t-value of .54 had an associated probability

of 0.59. This probability value is greater than the significance level 0.05. The researcher

therefore fails to reject the Ho. This implies that there is no significant difference in the

difficulty estimates of WAEC 2011 and WAEC 2012 practical physics tests using PCM

of IRT.

Hypothesis Nine (H09)

There is no significant difference (P<.05) in the difficulty estimates of practical

physics tests conducted by NECO 2011 and WAEC 2011.

Table 19: NECO 2011 and WAEC 2011 item difficulty estimates for practical physics tests.


NECO 2011 24 .00 .78 23 -.56 .58 NS

WAEC 2011 24 -.12 .77 23

α = .05, Not Significant

The result in Table 19 shows that the t-value of -.56was obtained with associated

probability of 0.58. This probability value is greater than the level of significance 0.05.

And so the researcher fails to reject Ho. This implies that there is no significant difference

in the difficulty parameters estimates of NECO 2011 and WAEC 2011 practical physics

questions.

88

Table 20: NECO 2012 and WAEC 2012. Item difficulty estimates for practical physics questions.


NECO 2012 24 .03 1.01 23 .13 0.90 NS

WAEC 2012 24 00 .82 23

α = 0.05, Not Significant

The results of the Table 20 indicate that the t-value obtained was .13 with

associated probability of 0.90. This probability value is greater than the level of

significance 0.05. Therefore, we fail to reject the Null hypothesis and by implication,

there is no significant difference in the difficulty parameter estimates of NECO 2012 and

WAEC 2012.

Summary of the Findings of the Study

Based on the data analysis in this study, the findings are summarized as follows:

1. The items of NECO practical physics tests has very low SEM and consequently

reliable, based on Partial Credit Model.

2. Also, based on the PCM, the items of WAEC practical physics tests has low SEM

and as a result are highly reliable.

3. The validity of items of the practical physics tests conducted by NECO is

discovered in this study to be sufficiently high.

4. The validity of items of WAEC practical physics tests using partial credit model

is very high

5. The items of NECO practical physics tests had difficulty parameters estimate

within the acceptable range that indicate that the items are of moderate difficulty

6. Item difficulty parameter estimates of WAEC practical physics tests were also

estimated in this model within the range that is acceptable and which showed that

item difficulty indices are of moderate difficulty.

7. Each of the two NECO tests studied had the item proportion fit to partial credit

model at 0.92.

8. WAEC 2011 and WAEC 2012 practical physics items had 0.92 each as their item

proportion fit to partial credit model.

9. There is significant difference in the standard error of measurement in the

practical physics tests conducted by NECO

89

10. There is no significant difference in the standard error of measurement in the

practical physics tests conducted by WAEC

11. (i) There is no significant difference in the SEM of NECO 2011 and WAEC 2011

conducted practical physics tests (ii) There is no significant difference in the SEM

of NECO 2012 and WAEC 2012 practical physics tests.

12. There is no significant difference in the validities of practical physics tests

conducted by NECO


conducted by WAEC.

14. (i) There is no significant difference in the validities of NECO 2011 and WAEC

2011 conducted practical physics tests. (ii) There is no significant difference in

the validities of NECO 2012 and WAEC 2012 conducted practical physics tests.

15. There is no significant difference between the difficulty indices of NECO

practical physics tests.

16. There is no significant difference between the difficulty indices of WAEC


17. (i) There is no significant difference between the difficulty indices of NECO 2011

and WAEC 2011 practical physics tests. (ii) There is no significant difference

between the difficulty indices of NECO 2012 and WAEC 2012 practical physics

tests.

90

CHAPTER FIVE

DISCUSSION, CONCLUSION, AND SUMMARY

This chapter discusses the findings of the study, conclusions reached from the

findings, limitations of the study, recommendation, suggestions for further studies and

summary of the study

Discussion of the Findings

. The discussions on the findings were organized under the following sub-headings,

− Standard error of measurements (S.E.M),

− Validity (fit statistics),

− item parameter or the difficulty estimates,

− Proportion of item fit to PCM and

− Stability of SEM, validity and item difficulty estimates in the hypotheses tested.

The standard error of measurements (SEM)

The aim of research questions one and two was to estimate the standard error of

measurement SEM for items of practical physics test of NECO 2011, NECO 2012,

WAEC 2011 and WAEC 2012 based on partial credit model of item response theory.

The SEM of NECO tests ranges from 0.06 - 0.16 and that of WAEC tests ranges

from 0.06 - 0.18. Baumgartner (2002) stated that in the response analysis every estimate

of item difficulty measure comes with its standard error, that the allowed limit of

standard error for test is 0.5 and the smaller the standard error, the better the test item and

the higher the reliability.

Tables one to four showed the standard error of physics practical items based on

the partial credit model. Table one reveals that 100% of the items have their SEM

between 0.06 – 0.13 for NECO 2011. Table two revealed that the SEM for all the item

between 0.06 – 0.16. For NECO 2012 practical test. The items SEM have their standard

90

91

deviations as 0.02 and 0.03; mean standard error of 0.09 and 0.11 respectively for NECO

2011 and NECO 2012 practical physics items.

Based on partial credit model therefore the implications for NECO 2011 and

NECO 2012 practical physics items are as follows (i) the S.E.M are very low (far below

the limit of 0.5), which implies high reliability for the two NECO practical tests. (ii) The

standard deviations were very low implying low variability for the SEM of the two

NECO tests. (iii) Their mean standard errors when compared with the limit of standard

error of 0.5 means that the tests are of high quality required for a good practice in test

construction.

Table three and four revealed the SEM of WAEC 2011 and WAEC 2012.They

had ranges 0.06 – 0.18 and 0.07 – 0.13 respectively with standard deviations of 0.2 for

both. The mean of their SEM are 0.09 and 0.10 respectively for WAEC 2011 and WAEC

2012 items.00

Therefore based on partial credit model the implication for WAEC 2011 and

WAEC 2012 practical physics items are as follows. (i) Since the SEM are very low

compared to the maximum limit allowed in literature (0.5), the items of the two WAEC

practical test are of high reliability. (ii) The standard deviations of their SEM were very

low which connotes low variability for the SEM of the two WAEC tests. (iii) Their mean

standard errors of 0.5 depicts that the test items are of high quality necessary for good test

construction.

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Validity

The essence of research questions three and four was to establish the validity of

test items of practical physics tests conducted by NECO and WAEC in the years 2011

and 2012 based on partial credit model.

In item response theory, validity connotes a fit to the model; that item

discrimination are uniform and substantial and that there is no error in scoring (Nkpone,

2001). According to Bryce (1981) an item will be valid or of good fit to the model if it

had fit statistics of 1.5 and below. A large positive fit indicate a poor fit, but fit statistic

nearer one (1) indicate a better fit. Specifically, for PCM fit Curtis and Boman (2007)

Lian and Idris (2006), Bond and Fox (2001) Opsomer et al (2002) noted that infit and

out fit statistics should be between 0.7 and 1.5 for items validity or fitness to be

acceptable for moderately rigorous assessment purposes and for such items to be

considered unidimensional.

In this study the items examined for NECO 2011 showed that the infit/out fit

statistics range between 0.70 and 1.73. For NECO 2012 the infit/outfit statistic range

between 0.78 and 2.37. On the whole NECO 2011 had two items and NECO 2012 had

two items with either infit and/or outfit outside the accepted infit /outfit range of 0.7-1.5.

Also the mean infit /outfit range between 1.01-1.06 for the two NECO tests studied were

observed.

The implications of this is that for 24 items of NECO 2011, two items had their

validity or fit statistic within the range that does not portray unidimensionality. The 24

items of NECO 2012 had two item fit statistics within the range that does not show

unidmensionality. Therefore PCM showed that only three items of NECO 2011 and two

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items of NECO 2012 test are not valid and therefore not unidmensional. Also that the

mean of the infit/outfit ranged between 1.01 to 1.06 implies high validity for the two

years understudied in NECO test since according to Bryce (1981) a fit statistic near one

(1) indicate a letter fit. Since the mean of the fit statistics for the two NECO tests are

sufficiently close to one ie (1.01 – 1.06). Then the mean results if the fit statistic

sufficiently demonstrates a good fit and undimensionality.

The items WAEC 2001 studies showed that the infit /outfit statistics range

between 0.76 to 3.07. For WAEC 2012 the infit /outfit statistics range between 0.76 –

2.14. In all WAEC 2011 had two items and NECO 2012 had two items with either infit

and/or outfit outside the accepted infit/outfit range of 0.7-1.5. More over their mean for

infit outfit range between 1.00 – 1.08 for the two WAEC tests studied were obtained.

This implies that for the 24 items of WAEC 2011, two items had their validity or

fit statistic with the range that does not depict undimensionality. The 24 items of WAEC

2012 had two items fit statistics within the range that does not show unidmensionality.

Hence PCM showed that two items each of WAEC 2011 and WAEC 2012 are not valid

and therefore not undimensional. Also that the mean of the infit/outfit range is between

1.00 and 1.08 connotes high validity for the WAEC 2011 and WAEC 2012 practical test.

This is because the mean fit statistic being close to one indicate a better fit (Bryce 1981)

On the whole therefore two items each for NECO 2011, NECO 2012, WAEC

2011 and WAEC 2012 were not valid, which implies that each of these test have 22 items

out of 24 with fit statistics that fit PCM. NECO 2011 had two items with bad fit and

twenty two with good fit. Therefore a significant percentage of both NECO and WAEC

practical tests are highly valid and thus demonstrate imidimensionality

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Item parameter (Difficulty) Estimates

The intent of research questions five and six was to estimate the items difficulty

of practical physics tests conducted by NECO and WAEC in years 2011 and 2012 using

PCM.

In items response theory the number of examinees responding correctly to an item

determines the estimates of the difficulty index ( b) of such item. Theoretically, b spans

- ∞ to +∞, but in practice the usual range of b is – 3 to +3, and values outside this usual

range are rare to come by (Baker, 2001). While negative estimates of b implies easy

items, positive estimates of b progressively imply difficult items.

In the table of item difficulty (b) NECO 2011 had the b range of -1.13 to +1.47.

From the Table, twelve (12) items had negative index and twelve items had positive

index. The implication is that 50% of the items were fairly easy and 50% of the items

were relatively difficult.

The NECO 2012 test had the b range of – 1.26 to 1.94. Even though the b range

of the items are within good range of items difficulty, 15 items had negative values. This

means that there were more of easy items in NECO 2012 practical test items than that of

NECO 2011. Generally the item difficulty of NECO practical tests are good for

moderately rigorous examination purposes

For WAEC 2011, the range of item difficulty was -1.24 to 1.53. In all thirteen

items had negative difficulty which implied that those thirteen items were fairly easy and

the remaining eleven items were fairly difficult. The item difficulty are within he

practical range for item difficulty of -3 to +3. The difficulty estimate of WAEC 2011

items are desirable hence both positive and negative indices of b range are close to zero

with low standard deviation of 0.84. And in items of WAEC 2012, the range of item

difficulty is -1.56 to 1.47. Eleven items had negative b estimates and thirteen have

95

positive b estimates. The spread of item b is clustered around zero for all the item. This

indicates that there is a fair balance for fairly easy and moderately difficult items.

Despite the fact that results from both WAEC 2011 and WAEC 2012 items have

about half of the items with negative difficulty, the item for both years, the item b are

relatively desirable since they are within the null point of the practical difficulty range.

Proportion of Item fit to PCM

The research questions seven and eight were aimed at investigating the proportion

of NECO and WAEC practical physics item that has a good fit to the PCM.

In theory, we are made to understand that items with infit and outfit that range

between 0.7 to 1.5 with expected mean = 1 and ZSTD of mean = O are of good fit to

PCM.

In NECO 2011, only two items had a poor fit to the model. Hence, 22 out of 24

item had a good fit to PCM. Therefore, 91.67% or .92 of the items of NECO 2011

practical physics examination had a good fit to partial credit model. Also, in NECO 2012,

two items had a poor fit to the model. So 22 out of 24 items had their infit and outfit

within the limits of good fit. That means that 91.67% or 0.92 of the items of NECO 2012

practical physics had good fit to PCM. The expected mean of 1.00 for infit and outfit for

both years range between 1.01 and 1.08. This means that very high proportion of the

items fit the PCM.

WAEC 2011 had two items with infit and /or outfit outside the good fit range for

PCM. It then means that 20 out of 24 items had a good fit to PCM. This implies that

91.57% or 0.92 of the items of WAEC 2011 had a good fit to the PCM. Finally, in

WAEC 2012, also two items had a bad fit, mostly due to their outfit. It therefore means

that 22 out of 24 items had a good fit to PCM. 91.57% or 0.92 of items of WAEC 2012

practical physics items therefore has a good fit to PCM.

While WAEC 2011 and WAEC 2012 items had 0.92 each of proportion of their

items fit PCM; NECO 2011 and NECO 2012 items had 0.92 each as well. This therefore

connotes that on comparative basis, NECO practical physics items have equal proportion

of their items fit PCM with WAEC practical physics items.

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Stability of S.E.M. in Hypotheses tested.

Hypothesis one compared the standard error of measurement SEM of NECO 2011

and NECO 2012 practical physics item based on the partial credit model. The result of

the t-test of difference indicated that there is a significant difference in the SEM of

NECO 2011 and NECO 2012 practical physics items conducted by NECO for the two

different years. This significant difference was caused by the difference in the SEM range

of NECO 2011 – (.06 to 0.13) and NECO 2012 – (0.06 – 0.16).

Hypothesis two also compared the standard error of measurement of WAEC 2011

and WAEC 2012 practical physics items using PCM. The test of difference indicated that

there is no significant difference in the SEM of WAEC 2011 and WAEC 2012 practical

physics examination conducted by WAEC for the two years studied. This indication of no

significant difference expresses that there is relative stability in the SEM / reliability of

examinations conducted by WAEC.

Hypothesis three explored whether there is any significant difference in the SEM

of practical physics exam conducted by NECO 2011 and WAEC 2011; NECO 2012 and

WAEC 2012 using PCM. The result indicated that there is no significant different in the

SEM of NECO 2011 and WAEC 2011 conducted practical physics examination. This

result show that reliability/SEM of WAEC and NECO is closely related. It indicated that

there is no significant different in the reliability / SEM of WAEC and NECO at least for

some years.

For the test of difference of NECO 2012 and WAEC 2012, the result of t-test

indicated that there is no significant difference in the SEM of NECO 2012 and WAEC

2012 practical physics examination.

Stability of Fit Statistics (Validity) in the Hypotheses tested.

The fourth hypothesis attempted to verify whether the difference in the validity or

fit statistics of NECO 2011 and NECO 2012 practical physics examina3tion is

significant. T test carried out on the fit statistics of NECO 2011 and NECO 2012 results

of the practical physics items showed that there was no significant difference in the fit

statistics of the items of the two examinations.

The fifth hypothesis aimed at testing whether there is significant difference in the

fit statistics of WAEC 2011 and WAEC 2012 practical physics examination. Based on

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partial credit model, there was no significant difference in validity / fit statistic of

practical physics examination conducted by WAEC for the two years under study. This

implies stability in the quality of WAEC examinations across the years.

Sixth hypothesis verified if there is significant difference in the fit statistics of (i)

NECO 2011 and WAEC 2011; (ii) NECO 2012 and WAEC 2012 practical physics items.

The test of difference in fit statistics conducted for NECO 2011 and WAEC 2011

revealed that there are no significant difference in the validity of NECO 2011 and WAEC

2011; NECO 2012 and WAEC 2012 practical physics examination. This result is also

consistent with hypothesis 3(a and b) that indicated no significant difference in the SEM

of WAEC 2011 and NECO 2011; WAEC 2012 and NECO 2012. All these are expression

of near equivalence of validity of WAEC and NECO examinations across the years.

Stability of the Difficulty parameter estimates

Hypothesis seven compared the item parameter (difficulty) (b) estimates of

NECO 2011 and NECO 2012. The difficulty estimates for NECO 2011 and NECO 2012

were subjected to t test. This revealed that there was no significant difference between the

difficulty estimates of NECO 2011 and NECO 2012 practical physics items using PCM.

This indicates that there is stability in the difficulty estimates of NECO examination in

practical physics.

The purpose of hypothesis eight was to compare the item difficulty estimates of

WAEC 2011 and WAEC 2012. The difficulty estimates for WAEC 2011 and WAEC

2012 were subjected to t-test analysis and it was found that there is no significant

difference between the difficulty estimates of WAEC 2011 and WAEC 2012 practical

physics items. This is an evidence that WAEC practical physics examinations have some

steady measure of difficulty estimates in their year to year examinations.

Finally, hypothesis nine attempted comparison of (i) NECO 2011 and WAEC

2011, (ii) NECO 2012 and WAEC 2012 item difficulty estimates of their practical

physics questions. The items of these paired tests and their item difficulties were

accordingly subjected to t-test of significance. It was discovered that there is no

significant difference in the item difficulty estimates of (i) WAEC 2012 and NECO 2011;

(ii) NECO 2012 and WAEC 2012 at α = 0.5. This simply implies that the difficulty index

for the NECO and WAEC conducted practical physics examinations is more or less the

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same. Since the results showed consistently that there is no significant difference in the

NECO to NECO; WAEC to WAEC and WAEC to NECO (twice), item difficulty

estimate. It then implies that the difficulty indices of both examinations are very

consistent and significantly stable.

Conclusion Reached from the Findings of the Study

Based on the data analysis in this study the following conclusions have been

drawn from the study.

The NECO practical physics tests analyzed in this study had the limits of SEM

from 0.06 to 0.16. This being far below the recommended limit of SEM (0.5) is an

indication that the NECO physics tests has very high reliability. More over the WAEC

practical physics test had their limits of SEM from 0.06 to 0.18. This as well is

sufficiently low SEM that defines high reliability for the practical physics tests of

WAEC.

Item validities of NECO practical physics tests demonstrate high proportion of

unidimensionalty. Both years of 2011 and 2012 NECO practical physics tests showed

that 0.92 proportion of the items had good fit to the PCM and so since both had 92% of

item statistics within the range that showed unidimensionality, it implies that the

validities for NECO practical physics tests are high. For WAEC 2011 and WAEC 2012

their fit statistics which showed 0.92 each for proportion of good fit to PCM, also

indicated that high proportion were unidimensional. To this extent therefore the WAEC

practical physics test are highly valid as well. But on comparative bases, the NEECO

practical physics tests are of exactly eqaul validity with that of WAEC for both years

under consideration.

The items of NECO practical physics tests had difficulty parameter estimates

within the acceptable range that indicate that the items are of moderate difficulty (- 1.31

to 1.94). For WAEC practical physics tests the item difficulty estimate (-1.56 to 1.53) are

within the range that typifies moderately difficult items. The four parts of the instrument

(WAEC 2011, WAEC 2012, NECO 2011 and NECO 2012 practical physics tests) had

nearly equal difficulty estimates of negative and positive values. This implies that for

both WAEC and NECO tests, easy items balances difficult items. Therefore both WAEC

and NECO tests studied had moderate item difficulty estimates.

99

For the hypothesis tested in the SEM, since NECO 2011- NECO 2012; showed

significant difference in their SEM it implies that there is a measure of instability in

NECO – NECO tests SEM and were of values that are not very related. Therefore there is

instability in SEM of NECO 2011-NECO 2012. Also SEM of ; NECO 2012 and WAEC

2012; WAEC 2011 – WAEC 2012; NECO 2011 – WAEC 2011 showed no significant

difference. Therefore there is stability in the SEM of WAEC practical tests for their SEM

and the SEM of WAEC 2011 and NECO 2011; NECO 2012 and WAEC 2012 are closely

related.

The hypotheses tested in fit statistics showed that there is stability in the validities

of NECO -NECO, WAEC –WAEC, and NECO-WAEC, Therefore the validity of NECO

and WAEC practical physics tests had consistent and nearly equal validities. Since all

NECO-WAEC showed no significant difference in their fit statistics, this implies that the

validities of two examination bodies were very similar across the years 2011 and 2012.

The difficultly estimates of both WAEC and NECO practical physics item

demonstrated consistently that there is no significant difference within NECO, WAEC

and NECO-WAEC in both years. Therefore this study found out that there is stability in

the difficulty estimates of the test conducted by both examination bodies. Also on

comparative bases, the item difficulties of the examination bodies are similar and that

was why there was no significant difference in the estimates across the exam bodies and

across the years. Therefore the difficulty estimates of WAEC and NECO examinations

are consistent and comparable.

Implications of the Study

The findings of this study revealed very close ties in the quality of the

examinations set by WAEC and NECO. The striking similarities on the SEM, item

difficulties range validity and the proportion of model fit of items to PCM, all indicate the

closeness in the qualities of exam set by the two bodies. Therefore, the society now, by

this study should have equal confidence in the examinations set by these two bodies.

The possibility of analysis of quality of a test through the invariant properties of

SEM, item difficulties, fit statistics etc through item response theory format has

implication for test analysis and developers in Africa. This has not been the case in Africa

100

and so this study encourages test developers in Africa to start making effectively the use

of IRT format for test development and analysis.

Examinees behaviour, strength and weaknesses in testing conditions could be

adequately explained using the findings of this nature. The counselor and test analysts

can use the various psychometric characteristics possible in partial credit model studies to

assess the examinee performance especially as it concern each item.

The study can attribute some failure of the examinee to some undesirable

psychometric properties of some items. Such undesirable property of an item that can

lead to massive failure in such items that have very high item difficulty estimate, item

misfit etc can be adequately ascertained for explanation.

The partial credit model studies could collapse the score categories to only two

categories without making it necessarily dichotomous. This increases the precision of the

model more than that of dichotomous model in IRT. The implication for this study is that

there was very precise item parameter estimates and other psychometric qualities

estimated on this study.

Limitations of the Study

1. This study is limited to one parameter PCM. This studies only b and no study of

item discrimination was carried out.

2. Relevant literatures to this study were obtained from foreign studies. This is

because item response theory researches are not yet common in Africa. Therefore

the peculiarities of partial credit model to African sub region (if any) could not be

ascertained since IRT researches are relatively new in this region.

3. Also, many relevant journals in the internet are to be exorbitantly subscribed to

before gaining assess to them. Therefore, the relevant literature consulted were

only the ones that the researcher could subscribe to and the ones that are of free

assess.

4. Softwares for the analysis of item response theory researches are not common in

Nigeria. The analysis of this study was done only in one of the few analysis

centres available in Nigeria.

5. It was impossible to retrieve the psychometric properties of the examination

bodies (WAEC and NECO) because they are classified information. Otherwise

101

this study would have compared the psychometric values obtained to that

obtained by the exam bodies.

Recommendations

The following general recommendations were made based on the results of this

study.

1. Psychometricians, test developers, teachers and other persons involved in any kind of

measurement should be trained in item response theory framework. This will enable

the advantage of the framework and its overall essence to be appreciated and

popularized in our local situation.

2. The government, ministries of education and high profile stakeholders in education

should procure the various IRT analytical software and sponsor the training of

individuals to learn the analysis using IRT framework. This way, the framework

would have been popularized and the interpretation of the results and usage of the

framework will thus be demystified.

3. Given the obvious advantages of IRT over other popular measurement framework,

the government should encourage our examination bodies such as WAEC, NECO,

NABTEB, NTI etc to adopt this measurement framework. This will ultimately

surmount the measurement problems we frequently encounter in Nigeria. Such

measurement problem as test score equating has nearly gone into extinction in the

foreign countries that have adopted the IRT measurement framework. IRT framework

can also do the magic for us in Nigeria.

4. Teachers in institutions of higher learning in Nigeria should be oriented on the usage

of IRT for psychometric analysis of their examinations. This way the quality of our

test items in such institution will get more refined and measurement problems

associated with the presently used framework will get obliterated.

Suggestions for Further Studies

This study – Psychometric Analysis of WAEC and NECO practical physics

examinations using Partial Credit Model – has the following suggested areas for further

research.

1. Items of physics theory (paper 3) has to be investigated using partial credit model

for the exam bodies such as WAEC, NECO etc.

102

2. Items of other subjects that are polytomously scored should be investigated using

the partial credit model.

3. The ability estimates of examinees in partial credit analyses should be studied.

4. Psychometric analysis of WAEC, NECO, NABTEB etc of practical physics items

other than those done in this study could be investigated.

5. This study can as well be subjected to generalized partial credit model analyses

6. Every other suggestion for further research can as well be subjected to

Generalized Partial Credit Model analyses.

Summary of the Study

West African Examination Council and National Examination Council are two

foremost examination bodies in secondary schools in Nigeria. In part, their responsibility

is assessing the psychomotor aspects of objectives achieved by students while undergoing

through the secondary school science curriculum. As ultimate test developer and agency

responsible for testing the psychomotor or practical aspect of secondary school sciences,

it is required that they employ best practices in practical test psychometric analysis. This

is by way of jettisoning of psychometric analysis saddled with frequent measurement

problems. The modern measurement framework that would reduce measurement

problems to the barest minimum is needed for psychometric analyses of items of these

vital and ultimate examining bodies especially in sciences that are needed to move the

nation to technological realm.

This study – the psychometric analysis of WAEC and NECO practical physics

examinations using Partial Credit Model –was purposed towards analyzing the items of

practical physics examination using the item response theory model. But because the

items of the practical physics examination are polytomously scored, the study had to use

the modern measurement theory IRT model for polytomously scored items -The Partial

Credit Model. This analysed various psychometric properties of practical physics

examination of WAEC and NECO for years 2011 and 2012 (internal) examinations.

In an attempt to sharpen the focus and have a guided direction for this study, a lot

of literature was reviewed on IRT generally and on work done using partial credit

analysis. This way the psychometric qualities such as SEM, item difficulty, fit analyses

etc possible with IRT researches were noted and the method used in their analysis

103

comparison and testing significance related to them were also noted. The works that have

been done using partial credit model were all foreign studies such as Lian and Idris

(2006), Opsomer et al (2002) etc. The studies that utilized item response theory format in

Nigeria used one or more of dichotomous model of IRT e.g. Obinne (2008), Nkpone

(2001), Akindele (2004). Nkpone (2001) happened to have done IRT study in physics but

then he used the dichotomously scored model of IRT 1,2,3 parameter logistic model in

development and standardization of physics achievement test. No study all over both

foreign and local has utilized Partial Credit Model for analysis in polytomously scored

item in physics. This made this study to be considered worthwhile.

To help in carrying out the study on psychometric analysis of practical physics of

WAEC and NECO items, eight research questions and nine hypotheses guided the study.

The research questions verified the Standard Error of Measurement, Validity, Item

Difficulty Parameter and item proportion fit to PCM for the WAEC and NECO questions

studied. While the hypotheses tested whether is any significant difference between the

psychometric qualities of WAEC- WAEC; NECO-NECO; and NECO-WAEC questions

within the years studied.

The area of the study was Enugu State and the sample of the was six hundred and

sixty eight SS III students selected through multistage sampling procedure across three

education zones of Enugu State. The sampling technique used was random samplings,

first of education zones, of local government and then proportionate random sampling of

schools from each local government in the selected education zones. The instruments

used for the study are 2011 and 2012 practical physics questions of WAEC (PPQW) (1

and 2) and 2011 and 2012 practical physics questions of NECO (PPQN) (1 and 2). The

data collected in this study were analysed using maximum likelihood estimation

procedure of WINSTEP Computer Programme of PCM analysis and the hypotheses were

tested using SPSS computer programme.

The results of the study are as follows:

1. Based on Partial Credit model, the items of NECO practical physics tests has very

low SEM and consequently reliable.

2. Also, based on the PCM, the items of WAEC practical physics tests has low SEM

and as a result are highly reliable.

104

3. The validity of items of the practical physics tests conducted by NECO is

discovered in this study to be sufficiently high.

4. The validity of items of WAEC practical physics tests using partial credit model

is very high

5. The items of NECO practical physics tests had difficulty parameters estimate

within the acceptable range that indicate that the items are of moderate difficulty

6. Item difficulty parameter estimates of WAEC practical physics tests were also

estimated in this model within the range that is acceptable and which showed that

item difficulty indices are of moderate difficulty.

7. Each of the two NECO tests studied had the item proportion fit to partial credit

model at 0.92.

8. WAEC 2011 and WAEC 2012 practical physics items had 0.92 each (as well) as

their item proportion fit to partial credit model.

9. There is significant difference in the standard error of measurement in the

practical physics tests conducted by NECO

10. There is no significant difference in the standard error of measurement in the

practical physics tests conducted by WAEC

11. (i) There is no significant difference in the SEM of NECO 2011 and WAEC 2011

conducted practical physics tests (ii) There is no significant difference in the SEM

of NECO 2012 and WAEC 2012 practical physics tests.


conducted by NECO


conducted by WAEC.

14. (i) There is no significant difference in the validities of NECO 2011 and WAEC

2011 conducted practical physics tests. (ii) There is no significant difference in

the validities of NECO 2012 and WAEC 2012 conducted practical physics tests.

15. There is no significant difference between the difficulty indices of NECO


16. There is no significant difference between the difficulty indices of WAEC


105

17. (i) There is no significant difference between the difficulty indices

of NECO 2011 and WAEC 2011 practical physics tests. (ii) There is no

significant difference between the difficulty indices of NECO 2012 and WAEC

2012 practical physics tests.

In summary, the following were inferred from results of the study:

(i) The items of WAEC and NECO practical physics examination both have very

low SEM and high reliability.

(ii) The items of both exam bodies are of high validity as indicated by fit statistics

(iii) The item difficulty estimates of WAEC and NECO practical physics both

consistently demonstrated moderate difficulty

(iv) High proportion of both WAEC and NECO practical physics items had good

fit to PCM.

A close look at the result of the hypothesis tested indicated that NECO item had

significant difference between their various years examination in SEM. The item

difficulties and fit statistics of NECO exams had no significant difference. Exactly, the

same results apply to WAEC items, fit statistics and item difficulty as it applies to

NECO. On comparison of NECO; WAEC; NECO - WAEC items consistently showed no

significant difference in the SEM, fit statistics, item difficulty. NECO and WAEC were

therefore intra and inter-related in their psychometric qualities the years studied.

In conclusion, therefore,

(1) The close relationship among psychometric qualities of WAEC and NECO items

will elevate the trust and confidence of the public the in these two examination

bodies.

(2) The test developers can comfortably explain examinees behaviour in testing

situation. This also has a far reaching implication for the guidance counsellors.

(3) It is recommended that examination bodies should adopt IRT framework and have

our measurement problems reduced to the barest minimum.

(4) Teachers, psychometricians, and other stakeholders in measurement should

procure IRT software analysis programme and have the people involved

sponsored in the training. This will enable interpretation and consequent

106

appreciation of the IRT framework advantages over other measurement

framework.

107

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118

APPENDIX B

Department of Science Education, University of Nigeria, Nsukka. 13 April 2013.

The Principal/Head Physics Teacher, Dear Sir/Madam, REQUEST TO USE YOUR PHYSICS LAB AND SS III PHYSICS STUDENTS AND TEACHER FOR Ph.D STUDIES I am a post graduate student of department of Science Education, University of Nigeria. In partial Fulfillment of the requirement of the course Ed. 690, I am carrying out an instrumentation research in which I will do a psychometric analysis of NECO and WAEC practical physics Tests (internal) for years 2011 and 2012 questions. I humbly request that you grant me access to your physics laboratory (equipment), SS III physics teacher (s) and students. The equipment will be used to conduct the practical questions that formed the instrument of the study, the physics teacher will help the researcher and his assistants in conducting the practicals (study), and the SS III students will help to carry out the practical activities and respond to the items in the instrument. Thank you so much in anticipation of your approval, cooperation and assistance.

Yours faithfully, Adonu, I. Ifeanyi PG/Ph.D/08/49721

119

APPENDIX C

Practical Physics Questions of NECO 1 (PPQN 1)

SENIOR SCHOOL CERTIFICATE EXAMINATION (INTERNAL) NATIONAL EXAMINATION COUNCIL (NECO)

JUNE/JULY 2011 1(a)

Using Fig (1) (a) above as a guide, carry out the following instructions.

(i) Place the metre rule provided on the knife-edge and adjust its position until it

balances horizontally.

(ii) Read and record the point of balance G of the metre rule

(iii) Suspend a mass M1 = 100g at A, a distance y = 5cm from the 0cm mark of the

metre rule.

x1 y G K1

0cm 100cm

Fig (1) (a) m1

G K2

x2 y

100cm 0cm

m2

Fig (1) (b)

120

(iv) Balance the whole arrangement horizontally on the knife-edge as shown in the

diagram above.

(v) Read and record the position of the knife edge K1. Also record the length K1A =

x1.

(vi) Repeat the procedure for values of y = 10, 15, 20 and 25cm respectively. In each

case, record the corresponding values of K1 and x1.

(vii) Repeat the entire procedure with a mass M2 = 150g suspended at distance y =

5.10, 15, 20 and 25cm as shown in fig 1(b). In each case, record the

corresponding values of K2 and x2.

(viii) Tabulate your readings in the space provided below:

(ix) Plot a graph of x1 on the vertical axis and x2 on the horizontal axis, starting both

axes from the origin (0,0).

(x) Determine the slope S of the graph.

Slope of graph, S.

(xi) Evaluate : = ; <=; =

(xii) State TWO precautions taken to ensure accurate results.

(b)(i) State TWO conditions that are necessary for a body to be in equilibrium under

three non-parallel, coplanar forces.

(ii) a uniform metre rule balances horizontally on a knife edge at the 15cm when a

mass of 350g is suspended at the zero cm mark. Calculate the mass of the metre

rule.

121

2(a)

(i) Trace the outline ABCD of the glass block on a sheet of paper as shown

above. Remove the block.

(ii) Mark a position N very close to A and draw a normal MNR at N.

(iii) Draw a line TN making an angle I = 20o with MN and produce it to meet DC

at Y.

(iv) Fix two pins at points P1 and P2 along the TN.

(v) Replace the block on its outline and fix two other pins at points P3 and P4 such

that the pins appear to be in a straight line with the images of the pins at P1

and P2 when viewed through the side DC of the glass block.

(vi) Remove the block and join the points at P3 and P4 producing the line to meet

DC at X.

(vii) Join NX.

(viii) Draw a line XZ = d perpendicular to NY.

(ix) Measure the record the angle of refraction r and the distance d. Evaluate sin (i-

r) and dcos r.

(x) Repeat the procedure for I = 25o, 30o and 40o respectively. In each case,

measure and record the corresponding values of r and d. Also evaluate sin (i-r)

and dcos r. Tabulate your readings in the space provided below.

P2

T

M P1

N i

B A

r

Z R

d

C

C Y P3

X D

P4

122

(xi) Plot a graph of dcos r on the vertical axis and sin (i-r) on the horizontal axis,

starting both axes from the origin (0,0).

(xii) Determine the slope S of the graph

Slope of graph, S =

(xiii) State TWO precautions taken to ensure accurate results.

b(i) State Snell’s law of refraction of light.

(ii) An object lies at the bottom of a pool of water 80cm deep. If the refractive index

of water is 1.33, calculate the apparent upward displacement of the object when

viewed vertically from above.

3(a)

(i) Measure and record the e.m.f E of the battery provided.

(ii) Connect the circuit as shown in the diagram above.

(iii) For a length C1C2 = L = 100cm of the wire P, close the key K.

(iv) Read and record the ammeter reading I.

(v) Evaluate > = ?@

(vi) Repeat the procedure for values of L = 90, 80, 70, 60 and 50cm respectively.

In each case, read and record the corresponding values of I. Also evaluate

> = ?@

Tabulate your readings in the space provided below.

(vii) Plot a graph of Q on the vertical axis and L on the horizontal axis, starting

both axes from the origin (0,0).

Determine the slope S of the graph and intercept C on the vertical axis.

Slope of graph, S =

P

2Ω

C2 C1

A

K

123

(viii) Evaluate K = C – 2.

(ix) State TWO precautions taken to ensure accurate results.

b(i) Define the internal resistance of a cell.

(ii) Given that > = A.B"C

D L + C

in the experiment above, use your graph to determine the value of A.

124

APPENDIX D

Practical Physics Questions of NECO (PPQN 2)

SENIOR SCHOOL CERTIFICATE EXAMINATION (INTERNAL) NATIONAL EXAMINATION COUNCIL (NECO)

JUNE/JULY 2012

PHYSICS (PRACTICAL) PHYSICS PAPER 1 (1)

(i) Place the metre rule provided on the knife edge and adjust its position until it

balances horizontally.

(ii) Read and record the point of balance G of the metre rule. Keep the knife edge at the

point G throughout the experiment.

(iii) Suspend the mass labelled M at P, the 25cm-rnark' of the metre rule, determine and

record the length PG = D.

(iv) On the other side of G, suspend the mass m = 30g and adjust its position until the

metre balances horizontally as shown in the diagram above.

(v) Read and record the position R, the point of suspension of m

(vi) Record the value of m. Also determine and record the length GR = d.

(vii) Evaluate d-1

(viii) Keeping the mass M at P, the same 25cm mark, repeat the procedure for mass m =

40. 50, 60, 70 and 80g to determine R. In each case record the values of m and (the .

corresponding distance d. Also evaluate d-1. Tabulate your readings in the space

provided below.

M M

D d

25cm

G R 100 O P

(ix) Plot the graph of m on the vertical axis and d

(x) Determine the slope S of the graph

(xi) Evaluate K = D

S

(xii) State TWO precautions taken to ensure accurate results.

b (i) Define the

(ii) A uniform metre rule balances horizontally on a knife edge at 55cm mark.

When an object of mass 1.0kg is placed at the 5cm mark, it balances at 35cm mark.

Calcaulte the magnitude of the weight of the metre rule. (g = 10m

2(a)

(2) Using the

diagram above as a guide, carry out the following instructions:

(i) Place an optical pin (object) at the bottom of the measuring cylinder

(ii) Pour water of volume V = 150cm

(iii) Measure and record the real depth, OS =

(iv) Move the search pin up and down, and locate the image I. Measure and record

the apparent depth: IS = h.

(v) Repeat the procedure for V = 175, 200, 225, 250 and 275cm

measure and record the values of H and the corresponding values of h.

Tabulate your readings in the space provided below.

(vi) Plot a graph of H on the vertical axis and h on the horizontal axis.

(vii) Determine the slope S of the graph

(viii) State TWO precautions taken to ensure accurate results.

Plot the graph of m on the vertical axis and d-1- on the horizontal axis.

Determine the slope S of the graph

precautions taken to ensure accurate results.

Define the centre of gravity of a body.

A uniform metre rule balances horizontally on a knife edge at 55cm mark.


Calcaulte the magnitude of the weight of the metre rule. (g = 10m

diagram above as a guide, carry out the following instructions:

Place an optical pin (object) at the bottom of the measuring cylinder

Pour water of volume V = 150cm-2 into the measuring cylinder.

Measure and record the real depth, OS = H

Move the search pin up and down, and locate the image I. Measure and record

the apparent depth: IS = h.

Repeat the procedure for V = 175, 200, 225, 250 and 275cm


late your readings in the space provided below.

Plot a graph of H on the vertical axis and h on the horizontal axis.

Determine the slope S of the graph


125

on the horizontal axis.

A uniform metre rule balances horizontally on a knife edge at 55cm mark.


Calcaulte the magnitude of the weight of the metre rule. (g = 10m-2)

Place an optical pin (object) at the bottom of the measuring cylinder

into the measuring cylinder.

Move the search pin up and down, and locate the image I. Measure and record

Repeat the procedure for V = 175, 200, 225, 250 and 275cm3. In each case,


Plot a graph of H on the vertical axis and h on the horizontal axis.

126

b(i) State Snell’s law of refraction

(ii) A glass of thickness t and refractive indeed n is laced on a dot of ink. If the

dot of ink is viewed through the glass, express the displacement d of the

dot in terms of n and t.

(i) Measure and record the electromotive force E of the battery provided.

(ii) Connect the circuit as shown in the diagram above.

(iii) Setting resistance box R = 1Ω, close the key. Read and record the current I on

the ammeter. Evaluate I-1

(iv) Repeat the procedure for R = 2, 3, 4 5 and 6Ω. In each case, read and record the

corresponding values of I. Also evaluate I-1

(v) Tabulate your readings in the space provided below.

(vi) Plot a graph of R on the vertical axis and 1-1 on the horizontal axis, starting both


(vii) Determine the slope S of the graph and the intercept C.

(viii) State TWO precautions taken to ensure accurate results.

b(i) Define the internal resistance of a cell.

(ii) A resistor of resistance R is connected across a cell of c.m.f. E. If the internal

resistance of the cell is one third of R. express the value of the terminal

potential different V of the cell in terms of E and R.

( )

Battery

Key

A

. . . . . . . .

. . .

. . . . . . . .

3(a)

Resistance box R

127

APPENDIX E

Practical Physics Question of WAEC 1 (PPQW 1)

WEST AFRICAN EXAMINATION COUNCIL (WAEC)

MAY/JUNE 2O11 SENIOR SCHOOL CERTIFICATE (SSCE)

PAPER 1 PRACTICAL

1(a)

You are provided with a wooden block to which a hook is fixed: set of masses, spring

balance and other necessary materials. Using the diagram above as a guide, carry out the

following instructions.

(i) Record the mass m0 indicated on the wooden block.

(ii) Place the block on the table.

(iii)Attach the spring balance to the hook.

(iv) Pull the spring balance horizontally with a gradual increase in force until the block

just starts to move. Record the spring balance reading F.

(v) Repeat the procedure by placing in turn mass m = 200, 400, 600 and 800 g on top of

the block. In each case, read and record the corresponding value of R

(vi) Evaluate M = m0 + m and R = 100

M in each case.

(vii) Tabulate your readings.

(viii)Plot a graph with F on the vertical axis and R on the horizontal axis.

(ix) Determine the slope, s, of the graph.

(x) State two precautions taken to ensure accurate results.

(b) (i) Define coefficient of the static friction.

Wooden block

Hook

Spiral spring

F

128

(ii) A block of wood of mass 0.5 kg is pulled horizontally on a table by a force of

2.5 N. Calculate the coefficient of static friction between the two surfaces. (g =

10ms-2)

2

Use the diagram above as a guide to carry out the following experiment.

(i) Trace the outline ABCD of the rectangular glass prism on the drawing paper

provided.

(ii) Remove the prism. Select a point N on AB such that AN is about one quarter of

AB.

(iii) Draw the normal LNM. Also draw a line-RN to make an angle 9 = 75° with AB

at N.

(iv) Fix two pins at P1 and P2 on line RN. Replace the prism on its outline.

(v) Fix two other pins at P3 and P4 such that they appear to be in a straight line with

the images of the pins at P1 and P2 when viewed through the prism from side

DC.

(vi) Remove the prism and the pins at P3 and P4 . Draw a line to join P3 and P4.

(vii) Produce line P4 P3, to meet the line DC at O. Draw a line to join NO.

(viii) Measure and record the values of MO and NO.

(ix) Evaluate φ = NO

MO and cos θ.

(x) Repeat the procedure for four other values of θ 65°, 55°, 45° and 35°. In each

case, evaluate φ and cos θ.

L

N B

E M D

A θ

R P1

P2

P3 P4

O

(xi) Tabulate your readings.

(xii) Plot a graph with cos

(xiii) Determine the slope,

(xiv) State two precautions taken to ensure accurate results'

(b) (i) State Snell 's law of refraction.

(ii) Calculate the critical angle f

above if its refractive index is 1.5.

3(a)

You are provided with cells, a potentiometer, an ammeter, a voltmeter, a bulb. a key, a

jockey and other necessary materials.

(i) Measure and record the emf E of the battery.

(ii) Set-up a circuit as shown in the dia

(iii) Close the key K and use the jockey to make a firm contact at J on the potentiometer

wire such that PJ = x =

(iv) Take and record the voltmeter reading

(v) Evaluate log V and log I

(vi) Repeat the procedure for other values of


(viii) Plot a graph with 1og1 on the vertical axis and log V on the horizontal axis.

(ix) Determine the slope, s. of the graph.

(x) Determine the intercept, c, on the vertical axis.

(xi) Slate two precautions taken to ensure accurate results.

Tabulate your readings.

Plot a graph with cos θ on the vertical axis and φ on the horizontal axis,

Determine the slope, s, of the graph.

precautions taken to ensure accurate results'

Snell 's law of refraction.

(ii) Calculate the critical angle for the glass prism used in the

above if its refractive index is 1.5.


jockey and other necessary materials.

Measure and record the emf E of the battery.

a circuit as shown in the diagram above.

Close the key K and use the jockey to make a firm contact at J on the potentiometer

= x = 10 cm.

Take and record the voltmeter reading V and the corresponding ammeter reading

Evaluate log V and log I

Repeat the procedure for other values of x = 20, 30, 40, 50 and 60 cm.


Plot a graph with 1og1 on the vertical axis and log V on the horizontal axis.

Determine the slope, s. of the graph.

Determine the intercept, c, on the vertical axis.


129

on the horizontal axis,

r the glass prism used in the experiment


Close the key K and use the jockey to make a firm contact at J on the potentiometer

ing ammeter reading

= 20, 30, 40, 50 and 60 cm.

Plot a graph with 1og1 on the vertical axis and log V on the horizontal axis.

130

b(i) How is the brightness of the bulb affected as x increase? Give a reason for

your answer

(ii)List the electrical devices whose actions do not obey ohm’s law.

131

APPENDIX F

Practical Physics Questions of WAEC 2 (PPQW 2) WEST AFRICAN EXAMINATION COUNCIL (WAEC)

MAY/JUNE 2012 SENIOR SCHOOL CERTIFICATE (SSCE) PAPER 1-PRACTICAL

1(a)

Study the diagrams beside and use them as guides in carrying out the following ins-

tructions.

(i) Using the spring balance provided, determine the weight of object of mass M=

50.0g.in air Record this weight as W2

(ii) Determine the weight of the object when it is completely immersed in water

contained in a beaker as shown in the diagram above. Record the weight as

W3

(iii) Determine the weight of the object when it is completely immersed in the

liquid labelled L. Record the weight as W3

(iv) Evaluate U = (W1 – W2) and V = (W1 – W3).

(v) Repeat the procedure with the objectives of masses M = 100g, 150g, 200g and

250g.

(vi) In each case, evaluate U = (W1– W2) and V = (W,- W,).

(vii) Tabulate your readings

(viii) Plot a graph with V on the vertical axis and U the horizontal axis.


(x) State two precautions taken to ensure accurate results.

b. (i) State Archimedes principle.

support pointer spiral spring balance

M

beaker

object water

M

support pointer spiral spring balance

beaker

object liquid L

(ii) A piece of brass 20.0g is hung on a spring balance from a rigid support and

completely immersed in kerosene of density 8.0 x 10

reading on the sp

(i) Pull the piston of the syringe, upward until it can no longer move.

(ii) Read and record this position of the piston on the graduated mark on the syringe

as V0

(iii) Clamp the syringe and ensure that it is vertical.

(iv) Place a mass M = 500g gently at the centre of the pertri

(v) Read and record the new position of the piston as V. (v) Evaluate V

(vi) Repeat the procedure for four other values of M = l00g, 150


(viii) Plot as graph with V


(ix) Determine the slope, s of the graph.

(x) Evaluate k = s-1

(xi) State two precautions taken to ensure a

(b) (i) When a weight is placed on the petri

syringe (∝) increases; (

(ii) What is responsible for the pressure exerted by a gas in a closed vessel?


completely immersed in kerosene of density 8.0 x 102kgm-3. Determine the

reading on the spring balance. (g = 10ms-2, density of brass =8.0 x l0kgm

Pull the piston of the syringe, upward until it can no longer move.

Read and record this position of the piston on the graduated mark on the syringe

Clamp the syringe and ensure that it is vertical.

Place a mass M = 500g gently at the centre of the pertri-dish.

Read and record the new position of the piston as V. (v) Evaluate V

Repeat the procedure for four other values of M = l00g, 1500g, 2000g and 2500g


Plot as graph with V-1 on the vertical axis and M on the horizontal axis, starting


Determine the slope, s of the graph.


(b) (i) When a weight is placed on the petri-dish. Which quantities of the gas in the

) increases; (β) decreases?


132


. Determine the

, density of brass =8.0 x l0kgm-3

Pull the piston of the syringe, upward until it can no longer move.

Read and record this position of the piston on the graduated mark on the syringe

dish.

Read and record the new position of the piston as V. (v) Evaluate V-1

0g, 2000g and 2500g

on the vertical axis and M on the horizontal axis, starting

ntities of the gas in the


133

(i) Set up a circuit as illustrated in the diagram above.

(ii) Close the key, K.

(iii) Read and record the ammeter reading. I0 and the volt-meter reading V0 when jockey

J is not making contact with the potentiometer wire OQ.

(iv) Using J make a contact with the potentiometer wire OQ at a point P such that OP =

10cm.

(v) Read and record the current and the corresponding value of the voltage V.

(vi) Repeat the procedure for other values of OP =20cm, 30cm,-40cm, 50cm and 60cm.

(vii) Tabulate your readings

(viii) Plot a graph with V on the vertical axis and. I on the horizontal axis, starting both



(x) Determine the value of V when I = O

(xi) State two precautions taken to obtain, accurate results.

b. (i) State two advantages of a lead-acid accumulator over a dry Leclanché cell

(ii) A cell emf 2V and internal resistance of IΩ passes current through an external load

of 9Ω. Calculate the potential drop across the cell.

134

APPENDIX G

NATIONAL EXAMINATION COUNCIL

SENIOR SCHOOL CERTIFICATE EXAMINATION (INTERNAL) JUNE/JULY 2012

PHYSICS (PRACTICAL)

FINAL MARKING SCHEME CANDIDATE ARE TO ANSWER TWO QUESTIONS OUT OF THREE GENERAL NOTES 1. Each question is marked on a total of 25marks under different sub-heading:

Observations, graph, slope, deductions, accuracy, precautions, and short answer

questions

2.i. Penalties earned under one sub-heading are not transferable if no marks have been

earned in that section.

ii. Units wrong or missing attract loss of ½ mark each. Units may be sated in table or

graph. There is no penalty for derived units.

iii. Inconsistent significant figures (s.f) attract loss of ½ mark per column up to a

maximum of 1 mark per table.

iv. Systematic errors (s.e.) attract loss of 1 mark

v. Disregard of instructions (d.i) attract loss of 1 mark

vi. Gross errors (g.e.) for instance, measurement of glancing angles where angles of

incidence are required should be treated as gross error and NOT as systematic

error. Award zero for gross error

vii. Quantities read from table must be recorded to at least 3 decimal places except for

exact values e.g. (Reciprocals, logs etc) or to 3 significant figures depending on

value required.

viii. For short-answer questions, deduct ½ mark for missing or wrong unit in final

answer of numerical problems

x. Deduct ½ mark for each wrong or missing heading.

135

3. GRAPH

i. For scales to be reasonable, graph must occupy at least a half of page/space provided

for use. Origin is part if requested or if intercept is required.

ii. Scales using multiples or sub-multiples of prime numbers such as 3.7.11.13 e.t.c. are

not acceptable.

iii. Points should be plotted correctly to nearest half square on both axes,

iv. To obtain the suitable line mark, at least three points must be correctly plotted.

v. Where points are matched, candidates should be awarded zero for plotted points

slope, intercept etc.

vi. If a candidate plotted unwanted variables, i c. gross error, score zero for graph, slope.

intercept, deduction, etc.

4. SLOPE

i. Large right-angled triangle implies that it occupies at least ½ of graph.

ii. To obtain correct arithmetic mark, candidate must have read AX or AY correctly.

NOTE: Coordinates are not acceptable

5. PRECAUTIONS

Must be stated in acceptable language e.g. 1 avoided conical swing of the pendulum bob

or conical swing of the pendulum bob was avoided, not you must avoid conical swing of

pendulum bob, not you should avoid conical swing and not avoid conical swing.

6. TIME SAVING

It has been decided to save time marking good consistent scripts. When a number of

processes such as multiplications, divisions, readings from tables, plotting etc are to be

repeated for all readings we begin by checking the first three. If all are correct. award full

marks for the process. Otherwise, check all and score accordingly. This does not apply to

observed readings.

l(a) OBSERVATION (9 MARKS)

(i). Point of balance G. read and recorded to at least 1 d.p. in cm............. ½

(ii). Value of D determined and recorded to at least 1 d.p. in cm.............. ½

136

(iii). 6 values of m recorded in grams. ....................................................... ½

(Deduct ½. mark for each wrong or missing value)

(iv). 6 values of the position R of m read and recorded to at least I d.p in cm and in

trend.........................................................................................3

(Trend: As m increases, R of m decreases: ½ mark each)

(v). 6 values ofd-1correctly determined and recorded ...................................2

(Deduct ½ mark for each wrong or mining value)

(vi). 6 values of d-1 correctly calculated and recorded to at least 3 d.p. .......1

(Deduct ½ mark for each wrong or missing value)

(vii). Composite table showing m, position R of m, d. d-1 at least................. 1

NOTE: If the value of G is not recorded score zero for observation (i). (ii) and (v).

GRAPH (6 MARKS)

(i). Axes distinguished (½ mark each).........................................................1

(ii). Reasonable scales (1/2 mark each).,…………………………..........1

(iii). 6 points correctly plotted (½ mark each)..............................................3

(iv). Line of best fit...,.................................................................................1

SLOPE (2 MARKS)

(i). l.arge right-angled triangle............................................................... ..½

(ii). ∆m correctly read and recorded........................................................... ½

(iii). ∆d -1correctly read and recorded ........................................................ ½

(iv). 1−∆

∆d

m correctly calculated.................................................................. ½

DEDUCTION (I MARK)

.

;,

PGLenghtD

SlopeSWherD

SK

=

==

Correct substitution ..................................................................................... ½

Correct arithmetic..........................................................................................½

ACCURACY (1 MARK)

137

Based on K = Mass of M as supplied by teacher to within ± 10%.

NOTE; If mass M is not supplied award zero for accuracy.

PRECAUTION (2 MARKS)

Award 1 mark each for any TWO of the following stated in acceptable language.

(i) I avoided draught (award zero if avoid air is used) OR Draught was avoided.

(ii) 1 avoided error of parallax on metre rule. OR Error due to parallax on metre rule

was avoided.

(iii) I avoided mass touching table. OR mass was not allowed to touch the table.

(iv) Zero error of metre rule was noted, OR I noted zero error of the metre rule.

(v) Repeated readings shown on the table.

-Any other valid point.

b(i) -The point through which the lines of action of the weight of

the body always passes irrespective of the position

of the body.......................................................................................2

OR

-The point through which the line of action of the weight always acts.

OR

-The point at which the resultant/entire weight of the body appears to be concentrated.

Correct diagram ..................................................................................2

Taking moment about the pivot

20 x w = 10 x30 ...................................................................................... ½

W= 15N............................................................................................... ½

2(a) OBSERVATION (11 MARKS)

(i). 6 values of H measured and recorded to 1 d,p in cm and in trend......... 5

30 20

10 W

5 35 55 100

138

(Trend: As V increases, H increases)

(Deduct 1 mark for each wrong or missing value)

(ii) 6 values ofh measured and recorded to I d.p. in cm and in trend ....... 5

(Trend: As H increases, h increases)

(Deduct 1 mark for each wrong or missing value)

(iii). Composite table showing V, H, and h at Ieast……………………….1

NOTE; H must be greater than h, otherwise penalize for wrong heading.

GRAPH (6 MARKS) - As in question 1

SLOPE (2 MARKS) - As in question 1



(i) Reading of the water level is taken from the lower meniscus.

(ii) Zero error of metre rule was noted OR I noted zero error of the metre rule.

(iii) Repealed readings shown on table.

(iv) Parallax error avoided on metre rule.

-Any other valid point.

b(i). The ratio of the sine of the angle of incidence to the sine of the angle of retraction

is a constant for a given pair of media…………………. 2 or 0

(ii). Let t be the real thickness and x be the apparent thickness of the

glass. Displacement d = Real thickness - Apparent thickness

d = t - x

x = t – d ...............................eq(l)............................................. ½

Also, n = thicknessapparent

thickenessalRe

Refractive index, n = x

1

139

nx

1= ……………………………………… eq (2)…………… ½

Equating (t) & (2), we have

n

t = t – d ........................................................................... ½

d = t - n

t

OR

d = t

−n

11 .................................................................................. ½

Alternatively

antna

t =⇒= , ……………………………………………….. ½

Where a = apparent displacement,

∴ displacement d = t – a

= t - n

t...................................................................... ½


(i). Value of E measured and recorded to 1 d.p. in volts ..................1

(ii). 6 values of I read and recorded to 1 d.p. in Amp and in trend

(1 mark each) …………………………………………………....6 (Trend: As R increases 1 decreases)

(iii). 6 values of 1-1 correctly calculated and recorded to at least 3 d.p

.......................................................................................... 2


(iv). Composite table showing R, I, 1-1 at least.................................1

GRAPH (6 MARKS)

As in question I

SLOPE (2 MARKS)

As in question 1

140

INTERCEPT, (1 MARK)

Correctly shown ………………………………………………..…………. ½

Correctly read…………………………………………..…………….…… ½

NOTE: Accept intercept on any axis.

PRECAUTIONS (2 MARKS)

Award one mark each for any TWO of the following stated in acceptable language.

i. Connections were made tight

ii. I ensured clean terminals.

iii. Key was opened when readings were not taken

iv. I avoided/noted zero error of ammeter

v. I repeated readings shown on table.

(vi). I avoided parallax error when reading the ammeter -Any other valid point.

b(i) -The opposition to the flow of current offered by the chemicals

and the poles..........2

(ii). E = I(R + r) …………………………………. ½

r = 3

R ………………………………….. ½

= 1(R + 3

R) …………………………………….. ½

E = IR + 3

IR ; E = V +

3

IR

∴ V = E - 3

IR……………………………………….….. ½

OR

E = I(R+r) ……………………………………..….. ½

r = 3

R…………………………………….….. ½

= 1(R + 3

R) …………………………………….. ½

141

= IR + 3

IR = IR +

3

V

3E = 3IR + V

V = 3E = 3IR

OR

V = 3(E – IR) ……………………………….. ½

142

APPENDIX H NATIONAL EXAMINATION COUNCIL (NECO)

2011 SENIOR SCHOOL CERTIFICATE EXAMINATION (INTERNA L)

PHYSICS (PRACTICAL) FINAL MARKING SCHEME (2011)

CANDIDATE ARE TO ANSWER TWO QUESTIONS OUT OF THREE GENERAL NOTES 1. Each question is marked on a total of 25 marks under different sub-heading:

Observations, Graph, Slope, Deductions, Accuracy, Precautions and Short answer

questions.

2.i. Penalties earned under one sub-heading are not transferable if no marks have been

earned in that section.

ii. Units wrong or missing attract loess of ½ mark each. Units may be sated in table or

graph. There is no penalty for derived units.

iii. Inconsistent significant figures (s.f) attract loss of ½ mark per column up to a

maximum of 1 mark per table.

iv. Systematic errors (s.e.) attract loss of 1 mark

v. Disregard of instructions (d.i) attract loss of 1 mark

vi. Gross errors (g.e.) for instance, measurement of glancing angles where angles of

incidence are required should be treated as gross error and NOT as systematic

error. Award zero for gorses error

vii. Quantities read from table must be recorded to at least 3 decimal places except for

exact values e.g. (Reciprocals, logs etc) or to 3 significant figures depending on

value required.

viii. For short-answer questions, deduct ½ mark for missing or wrong unit in final

answer of numerical problems

xi. Deduct ½ mark for each wrong or missing heading.

3. GRAPH

i. For scales to be reasonable, graph must occupy at least a hall of page/space

provided for use. Origin is part if requested or if intercept is required.

ii. Scales using multiples or sub-multiples of prime numbers such as 3.7.11.13 e.t.c.

are not acceptable.

143

iii. Points should be plotted correctly to nearest half square on both axes,

iv. To obtain the suitable line mark, at least three points must be correctly plotted.

v. Where points are matched, candidates should be awarded zero for plotted points

slope, intercept etc.

vi. If a candidate plotted unwanted variables, i e. gross error, score zero for graph,

4. SLOPE

i. Large right-angled triangle implies that it occupies at least ½ of graph.

ii. To obtain correct arithmetic mark, candidate must have read AX or AY correctly.

NOTE: Coordinates are not acceptable

5. PRECAUTIONS

Must be stated in acceptable language e.g. 1 avoided conical swing of the pendulum bob

or conical swing of the pendulum bob was avoided, not you must avoid conical swing of

pendulum bob, NOT you should avoid conical swing and NOT avoid conical swing.

6. TIME SAVING

It has been decided to save time marking good consistent scripts. When a number of

processes such as multiplications, divisions, readings from tables, plotting etc are to be

repeated for all readings we begin by checking the first three. If all are correct. award full

marks for the process. Otherwise, check all and score accordingly. This does not apply to

observed readings.


i. Point of balance, G = 50.0cm read and recorded to at least 1 d.p.

in cm and within tolerance of ± 1.0cm ……………………….. 1mark

ii. 5 values of K1 read and recorded to at least 1 d.p in cm and in

trend ( ½ mark each) …………………………………… 2 ½ marks

(Trend: As y increase, K1= increases)

iii. 5 values of K2 read and recorded to at least 1 d.p in cm and in

trend ( ½ mark each) …………………………………. 2 ½ marks

144

(Trend: As y increase, K2 increase)

iv. 5 values of x1 correctly calculated …………………….. 1 mark


v. 5 values of x2 mark for each wrong or missing value)


vi. Composite table showing y, k1, K2, x1, and x2 at least …….. 1 mark

GRAPH (6 MARKS)

i. Axes distinguished .. ( ½ mark each) …………………… 1mark

ii. Reasonable scales … ( ½ each) ………………………… 1mark

iii. 5 points correctly plotted ……………………………….. 3marks

(Deduct 1 mark for each wrong or missing point)

iv. Line of best fit …………………………………………… 1mark

SLOPE (2 MARKS)

i. Large right-angled triangle ………………………………… ½ mark

ii. ∆x1 correctly read and recorded ……………………………… ½ mark

iii. ∆x2 correctly read and recorded ……………………………. ½ mark

iv. ∆"< ∆"< correctly calculated ……………………………… ½ mark

EVALUATION (1 MARK)

K = E< =;

F

Where S = slope Correct substitution ………………………………………….. ½ mark Correct arithmetic …………………………………………… ½ mark ACCURATE (1 MARK) Based On K – mass of metre rule as supplied by teacher within ± 10% NOTE: If mass of metre rule is not supplied award zero. PRECAUTIONS (2 MARKS) Award 1 mark each for any TWO of the following, stated in acceptable language.

i. I avoided draught / Draught was avoided

ii. I avoided error of parallax in reading metre rule

iii. I avoided mass touching table/floor

145

iv. Repeated reading shown on the table

v. I avoided zero error of the metre rule.

(b)i I - The forces must be concurrent. II - The resulting of the forces must be equal to zero. OR

- The resolved components of the forces along two mutually perpendicular

directions must separately be equal to zero.

III - The algebraic sum of the moments of the forces about a given axis must be

equal to zero.

Any Two of these three x 1 mark each = 2 marks.

ii.

Correct diagram – ½ mark

Taking moments about P gives that

350 x g x 15 = m x g x 35 …………………………………… ½ mark

m = HIC'I'JFHI'J ………………………………………........ ½ mark

= 150 grammes ………………………………………........ ½ mark


i. 5 complete and correct traces …………………………....... 2marks

(Deduct ½ mark for each incomplete, incorrect or missing trace)

(For trace to be complete and correct, the incident ray, refracted ray, emergent ray

from DC and the normal must be shown as in the diagram)

NOTE: Do not accept traces combined on one ray diagram

ii. 5 values of r correctly measured and recorded to 1o and in trend …. 2marks

(Trend: As i increases, r increases)


P

m 35cm 15cm 350

146

iii. 5 values of d correctly drawn and recorded in cm to at least 1 d.p.

and in trend …………………………........................ 2mark

(Trend: as I increase, d increase)


iv. 5 values of (i-r) correctly evaluated. …………………….. 1 mark


v. 5 values of sin(i-r) correctly evaluated to at least 3 d.p. ….. 1mark


vi. 5 values of cosr correctly evaluated to at least 3 d.p……….. 1mark


vii. 5 values of dcosr correctly calculated to at least 3 d.p……. 1mark


viii. Composite table showing I, r, d, sin (i-r) and dcosr at least …. 1mark

NOTE:

(i) If traces are not attached score zero for I, ii and iii

(ii) If no pin marks, treat as if no traces were attached

(iii) Do not accept group work

(iv) Where a candidate has calculated and recorded dcosr and sin(i-r)

without recording cosr and i-r separately award …………… 2marks

GRAPH (5 MARKS)

(i) Both axes correctly distinguished ……………………….. 2 marks

(ii) Both scales reasonable …………………………………… ½ mark

(iii) 5 points correctly plotted ………………………………… 3 marks

(Deduct ½ mark for each wrong or missing point)

(iv) Line of best fit ………………………………… ………… 1 marks

SLOPE (2 MARKS)

As in Question 1(a)

147

ACCURACY (1 MARK)

Based on slope, S = Width of the glass block within ± 10% as measured from candidate’s trace.

PRECAUTIONS (2 MARKS)


i. Ensure pins are vertical/upright

ii. Sharp pencil/neat traces as shown from traces

iii. Ensured reasonable spacing of pins/Ensured minimum spacing of 4cm of the pins.

iv. Avoided parallax error in reading protractor/ruler

Accept any other valid precaution

i. Snell’s law states that:

The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a

constant for a given pair of media.

OR

For any pair of media, the ratio of the sine of the angle of incidence to the sine of the angle of

refraction is a constant.

(2 marks or zero)

ii. Refractive index = KLMN OLPQ5

DPPMRLSQ OLPQ5 (") …………………………….. ½ mark

1.33 = UC'

x = UC.HH

= 60.15cm …………………………………………… ½ mark Displacement = Real depth = Apparent depth …………………… ½ mark = 80 -60.15 = 19.85cm…………………………………………… ½ mark OR

d = r X1 − YZ ………………………………………………..1mark

where d = displacement, r = real depth, n = refractive index

d = 80 X1 − .HHZ………………………………………………… ½ mark

÷ 80 – 60.15

= 19.85cm…………………………………………… ½ mark

148

3(a) OBSERVATION (8 MARKS) i. E.m.f. of battery recorded in volt to at least 1 d.p………………. 1mark

ii. 6 values of L measured and recorded to at least 1 d.p. in cm …… 1mark

(Deduct ½ mark for each wrong or missing value) iii. 6 values of 1 read and recorded at least 1 d.p. in Amperes

and in trend …………………………………………………… 4marks (Trend: As L decreases, 1 increases) (Deduct 1 mark for each wrong or missing value)

iv. 6 values of Q correctly calculated and recorded to at least 2 d.p. …. 1mark

(Deduct ½ mark for each wrong or missing value) v. Composite table showing L, 1 and Q at least …………………… 1mark

GRAPH (6 MARKS) i. Axes distinguished … ( ½ mark each ………………………… 1mark

ii. Reasonable scales .. ( ½ mark each) …..…………………….. 1mark

iii. 6 points correctly plotted .. ( ½ mark each)………………… 3marks

iv. Line of best fit ……………………………………………….1mark

SLOPE (2 MARKS) As in Question 1(a) INTERCEPT C (1 MARK) Correctly shown …………………………………………………….. ½ mark Correctly read …………………………………………………….. ½ mark EVALUATION (1 MARK) K = C – 2, where C = intercept

i. Correct substitution ………………………………………………..½ mark

ii. Correct arithmetic ………………………………………………..½ mark

ACCURACY (1 MARK) Based on value of K – internal resistance of cell to within ± 10% of teacher’s value ……………………………………………………….. ½ mark NOTE: If internal resistance of cell is not supplied, score zero for accuracy. PRECAUTIONS (2 MARKS) Award 1 mark each for any TWO of the following, stated in acceptable language.

i. Connections were made tight/ I ensured clean terminals.

ii. Key opened when readings are not taken

149

iii. Avoided/Noted zero error of ammeter

iv. Avoided parallax error when reading the ammeter/meter rule

v. Repeated readings shown on table

vi. Any other valid precautions

(b)i. Opposition to current flow offered by the chemicals and the poles of the cell. (2 or 0) ii. Slope from plotted graph ………………………………………..½ mark

[ = A.B"C

D

OR

\ = A.B"C

= ………………………………………….. ½ mark

Correct substitution ……………………………………….. ½ mark

Correct arithmetic ………………………………………… ½ mark

150

APPENDIX I

WEST AFRICAN EXAMINATION COUNCIL 2011 MAY JUNE SENIOR SCHOOL CERTIFICATE MARKING SCH EME O’ LEVEL

PRACTICAL PHYSICS i) A) Observation (12 Marks)

i) The value of Mo read and recorded to at least one decimal place in gram - - - - - 1 mark.

ii) 4 values of F (N) force recorded to at least one (deduct ½ mark for each missing value) - - - 1 mark.

iii) 4 values of M = (Mo + M (g)) read and recorded to one decimal place and in increasing trend - - - - 3 marks.

iv) 4 values of F = R = M/100g calculated and in increasing trend - - - 3 marks

v) 4 values o f mass m(g) recorded to 1 decimal place1 mark

vi) Composite table showing O M, F, M and R

vii) Correct units for each quantity (column) – 1 mark;

viii) Consistency with decimal place– 1 mark

GRAPH (5 marks) i) Axes distinguished – (1/2 mark each) -------1

ii) Reasonable scale – (1/2 mark each) ----------1

iii) 4 points correctly plotted - - - - 2 (deduct ½ mark for each wrong or missing point).

iv) Line of test fit - - - - - - 1

SLOPE (2 Marks) i) Large right angled triangle - - - ½

ii) ∆F correctly read and recorded - - ½

iii) ∆R correctly read and recorded - - ½

iv) ∆F/∆R correctly calculated - - - ½

PRECAUTIONS (2 marks) Award 1 mark each for any two correct precautions stated in acceptable language

i) 1 avoided parallax error when taking readings on the spring balance (award zero if avoid error due to parallax is used; and award zero if spring balance was not mentioned).

ii) 1 avoided zero error of spring balance .

Accept any other acceptable precaution stated in appropriate language.(b) i) Coefficient of static fraction is the ratio of frictional force to normal reaction between two surfaces in contact mark if two surfaces in contact was not mentioned)ii) M = 0.5kg, F = 2.5v, g = 10m/s F = UR = Umg

Or U = = 2 a) OBSERVATION (12 Marks)

i) Five values of Mo, (cm) read and recorded to 1 decimal place

ii) Five values of No (cm) read and recorded to 1 decimal place

iii) 5 values in trend increasing as recorded to at least 2 decimal place

iv) 5 values of cos

v) Five traces of the RN and NO with traces for the emergent and incident rays - -

vi) Correct unit for each quantity

vii) Constituency decimal place

GRAPH (5 Marks) i) Axes distinguished ½ mark each

ii) Reasonable scale (1/2 mark each)

iii) 5 points correctly plotted

iv) Line of best fit

SLOPE (2 Marks) i) Large right angled triangle

ii) ∆θ correctly read and recorded

iii) ∆θ correctly read and recorded

iv) ∆θ/∆θ correctly calculated

PRECAUTIONS (2 Marks) Award 1 mark each for any two correct precautions stated in acceptable language.

i) Error of parallax on metre rule

1 avoided zero error of spring balance .

Accept any other acceptable precaution stated in appropriate language.(b) i) Coefficient of static fraction is the ratio of frictional force to normal reaction

tween two surfaces in contact - - - 2 marks or zero (award 1 mark if two surfaces in contact was not mentioned) ii) M = 0.5kg, F = 2.5v, g = 10m/s

- - - - - 1 mark

= 0.5 ---------1 Mark OBSERVATION (12 Marks)

Five values of Mo, (cm) read and recorded to 1 decimal place

Five values of No (cm) read and recorded to 1 decimal place

5 values in trend increasing as θ increase of θ = correctly calculated and recorded to at least 2 decimal place--------2 marks

5 values of cos θ recorded to 4 decimal place---1 mark

Five traces of the RN and NO with traces for the emergent and incident rays - - - - 1 mark

Correct unit for each quantity - - 1 mark

cy decimal place - - - 1 mark

Axes distinguished ½ mark each - - 1 mark

Reasonable scale (1/2 mark each) - - 1 mark

5 points correctly plotted - - - 2 marks

Line of best fit - - - - - 1 mark

Large right angled triangle - - - ½

correctly read and recorded - - ½

correctly read and recorded - - ½

correctly calculated - - - ½

PRECAUTIONS (2 Marks) Award 1 mark each for any two correct precautions stated in acceptable language.

Error of parallax on metre rule was avoided

151

Accept any other acceptable precaution stated in appropriate language. (b) i) Coefficient of static fraction is the ratio of frictional force to normal reaction

2 marks or zero (award 1

1 mark

Five values of Mo, (cm) read and recorded to 1 decimal place----3 marks

Five values of No (cm) read and recorded to 1 decimal place-----3 marks

correctly calculated and

Five traces of the RN and NO with traces for the emergent and incident rays

1 mark

1 mark

1 mark

Award 1 mark each for any two correct precautions stated in acceptable language.

152

ii) I noted zero error of the metre rule

iii) I took repeated reading to ensure accurate result.

iv) I ensured that the normal is perpendicularly drawn to the rectangular block.

Take any other good precaution

b(i) Snells law of refraction states that the ratio of the sine of angle of incidence to the sine of angle of refraction is a constant for a given pair of media - - - - - - - 1mark

µ=rSin

iSin (a constant) - - - 1 mark

ii) Sin C = ga n

1

Sin C = 5.1

1 = 0.6666 - - - - - - - 1 mark

or C = Sin-1 0.6666 = 41.60 - - - - - - - - 1mark (3a) OBSERVATION (12 Marks)

i) Value of E read and recorded to 1 decimal place in volts - - 1 mark

ii) 6 values of V(v) read and recorded to 2 decimal place(trend V

increase as 1 increase, deduct ½ mark for missing value) - - 3 marks

iii) 6 values of 1 (A) read and recorded to 2 decimal point - - 3 marks

iv) Log I correctly evaluated - - 11/2 marks

v) Log V correctly evaluated - - - - 11/2 marks

vi) Correct unit for each quantity - - - - - 1 mark

vii) Consistency in decimal place - - - - 1 mark

viii) Composite table showing X,V,I, log I, Log V - - 1 mark

GRAPH (5 Marks) i) Axes distinguished ½ mark each - - - - - 1 mark ii) Reasonable scale ½ mark each - - - - - 1 mark

iii) 6 points correctly plotted (deduct ½ mark ) - - - 1 mark

iv) Line of best fit - - - - - - 1 mark

SLOPE (2 Marks)

i) Large right angled triangle - - - - ½

153

ii) ∆log I correctly read and recorded - - - - ½

iii) ∆log V correctly read and recorded - - - - - ½

iv) ∆Log I/∆Log V correctly calculated - - - - ½

INTERCEPT (2 Marks ) 1. Intercept C on the vertical axis

Correctly show - - - - - - - 1 mark

Correctly read - - - - - - - 1 mark

PRECAUTIONS (2 Marks) Award 1 mark each for any two correct precaution stated in good language such as: i) I made sure that the key was opened when the circuit was not in use to avoid running down the cell ii) I avoided error due to parallax when taking reading from potentiometer and/or voltmeter/ammeter. (Bi)T he brightness increases. This is because as the length x increases - 1mark Therefore the current that flows through it reduces while that through the bulb increases - - - 1 mark ii) Diode valve, rectifier, transistor - - - 1 mark each = 2

154

APPENDIX J

WEST AFRICAN EXAMINATION COUNCIL 2012 MAY JUNE SENIOR SCHOOL CERTIFICATE MARKING SCH EME O’ LEVEL PRACTICAL PHYSICS 1 (a) OBSERVATION (12 MARKS)

i) The 5 values of W1(N) measured and recorded to 2 decimal points - - - - - - - - 2 marks

ii) 5 values of W2 (N) measured and recorded to 2 decimal points intend as W1 increases W2 increases (remove ½ of mark for missing value - - - - - - - - 2 marks

iii) 5 values of W3 (N) measured and recorded to 2 decimal points (in trend increases as W1 and W2 increase) - - 2 marks

iv) 5 values of U (W1- W2) correctly evaluated -2 marks

v) 5 values of V (W1 – W3) correctly evaluated -2 marks

vi) Composite table of m,w1, w2, w3, u,v - 1mark

vii) Consistency in writing the decimal place - 1 mark

GRAPH (5 MARKS) i) Axes distinguished ½ mark each - - 1mark

ii) Reasonable scale ½ mark each - - 1 mark

iii) Five points correctly plotted - - - 2marks

iv) Line of best fit - - - - 1 mark

SLOPE (2 MARKS) i) Large right angled triangle - - - ½

ii) ∆V correctly read and recorded - - ½

iii) ∆U correctly read and recorded - - ½

iv) ∆V/∆U correctly calculated - - - ½


Award I mark each for any two correct precaution stated in acceptable language

i) I avoided error due to parallax when reading the spring balance

155

ii) I ensured that the suspended weight did not touch beaker or any, other good

precaution

Bi) Archimedes principle states that when a body is totally or partially immersed in a

fluid, (liquid or gas), it experiences an up thrust which is equal to the weight of the fluid

displaced. - - 2 marks

iii) Mass of brass = 20g = 0.02kg; Density of brass = 8.0 X 103 kg/m3

Volume = 33 /108

02.0

mkgX

kg

Density

Mass = = 2.5 X 10-6m3

upthrust = 2.5 X 10 X 8.0 X 103 X 10 - 1mark

= 20 X 10-3 N - - - - 1 mark 2a) OBSERVATION ( 10 MARKS)

i) The value of Vo read and recorded to 1 decimal place - 1 mark

ii) Five values of V recorded to at least 1 decimal place (deduct 1 mark for each missing

value trend –V increases as M increase - 3marks

iv) 5 values of V-1 recorded to at least 3 decimal points

(increases as M increase) - - - - 3 marks

v) Consistency in recording the decimal points - 1 mark

vi) Correct unit for each quantity - - - - 1 mark

vii) Composite table of m,v,v-1 - - - 1 mark

GRAPH (5 MARKS)

i) Axes distinguished ½ mark each - - - - 1mark

ii) Reasonable scales ½ mark each - - - 1 mark

iii) Five points correctly plotted (deduct ½ mark for each wrong plotting) -- -

- - - - - - - 2 marks

iv) Line of best fit - - - 1 mark

SLOPE (2MARKS)

i) Large right angled triangle - - - 1/2

ii) ∆V-1 correctly read and recorded - - 1/2

iii) ∆M correctly read and recorded - - ½

156

iv) ∆V-1/∆M correctly calculated - - - ½

EVALUATION (2 MARKS)

R=5-1 = 1/5 - - - - - 1 mark

Correct substitution and final answer - 1 mark

PRECAUTION (2 MARKS) 1 mark each for any two good precaution stated in correct

language.

1. I ensured that the syringe was vertically erect .

2. I avoided error due to parallax while taking reading from syringe and any other

good precaution.

Bi) Pressure ,volume (1mark X 2)

ii) Collision between gases and walls of the container - - 2 marks

3a) OBSERVATION (11 MARKS)

i) The value of I0 and V0 to 1 decimal place - - 1 mark X 2

ii) The value 5 for OP ie length in cm - - - 2marks

iii) 6 values of I(A) read and recorded to 2 decimal points (trend I increase as Op increase

deduct ½ mark for any missing value - - 2 marks

iv0 6 Values of V (v) recorded to 2 decimal points (trend increases as OP and I increase

deduct ½ mark for a missing value) - - 2 marks

v) Consistency in writing the decimal places - - 1 mark

vi) Composite table for OP, 1 and V - - - 1 mark

viii) Correct unit for each quantity - - - 1 mark

GRAPH (5 MARKS)

i) Axes distinguished ½ mark each - - - 1 mark

ii) Reasonable scale – ½ mark each - - - 1 mark

iii) Six points correctly plotted (deduct ½ mark for any wrong plotting -

- - - 2 marks

iv) Line of best fit - - - - - - 1 mark

SLOPE (2 MARKS)

i) Large right angled triangle

ii) ∆V correctly read and recorded

iii) ∆I correctly read and recorded

iv) ∆V/∆I correctly calculated

EVALUATION (1 MARK)

The value of V when I = 0 correctly read from graph


Any good precaution – 1 mark for two

i) I always removed the key when not taking reading to avoid running down the

battery

ii) I avoided error due to parallax when reading the me

Bi) it can be recharged

ii) It can maintain large current for a long time

iii) R = 90hms, r = 1 ohm, E = 2v

I =

V = IR = 0.2 X 9 = 1.8V

Potential Drop = 2 – 1.8V + 0.2V

i) Large right angled triangle - - - - - ½

V correctly read and recorded - - - - ½

I correctly read and recorded - - - - ½

I correctly calculated - - - - -

EVALUATION (1 MARK)

The value of V when I = 0 correctly read from graph 1 mark


1 mark for two

I always removed the key when not taking reading to avoid running down the

I avoided error due to parallax when reading the metre rule, ammeter

- - - 1 mark

ii) It can maintain large current for a long time - 1 mark

iii) R = 90hms, r = 1 ohm, E = 2v

0.2A - - - - - 1 mark

V = IR = 0.2 X 9 = 1.8V

1.8V + 0.2V - - - 1 mark.

157

½

1 mark

I always removed the key when not taking reading to avoid running down the

tre rule, ammeter

158

APPENDIX X

Summary of Sample Size used for Data Collection as Distributed in Sampled Education Zone, Local Government and Schools

Education

zone Local Govt.

Area School WAEC

2011 WAEC

2012 NECO 2011

NECO 2012

Total

Obollo Afor Igbo Eze N CSS Amufie 8 7 8 8 31 ISS Enugu Ezike 8 8 8 8 32 Igbo Eze S Iheaka GSS 8 8 7 8 31 CSS Iheakpu Awka 8 8 8 8 32 Udenu CSS Obollo aFor 8 9 8 8 33 CSS Ezimo Uno 7 9 9 7 32 Nsukka Nsukka STC Nsukka 8 9 8 9 34 NHS Nsukka 8 8 8 8 32 BSS Aku 8 8 8 8 32 GSS Aku 7 7 10 6 30 CSS Nrobo 9 10 7 8 34 CSS Nimbo 8 8 8 8 32 Enugu Isi Uzo CSS Umuhu 8 8 8 7 31 CSS Eha Ohuala 8 8 7 8 31 Enugu East GSS Abakpa 7 7 8 7 29 New Heaven BSS 8 8 8 8 32 Enugu North CSS Iva Valley 8 8 7 8 31 Urban GSS Enugu 8 8 8 8 32 Obollo-Afor Igbo Eze North CHS Ogrute 8 10 6 8 32 Udenu GSS Obollo Afor 8 8 8 8 32 BHS Orba 8 8 9 8 33 Total 166 172 166 164 668

159

APPENDIX W

Educational Zone Local government area

Total Number of School

Number of Sampled School

Enugu Isi Uzo

Enugu East

Enugu North

8

10 10

2

2 2

Nsukka Nsukka

Igbo Etiti

Uzo Uwani

24

15

13

2

2

2

Obollo Afor Udenu

Igbo Eze South

Igbo Eze North

16

9

23

2

2

2

Total 18

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