The significance of class size in student evaluations and motivation in introductory courses

Master Thesis

BA 399 MBA Research Project

Lincoln University, California Singidunum University, Belgrade

May 2009

The Significance of Class Size in Student Evaluations and

Motivation During Introductory Courses

Professor:

Pete Bogue

Author:

Ivan Paunovic

Significance of class size in student evaluations

2

Table of Contents 1. Introduction .......................................................................................................................................... 3

1.1 Definitions of Terms ...................................................................................................................... 3

1.2 Purpose of the Study ..................................................................................................................... 3

1.3 Delimitations ................................................................................................................................. 4

2. Review of the Literature ....................................................................................................................... 5

2.1 Importance of Small and Medium Sized Enterprises in Serbian Economy ................................... 5

2.2 SADSMEE and Entrepreneurship Development ............................................................................ 7

2.3 Class Size Reduction in Primary and Special Education ................................................................ 9

2.4 Class Size Effect in Higher Education .......................................................................................... 11

3. Research Design .................................................................................................................................. 15

4. Collection of the Data ......................................................................................................................... 17

5. Report of Findings ............................................................................................................................... 18

5.1 Testing hypothesis H1 ................................................................................................................. 18




6. Analysis of findings.............................................................................................................................. 22

7. Conclusions (and recommendations) ................................................................................................. 23

8. Bibliography ........................................................................................................................................ 24

9. Appendix ............................................................................................................................................. 25

9.1 Student evaluations of the course, material used, and professor .................................................... 25

9.2 Student motivation after successful completion of the course ........................................................ 27


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1. Introduction

1.1 Definitions of Terms

SME-Small and medium sized enterprises

SADSMEE- Serbian Agency for Development of Small and Medium sized Enterprises and

Entrepreneurship

RN-Republic network (that consists of regional agencies for SME development)

NBE-National bureau for employment

NBLM-National bureau for labor market

GFD-Government fund for development

EU-European Union

Privatization-The process of transforming the ownership over production assets from mainly

government to mainly private

GVA -Gross Value Added is a measure of the value of goods and services produced in an area or

sector of an economy

GDP-Gross domestic product

1.2 Purpose of the Study

During the early 2000s the unemployment rate in Serbia was growing year after year, because of the

rapid privatization, many people went to an early retirement or simply lost their jobs. The level of

unemployment is still one of the biggest problems of the contemporary economic policy in Serbia,

although it is in slow decline in recent years. The Survey rate of unemployment, according to the latest

disposable data, in Serbia in 2006 was 21,8% and is the largest in Europe. In EU 25 the average rate of

the survey of unemployment in 2006 was 8,7%, and in 2007 it was 7,1%. In Slovakia it was 11,3%, in

Poland 9,6%, in Croatia 9%, and in Hungary 7,2% (Serbian agency for development of small and medium

sized enterprises and entrepreneurship, 2007).

In 2002. the National bureau for labor market and Serbian agency for development of small and medium

sized enterprises and entrepreneurship, started conducting courses with the purpose of promoting

entrepreneurship as an alternative employment option to the growing number of unemployed people.

During the realization of the courses, one of the identified obstacles was that class size varied

significantly (from 3 to 89 students for the course “How to start a business?”). (Filipovid, 2005) The

question that emerged out of this situation was: Does class size affect the effectiveness of the courses?


4

Since the basic course has a motivational component in promoting new life options to unemployed, the

question has a important implications to government agencies. Effectiveness of the course is important

in meeting one of the major goals of SADSMEE: Development of entrepreneurship. The following 4

hypothesis are tested in this research:

H1: Student evaluations of the course are lower in the large classes.

H2: Student evaluations of material used are lower in the large classes.

H3: Student evaluations of professor are lower in the large classes.

H4: Students are less motivated about the subject matter in the large classes.

1.3 Delimitations

The findings in this paper cannot be directly used to make conclusions about class size effects in

environments that, in any sense, differ from the ones examined in this study.

Potentially useful data, about the number of students that actually started their own businesses in the

years after the completion of the course, were not collected because of the scope of this work. This data

would give us means to measure the effectiveness of these courses more accurately.


5

2. Review of the Literature

2.1 Importance of Small and Medium Sized Enterprises in the Serbian

Economy

The SME sector has become the most important part of the economy during the last 7 years, as

privatization started taking place rapidly. The SME sector has become dominant in almost all aspects of

business. In the year 2007 it created 65,5% of employment, realized 67,6% of the total turnover, and

58,3% of gross added value. In the period 2004-2006, the number of the employed in this sector has

increased by 15,7%, while in big companies it has decreased by 18,2%. While total employment has

decreased, entrepreneurial employment has increased by 2,2%. (Serbian agency for development of

small and medium sized enterprises and entrepreneurship, 2007)

(Serbian agency for development of small and medium sized enterprises and entrepreneurship, 2007)

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

2004. 2005. 2006. 2007.

54.70%59%

63.10% 65.50%

Employees working in SME


6


(Serbian agency for development of small and medium sized enterprises and entrepreneurship,

2007)

The SME sector is the more efficient part of the Serbian economy. Profitability rate in 2006 was 38,9%,

while the total for the economy was 36%. However, the prevailing influence of SME sector on total

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

2004. 2005. 2007. 2008.

68.20%65.50% 67.50% 67.60%

Turnover

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

2004. 2005. 2006. 2007.

51.80%54.10%

56.90% 58.30%

Gross Added Value


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profit of Serbia was a result of quick growth of GDP, and not of a decrease in labor expenses. (Serbian

agency for development of small and medium sized enterprises and entrepreneurship, 2007)

Regional structure of SME is characterized by disproportions between the City of Belgrade and the South

Backa region on one side, and the rest of the Serbia on the other side. Regional disproportions are

confirmed by all indicators. The measures for more balanced regional development of Serbia are

therefore especially focused on helping the SME development in underdeveloped municipalities.



2.2 SADSMEE and Entrepreneurship Development

During the late 2000, the Government of Serbia recognized the need for coordination of development

programs for small and medium sized enterprises. Consequently, in 2001 government founded an

agency: SADSMEE (Serbian Agency for Development of Small and Medium sized Enterprises and

Entrepreneurship). The Focus of the agency is on supporting, helping, advising, representing and

protecting the development and interests of SME’s. Also, it is identifying problems of SME’s, initiating

City of Belgrade42%

South Backa county11%

Other municipalities together, 47%

Regional structure of SME


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solutions to problems of founding new enterprises and accelerating the development of the existing

SMEs. (Serbian agency for development of small and medium sized enterprises and entrepreneurship,

2007)

The agency manages objectives and tasks set by its board of directors. It creates and implements

national strategy and development policies of SME, and implements the European charter on small

business, various donations and programs for SME development.

The realization of SADSMEE activities relies on intensive cooperation between the Republic network

(RN) members (these are regional agencies with headquarters in Subotica, Novi Sad, Zrenjanin, Sombor,

Belgrade, Zajecar, Uzice, Kragujevac, Nis, Krusevac, Leskovac, Vranje, Novi Pazar, Sabac). Regional

agencies represent an essential infrastructure for participation of both domestic and foreign institutions

and organizations, local self government, donors, banks and others to support the development of

entrepreneurship in Serbia. The users of SADSME services are public institutions, Republic network,

donating organizations, potential and existing SME and other corporate clients.

From the very foundation of the agency, a number of obstacles were identified regarding

entrepreneurship development: finance, government regulation, level of competitiveness of the

economy, low level entrepreneurship culture, low educational levels, outdated technology, lack of

management skills, low awareness of quality standards, and no infrastructure for SME development.


One of the most important issues was lack of knowledge and skills for running a business successfully,

and unawareness of the need for continuous education during a lifetime.

Large population of unemployed people on the payroll of the National bureau for employment, with a

tendency of growing further, called for a motivational seminar that would present to people alternatives

they have, such as entrepreneurship. GFD (Government fund for development) finances start-ups with

very favorable repayment conditions, and SADSMEE gives consultancy services for free.

During February 2002. National bureau labor market and SADSMEE started a cooperation regarding

entrepreneurship development. Part of this cooperation was the realization of courses in different areas

of business. The foundation course, and the most popular one was “How to start a business?”

The Course “How to start a business?” consisted of four parts:

1. Motivational introduction to entrepreneurship

2. Generation and evaluation of idea

3. Legal foundations for doing business

4. Methodology of writing business plans

5. Analysis of sources of finance

There is much space in the Serbian economy for new entrepreneurs. According to the business

demography data, analyzed by Eurostat, “birth” rate of firms in Serbia, in 2006, was 11,5% and the rate

of mortality 10,5%. The percentage of active firms which have survived during the first two years of


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business in Serbia was high, about 85%. These indicators are higher than in EU 27. “Birth” rate of

companies in EU 27 is 9,9%, and mortality is 8,3%, whereas the share of firms that survived the initial

two years of business was 77%. These statistics call for more institutional work on developing

entrepreneurial values in Serbia, so people would hopefully have less fear of failure. (Serbian agency for

development of small and medium sized enterprises and entrepreneurship, 2007)

2.3 Class Size Reduction in Primary and Special Education

Policymakers frequently express an interest in whether class size significantly predicts student

achievement in all levels of education. However, the literature is very inconsistent when it comes to

assessing effects of class size on educational outcomes. There is also a variety of indicator variables

used: academic achievement, discipline, grade retention, and attendance. Some studies found strong

evidence that economically disadvantaged students and those representing ethnic minorities tend to

perform better academically in smaller classes and demonstrate increased aspiration to attend college.

Substantial class size reduction rarely occurs on any significant scale because it is extremely expensive to

accomplish. (Zarghami & Schnellert, 2004)

There no better example of the trade-off between desire and fiscal reality than in California, where class

size reduction has been discussed and desired for years, but class size has inexorably increased

beginning in the 1970s. When school districts faced funding reductions, many found that incremental

increases in class size were more politically palatable than other possible cost-cutting measures. (The

California State University Institute for Education Reform, 1996)

No identifiable caseload size or administrative arrangement has consistently produced positive

outcomes for academic achievement of students with disabilities. However, smaller classes produced

fewer behavioral problems. Also, when caseloads were increased (from 3 to 35), a significant decrease

in student achievement was observed. (Zarghami & Schnellert, 2004)

There is not enough evidence to prove that class size reduction programs produce significant increments

in academic achievement of students with special needs, because other factors would also have to be

considered: methods of teaching, teacher’s qualifications and one-to-one tutoring. Teachers hired to

reduce class size must be certified and must demonstrate content-area competence before they are

brought on board merely to reduce class size.

Canadian research on grade 3 students’ achievement found that students’ sex, language and

socioeconomic background were all significantly associated with student achievement on the test. For

example, girls scored 3 points higher than boys. Grade 3 students whose second language was English

recorded performance 3 points lower than those whose mother tongue was English. Grade 3 students

whose parents were not involved with the school scored 1 point less than the rest. Students scored 1


10

point higher when taught by teachers who had more than 10 years of teaching experience in the lower

elementary school grades. Smaller class size, proxied by the number of Grade 3 students in the class, can

positively influence achievement. By adding 8 more Grade 3 students to a class, students performed

almost 1 point lower than students in classes of average size. Student characteristics account for 67% of

variation, classroom environment accounts for 20% of variation, and school environment or

neighborhood accounts for 13% of variation. While factors that students “bring to the classroom”

(natural academic ability, motivation), can explain the majority of student achievement, a surprisingly

large amount of variation was attributable to types of classes and schools. The influences of schools and

neighborhoods on child performance are particularly important from a policy perspective because they

are amenable to change through policy intervention. (Tremblay, Ross, & Berthelot, 2001)

Based on the data, a reference group was created to assess the impact on test scores of changes in

student, class and school characteristics. The reference group embodies the most common

characteristics of Grade 3 students: It represents an English speaking girl in a public school, with a

reference score of 51 out of 100 who is not in a split-grade class and whose school is located in an urban

neighborhood with a median household income of $42,500. The model developed for this study shows

how test scores change when a student’s characteristics deviate from that of the reference group.

(Tremblay, Ross, & Berthelot, 2001)

Grade 3 students’ achievement

Base test score for reference group 51

Student-level characteristics Change in base test score Sex(male) -3

English is the student’s second language -3 French immersion 0

No computer at home -3 Less than 100 books at home -3

Language other than English spoken at home -1 Parents not actively or somewhat involved with

school -1

Class level characteristics Teacher characteristics

More than 10 years of teaching experience 1 Comfortable with curriculum 1

Teaching practice1. 1 Class environment

Average number of grade 3 students in class+ 8 more Grade 3 students2.

-1

Limited access to computer in class 0 No access to computer in class 0

School-level characteristics School environment


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Small school-less than 230 students 0 Large school-more than 471 students 0

School neighborhood Rural3. -2

%of population with less than high school4. -1 Less than 0.6% of population are recent

immigrants5. -1

More than 8.2% of population are recent immigrants5.

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Median income6. 1 1. Change in student achievement when teachers followed the curriculum more closely by one

standard deviation. 2. Change in student achievement when eight more Grade 3 students are added. 3. Rural schools include those in towns, villages and other populated places with less than 1,000

population, and rural fringes of census metropolitan areas and census agglomerations that may contain estate lots and agricultural or underdeveloped land with a population density of less than 400 people per square kilometer.

4. Change in student achievement when the percentage of the population with less than high school graduation increases by 13 points.

5. Recent immigrants are those who entered Canada between 1991 and 1996. 6. Change in student achievement when median school neighborhood income is increased by $

10,000

(Tremblay, Ross, & Berthelot, 2001)

Great attention is paid to the Tennessee STAR project. A cohort of pupils and teachers at kindergarten

through to Grade 3 were assigned at random to three types of class within the same school: a small class

(around 17 pupils), a ‘regular’ class (around 23 students) and a regular class with a teacher- aide. In

brief, the researchers found that in both reading and math pupils in small classes performed significantly

better than pupils in regular classes, and children from minority ethnic group backgrounds benefited

most from small classes. In fourth grade the pupils returned to regular classes and the experiment

ended, but gains were still evident after a further three years, that is, grades 4-6. (Mosteller, 1995)

2.4 Class Size Effect in Higher Education

There is widely held belief in Canada today that small classes are better. It is assumed that the higher

amount and intensity of faculty-student contact results in better learning, especially higher order and

complex reasoning. Large classes, on the other hand, often involve lectures, little interaction, and

multiple choice examinations, and so, it is often felt, less learning.

Class sizes are used as an important indicator of an institution’s commitment to undergraduate

education or of the value system and priorities of the institution and the nature of the experience


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students will have. Some Canadian Universities have even developed policy guidelines that limit class

size in order to maintain consistent quality of education. Also, under public pressure, universities are

urged to develop performance indicators. Student/teacher ratios and class sizes are usual indicators of

instructional load or resources. (Gilbert, 1995)

Early research literature on class size showed a link between small classes and improved learning.

Although the literature suggests that class size alone has little or no impact on the acquisition of

substantive knowledge or academic skills, it also suggests that smaller classes are more effective than

large ones in motivating students, producing attitudinal changes and enhancing higher order thinking

and reasoning.

Class size research usually uses final course grades, standardized test scores or course evaluation data as

the outcome measures. In 1924, researchers compared the performance of students in a 100+ class

with a 40+ class in the same course. Students in the small class did slightly better on an essay and

midterm test, while students in the large class did slightly better on quizzes and the final examination.

Several other studies, however, have found that class size has little effect on common examination

results, especially when compared to instructor enthusiasm, organization and clarity. In the initial

research, when measures other than the standard academic achievement measures were used, class

size appeared to have some impact. Smaller classes were found to produce statistically significant

differences in problem solving, student attitudes to teaching and knowledge retention. The impact of

class size, it was suggested, depended in part upon the educational goal. If the acquisition of factual

knowledge was the primary objective, then size was not of great consequence. If higher level thinking,

application, motivation and attitudinal change were primary, then smaller classes were best. (Gilbert,

1995)

An examination of the relationship between class size and overall student evaluations for more than

4000 courses at 16 campuses in the United States has produced confusing results. The researcher found

that student evaluations became less favorable as class sizes approached 250, and then became more

favorable as class size went up from 250. A background variable that seemed to influence class size

effect was “year in university”. Researchers found that first-year college students prefer small classes

and upper division students prefer larger classes. Their conclusion was that experience in larger classes

resulted in stronger preference for larger classes. (Gilbert, 1995)

Despite a long-running debate over class size differences in the public school setting, very few studies

have assessed the impact of class size on the student learning experience in academic context.

University studies mainly focus on the relationship between class sizes and student’s performance as

means of predictor for effortful study behavior. These studies express pedagogical concerns about large

classes because students are more prone to distraction and feelings of anonymity, which can negatively

affect student achievement. Furthermore, small classroom community contexts often foster positive

teacher-student and student-student relationships that are more likely to enhance mutual

responsibilities for achieving learning objectives.


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It was measured that students in smaller groups spend significantly more time in spontaneous

interactive discussion.

(Laria & Hubball, 2008)

In large class size, three out of 150 students responded to the DQT by sharing their sense of direction.

The interaction between these students lasted 2 minutes and 30 seconds. None of the students

responded to interactive prompts QT 1, QT 2 and QT 3.

In the small class size, 11 out of 17 students responded to the DQT. Their interaction lasted 13 minutes

and 30 seconds. Students were actively involved in sharing their experience regarding their own

topographical orientation skills. At the QT 1, QT 2, and QT 3, 15 students interacted among each other

and with the instructor for a total of 37 minutes and 30 seconds. (Laria & Hubball, 2008)

These insights have important implications for curriculum design. Senior undergraduate students may

be better positioned to participate in large size classes, while enabling first and second year students to

strategically participate in small size class introductory courses, particularly when academic units are

facing decreasing budgets.

Wilson examined data on the first finance class in the university for the period of 6 years. It is a

foundation course required for all students. He discovered that there are good and bad times for the

course. Students who take sections that begin at 11:00am or 12:30 pm receive higher grades than their

colleagues, despite no differences in performance on the standardized exam. Further, students in night

0

5

10

15

20

25

30

35

40

Large Size Class Direct Question

Time

Large Size Class Question Time 1,2,3

Small Size Class Direct Question

Time

Small Size Class Question Time 1,2,3

Tim

e (i

n m

inu

tes)

sp

ent

in a

ctiv

e d

iscu

ssio

n


14

classes appear to outperform their daytime compatriots, but are not rewarded for it with higher grades.

Similarly, students in classes that are of longer duration but with fewer weekly meetings outperform and

are more satisfied than students in shorter, more frequent classes. Course grades, however, show

students are not rewarded for this superior performance. Increased class size is frequently seen as a

negative predictor for student performance, but this study shows that size does not matter in

performance, but is rewarded with higher grades. The status of the instructor is a significant variable,

but in a surprise result, adjunct lecturers outperform their full time tenured/tenure track colleagues in

imparting knowledge necessary for superior performance on the standardized exam. (Wilson, 2002)

(Wilson, 2002)


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3. Research Design

This research focuses on the effect class size has on student evaluations and motivation. This

phenomenon was evaluated through testing of four hypothesis. For the purpose of testing the null

hypothesis were created:

H10: Class evaluations of the course are not affected by the class size.

H11: Class evaluations of the course are negatively related to the class size.

H20: Class evaluations of material used are not affected by the class size.

H21: Class evaluations of material used are negatively related to class size.

H30: Class evaluations of professor are not affected by the class size.

H31: Class evaluations of professor are negatively related to class size.

H40: Class motivation is not affected by the size of the class.

H41: Class motivation is lower in larger classes.

The first three hypothesis were posed in order to prove whether class size affects student evaluations.

On the other hand, the fourth hypothesis was posed in order to prove whether class size affects student

motivation after the completion of the course. Student (potential entrepreneur) satisfaction and

motivation are essential to meet the goals of the education department. Two sample tests of hypothesis

were used to test these four hypotheses, along with a five-step hypothesis testing procedure.

(Douglas A. Lind, 2003)

Step 1: Posing null

and alternate hypotheses

Step2: Selecting a

level of significance

Step 3: Identifying

the test statistic

Step 4: Formulate a decision rule

Step 5: Take a sample, arrive at decision


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For the purpose of two sample analysis, two groups of samples were created:

Class size from 3 to 24, and

Class size from 28 to 48

Both groups had 30 or more samples which is a necessary requirement for the distribution to be normal.

These two groups were then used to compare whether evaluation and motivation differ in class size 3-

24 and 28-48.


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4. Collection of the Data

The data was collected during the regular activities of the education department of SADSME. It was

collected during the period of three years: from 2002 to 2005. Classes were held in various towns in

Serbia. Data for evaluations of the course, material and professor are in the table in Appendix 9.1. Data

for motivation of students after the course are in the table in Appendix 9.2. Since there was very low

response rate in some cases, only classes with response rate over 60% were considered as valid, and

included in the table.


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5. Report of Findings

5.1 Testing hypothesis H1

Class size Sample mean Sample standard deviation Sample size

3 to 24 4.06 0.34 30

28 to 48 4.05 0.31 32

The null hypothesis was that class evaluations of the course are not affected by the class size. In other

words, the difference of 0.01 in the mean grade between large and small classes was due to chance. The

alternate hypothesis was that class evaluations of the course are negatively related to the class size. We

let µL refer to the mean grade given by the large classes, and µ0 the mean grade given by the small

classes. The null and alternate hypothesis were:

H0: µL≥µ0

H1:µL<µ0

The significance level selected was .01. Z distribution was used as the test statistic. The alternate

hypothesis was set to indicate that the mean grade was lower when given by the large groups then by

the small ones. Hence the rejection region was in the upper tail of the standard normal distribution. To

find the critical value we placed 0.01 of the total area in the upper tail. This meant that .4900 (.5000-

.0100) of the area is located between the Z value of 0 and the critical value. Value located near .4900 is

2.33, so our decision was to reject H0 if the value computed from the test statistic exceeds 2.33. We

used the following formula to compute the value of the test statistic.

𝑍 =0 − 𝐿

𝑆02

𝑛0+𝑆𝐿2

𝑛𝐿

=4.06− 4.05

0.342

30 +0.312

32

=0.01

0.08= 0.125

The computed value of 0.125 was lower than the critical value of 2.33. Our decision was to accept the

null hypothesis. The difference of 0.01 in the mean grades given by the large and small groups was too

small, and has occurred by chance. The p-value for the test statistics was 0.4013, found by .5000-.0987.

The conclusion was that there is very high likelihood that the null hypothesis is true.


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3 to 24 4.33 0.39 30

28 to 48 4.29 0.27 32

The null hypothesis was that class evaluations of material used are not affected by the class size. In

other words, the difference of 0.04 in the mean grade between large and small classes was due to

chance. The alternate hypothesis was that class evaluations of material used are negatively related to

class size. We let µL refer to the mean grade given by the large classes, and µ0 the mean grade given by

the small classes. The null and alternate hypothesis were:

H0: µL≥µ0

H1:µL<µ0


hypothesis was set to indicate that the mean grade was lower when given by the large classes then by

the small ones. Hence, the rejection region was in the upper tail of the standard normal distribution. To

find the critical value we placed 0.01 of the total area in the upper tail. This meant that .4900 (.5000-

.0100) of the area was located between the Z value of 0 and the critical value. Value located near .4900

is 2.33, so our decision was to reject H0 if the value computed from the test statistic exceeds 2.33. We

used the following formula to compute the value of the test statistic.

𝑍 =0 − 𝐿

𝑆02

𝑛0+𝑆𝐿2

𝑛𝐿

=4.33− 4.29

0.392

30 +0.272

32

=0.04

0.09= 0.44

The computed value of 0.44 was lower than the critical value of 2.33. Our decision was to accept the null

hypothesis. The difference of 0.04 in the mean grades given by the large and small classes was too small,

and has occurred by chance. The p-value for the test statistics was 0.33, found by .5000-0.1700. The

conclusion was that there is very high likelihood that the null hypothesis is true.


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3 to 24 4.72 0.24 30

28 to 48 4.69 0.19 32

The null hypothesis was that class evaluations of professor are not affected by the class size. In other

words the difference of 0.03 in the mean grade between large and small classes was due to chance. The

alternate hypothesis was that class evaluations of professor are negatively related to class size. We let µL

refer to the mean grade given by the large classes, and µ0 the mean grade given by the small classes. The

null and alternate hypothesis were:

H0: µL≥µ0

H1:µL<µ0


hypothesis was set to indicate that the mean grade is lower when given by the large groups then by the

small ones. Hence the rejection region was in the upper tail of the standard normal distribution. To find

the critical value we placed 0.01 of the total area in the upper tail. This meant that .4900 (.5000-.0100)

of the area was located between the Z value of 0 and the critical value. Value located near .4900 is 2.33,

so our decision was to reject H0 if the value computed from the test statistic exceeds 2.33. We used the

following formula to compute the value of the test statistic.

𝑍 =0 − 𝐿

𝑆02

𝑛0+𝑆𝐿2

𝑛𝐿

=4.72− 4.69

0.242

30 +0.192

32

=0.03

0.06= 0.5

The computed value of 0.5 was lower than the critical value of 2.33. Our decision was to accept the null

hypothesis. The difference of 0.03 in the mean grades given by the large and small groups was too small,

and has occurred by chance. The p-value for the test statistics was 0.3085, found by .5000-0.1915. The

conclusion was that there is very high likelihood that the null hypothesis is true.


21



3 to 24 72.37% 15.31% 30

28 to 48 65.87% 9.46% 32

The null hypothesis was that class motivation was not affected by the size of the class. In other words

the difference of 6.5 % between large and small classes was due to chance. The alternate hypothesis

was that class motivation was lower in larger classes. We let µL refer to the mean motivation in large

classes, and µ0 to the mean motivation in small classes. The null and alternate hypothesis were:

H0: µL≥µ0

H1:µL<µ0


hypothesis was set to indicate that the motivation in large groups was lower then in smaller ones. Hence

the rejection region was in the upper tail of the standard normal distribution. To find the critical value

we placed .01 of the total area in the upper tail. This meant that .4900 (.5000-.0100) of the area was

located between the Z value of 0 and the critical value. Value located near .4900 is 2.33, so our decision

was to reject H0 if the value computed from the test statistic exceeds 2.33. We used the following

formula to compute the value of the test statistic.

𝑍 =0 − 𝐿

𝑆02

𝑛0+𝑆𝐿2

𝑛𝐿

=0.72− 0.66

0.152

30+0.12

32

=0.06

0.02= 3

The computed value of 3 was higher than the critical value of 2.33. Our decision was to accept the

alternate hypothesis. The difference of 6.5% between large and small classes was too large to have

occurred by chance. The p-value for the test statistics was 0.0013, found by .5000-0.4987. The

conclusion was that there is very little likelihood that the null hypothesis is true.


22

6. Analysis of findings

The first hypothesis (H1) was addressing the question whether evaluations of the course, done by

students change in large classes compared to small ones. This hypothesis was not proved, because the

difference between the mean grades in large and small classes was not statisticaly significant. That is,

the null hypothesis was accepted for hypothesis H1. Thus, it cannot be stated that class size affects

student evaluations of the course. In other words, class size does not affect student evaluations of the

course.

The second hypothesis (H2) was addressing the question whether evaluations of the material, done by

students, change in large classes compared to small ones. This hypothesis was not proved, because the



student evaluations of the material. In other words, class size does not affect student evaluations of

material.

The third hypothesis (H3) was addressing the question whether evaluations of the professor, done by

students, change in large classes compared to small ones. This hypothesis was not proved, because the



student evaluations of professor. In other words, class size does not affect student evaluations of

professor.

The fourth hypothesis (H4) was addressing the question whether motivation of students after the course

about the subject matter is lower in large classes than in small ones. The fourth hypothesis was proved,

because the difference between the mean motivation of large and small classes was statistically

significant. That is, the null hypothesis was rejected for hypothesis H4. Thus, it can be stated that class

size affects student motivation about the subject matter.


23

7. Conclusions (and recommendations)

Class size is not statisticaly significant factor in student evaluations. On the other hand, class size is

statistically significant factor in student motivation. Student motivation is lower in large classes. This has

implications for the conduct of all the courses by the education department of SADSMEE (Serbian

Agency for Development of Small and Medium sized Enterprises and Entrepreneurship). It means that

effectivenes of these courses is lower when the group is large (28-48 students). Especially, the

implications are strong for the conduct of the course “How to start a business?”, which was used to

collect the data. One of the main goals of this course is to motivate the unemployed citizens to consider

new employment options. Motivational component is very important in this course. Thus, a new policy

should be considered, that would keep the classes small (e.g. down to 24 students).

Potentially useful data, about the number of students that actually started their own business in years

after the completion of the course, were not collected because of the scope of this work. This data

would give us means to measure effectiveness of these courses more accurately.


24

8. Bibliography

Douglas A. Lind, W. G. (2003). Statistical techniques in business and economics. Singapore: McGraw-Hill

Education.

Filipovid, S. (2005). Едукација у републичкој агенцији ѕа МСПП-три године рада. Београд:

Републичка агенција ѕа раѕвој МСПП.

Gilbert, S. (1995). Quality Education: Does Class Size Matter? Research File .

Laria, G., & Hubball, H. (2008). Transformative Dialogues: Teaching & Learning Journal .

Mosteller, F. (1995). The Tennessee Study of Class Size in the Early School Grades. The Future of Children

.

Serbian agency for development of small and medium sized enterprises and entrepreneurship. (2007).

Annual report. Belgrade: FRAME art.

The California State University Institute for Education Reform. (1996). Is Less More? Exploring

California's New Class Size Reduction Initiative. The California Education Policy Seminar.

Tremblay, S., Ross, N., & Berthelot, J.-M. (2001). Factors affecting Grade 3 Student Performance in

Ontario: A Multilevel Analysis. Education Quarterly Review .

Wikipedia. (2009, April 13). Correlation. Retrieved April 14, 2009, from Wikipedia The free Encyclopedia:

http://en.wikipedia.org/wiki/Correlation

Wilson, A. (2002). Exogenous Determinants of Student Performance In First Finance Classes. Financial

Decisions .

Zarghami, F., & Schnellert, G. (2004). Class size reduction: No silver bullet for special education students'

achievement. 19.


25

9. Appendix

9.1 Student evaluations of the course, material used, and professor

Sam

ple

C

lass

siz

e

Res

po

nse

rat

e (%

)

A

vera

ge g

rad

e

for

the

cou

rse

A

vera

ge g

rad

e

for

the

mat

eri

al

Ave

rage

gra

de

for

the

pro

fess

or

1 18 72.22% 3.69 4.38 4.92

2 3 100.00% 5 5 5

3 5 100.00% 4.4 4.8 4.7

4 9 77.78% 4.2 3.71 4.81

5 48 75.00% 3.86 4.23 4.37

6 12 75.00% 3.78 4.44 4.56

7 35 80.00% 3.82 4.04 4.68

8 36 72.22% 3.84 3.8 4.45

9 36 63.89% 4.09 4.39 4.54

10 36 69.44% 4.08 4.26 4.84

11 20 80.00% 3.69 3.81 4.81

12 26 84.62% 3.55 4.05 4.47

13 12 91.67% 4.45 4.36 4.85

14 25 64.00% 4.13 4.53 4.93

15 15 80.00% 4 4.29 4.86

16 33 66.67% 3.48 3.75 4.48

17 27 70.37% 4.26 4.53 4.87

18 27 62.96% 3.76 4.14 4.71

19 29 100.00% 4.14 4.21 4.67

20 22 72.73% 3.86 4.53 4.96

21 16 100.00% 4.19 4.44 4.81

22 36 77.78% 4.04 4.62 4.8

23 26 80.77% 4.05 4 4.72

24 21 76.19% 4.19 4.31 4.85

25 36 80.56% 4.45 4.5 4.81

26 24 75.00% 3.47 3.47 4.56

27 23 82.61% 4.12 4.56 4.96

28 28 78.57% 3.71 4.27 4.42


26

29 21 80.95% 4.13 4.53 4.79

30 22 63.64% 3.71 4.62 4.95

31 30 70.00% 4.32 4.5 4.8

32 28 60.71% 4.25 4.19 4.44

33 35 77.14% 4.26 4.41 4.78

34 14 100.00% 4.82 4.54 4.79

35 29 86.21% 3.8 4.2 4.82

36 20 60.00% 4.42 4.67 4.92

37 28 75.00% 3.86 4.43 4.74

38 31 64.52% 3.7 4 4.34

39 31 67.74% 4.1 4.48 4.83

40 35 60.00% 3.95 4.11 4.86

41 30 66.67% 4.29 4.05 4.69

42 31 74.19% 4 4.48 4.5

43 35 60.00% 4.19 4.33 4.85

44 10 100.00% 4.1 3.8 4.65

45 19 68.42% 4.23 4.25 4.54

46 18 72.22% 3.85 4.54 4.85

47 27 70.37% 3.89 4.58 4.95

48 24 66.67% 4 4.38 4.81

49 30 70.00% 4.5 4.9 4.93

50 18 83.33% 3.73 4.2 3.89

51 27 100.00% 4.25 4.3 4.74

52 17 76.47% 4.15 4.92 4.92

53 30 60.00% 4.61 4.67 4.89

54 30 63.33% 3.71 4.16 4.68

55 22 90.91% 4.2 4.7 4.48

56 26 80.77% 4.29 4.43 4.76

57 17 88.24% 3.71 3.4 4.7

58 32 68.75% 4 4.27 4.88

59 43 76.74% 3.64 4.06 4.9

60 25 68.00% 4.31 4.38 4.76

61 20 60.00% 4.25 4.08 4.44

62 19 68.42% 3.82 4.75 4.47

63 20 70.00% 4.21 4.36 4.96

64 15 73.33% 3.82 4.22 4.45

65 8 62.50% 4 4.4 4.56

66 30 60.00% 4.41 4.94 4.87

67 26 61.54% 3.88 4.44 4.8

68 28 71.43% 3.95 4.3 4.77


27

69 36 83.33% 4.6 4.37 4.35

70 32 81.25% 3.6 3.88 4.48

71 28 60.71% 4.47 4.4 4.89

72 25 60.00% 4.07 4.27 4.76

73 31 61.29% 4.28 4.37 4.74

74 25 76.00% 4.21 4.47 4.75

9.2 Student motivation after successful completion of the course

After the course, my plans about future business are:

Sa

mp

le

C

lass

siz

e

I am

th

inki

ng

abo

ut

givi

ng

up

o

n m

y id

ea.

I am

dec

isiv

e ab

ou

t m

y p

lan

s.

I'm e

nco

ura

ged

eve

n f

urt

her

.

N

o r

esp

on

se.

D

ecis

ive+

en

cou

rage

d

(mo

tiva

ted

)

P

erce

nta

ge o

f

dec

isiv

e+en

cou

rage

d

(mo

tiva

ted

) st

ud

ents

1 18 1 5 7 12 66.67%

2 3 1 2 3 100.00%

3 5 1 4 5 100.00%

4 9 3 4 7 77.78%

5 48 18 16 2 34 70.83%

6 12 4 5 9 75.00%

7 35 1 12 15 27 77.14%

8 36 1 14 9 2 23 63.89%

9 36 7 14 2 21 58.33%

10 36 2 10 10 3 20 55.56%

11 20 10 4 2 14 70.00%

12 26 1 11 10 21 80.77%

13 12 4 7 11 91.67%

14 25 10 6 16 64.00%

15 15 1 6 4 1 10 66.67%


28

16 33 2 13 7 20 60.61%

17 27 1 5 13 18 66.67%

18 27 10 7 17 62.96%

19 29 1 12 15 1 27 93.10%

20 22 1 7 8 15 68.18%

21 16 8 8 16 100.00%

22 36 16 11 1 27 75.00%

23 26 14 7 21 80.77%

24 21 7 9 16 76.19%

25 36 9 19 1 28 77.78%

26 24 3 9 6 15 62.50%

27 23 8 9 2 17 73.91%

28 28 1 13 7 1 20 71.43%

29 21 1 8 8 16 76.19%

30 22 7 5 2 12 54.55%

31 30 7 13 1 20 66.67%

32 28 8 7 2 15 53.57%

33 35 8 18 1 26 74.29%

34 14 1 5 8 13 92.86%

35 29 12 11 2 23 79.31%

36 20 4 8 12 60.00%

37 28 1 9 7 4 16 57.14%

38 31 1 11 8 19 61.29%

39 31 2 9 10 19 61.29%

40 35 12 9 21 60.00%

41 30 12 8 20 66.67%

42 31 1 13 9 22 70.97%

43 35 11 10 21 60.00%

44 10 5 5 10 100.00%

45 19 1 8 3 1 11 57.89%

46 18 5 8 13 72.22%

47 27 6 13 19 70.37%

48 24 8 6 2 14 58.33%

49 30 9 10 2 19 63.33%

50 18 9 6 15 83.33%

51 27 8 19 27 100.00%

52 17 9 4 13 76.47%

53 30 11 7 18 60.00%

54 30 1 14 4 15 50.00%

55 22 18 2 18 81.82%

56 26 10 11 21 80.77%

57 17 8 7 15 88.24%


29

58 32 17 5 22 68.75%

59 43 15 17 1 32 74.42%

60 25 7 10 17 68.00%

61 20 4 8 12 60.00%

62 19 2 7 3 1 10 52.63%

63 20 4 10 14 70.00%

64 15 3 8 8 53.33%

65 8 1 3 1 4 50.00%

66 30 5 13 18 60.00%

67 26 1 8 6 1 14 53.85%

68 28 1 12 7 19 67.86%

69 36 3 16 10 1 26 72.22%

70 32 9 17 26 81.25%

71 28 5 11 1 16 57.14%

72 25 5 9 1 14 56.00%

73 31 7 11 1 18 58.06%

74 25 5 14 19 76.00%

The significance of class size in student evaluations and motivation in introductory courses

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