ED 063 804

AUTHORTITLE

INSTITUTION

SPONS AGENCY

BUREAU NOPUB DATEGRANTNOTE

EDRS PRICEDESCPIPTORS

IDENTIFIERS

DOCUMENT RESUME

24 EM 010 055

Thomas, Warren H.The Development of a statistical ExperimentSimulator. Final Report.State Univ. of New York, Albany. ResearchFoundation.Office of Education (DHEW) Wasliington D.C. Bureauof Research.BR-7-0581Jan 72OEG-2-9-420581-1047-010164p.

MF-$0.65 HC-$6.58*College Mathematics; *Computer Assisted Instruction;Computer Programs; Experiments; *ProgramDescriptions; *Simulation; statistical Analysis;*StatisticsApplied Statistics; *Statistical ExperimentSimulator; STEXSIM

ABSTRACTA Statistical Experiment Simulator (STEXSIM) has been

developed which permits one to stimulate on a digital computer a wideralge of experimental environments. As a teaching aid in appliedstatistics, it provides a means for an instructor to define acompletely crossed factorial model with up to seven fixed or randommain effects, three two-factor interactions, and one three-factorinteraction. A student designs an experiment which probes this modelin order to draw appropriate inferences. STEXSIM reads the design and"conducts" the experiment he has specified providing the resultant"observations" which the student then analyzes. This report discussesin detail the program including input specifications and outputinterpretation. Sufficient detail is presented to permit one to usethe model himself. (STEXSIM is programed in FORTRAN IV.) The reportalso describes the formulation, execution, and analysis of 30"student" experiments run using seven different "instructor" models.(Author/JY)

fra.

FINAL REPORT

Project No. 7-0581

Grant No. 0EG-2-9-420581-1047-010

42

-;

U.S. DEPARTMENT OF HEALTH,EDUCATION & WELFAREOFFICE OF EDUCATION

THIS DOCUMENT HAS SEEN REPRO-DUCED EXACTLY AS RECEIVED FROMTHE PERSON OR ORGANIZATION ORIG-INATING IT POINTS OF VIEW OR OPIN.IONS STATED DO NOT NECESSARILYREPRESENT OFFICIAL OFFICE OF EDU-CATION POSITION OR POLICY.

THE DEVELOPMENT OF A STATISTICAL EXPERUAMTI SIMULATOR.

Warren H. ThomasState University of New York at Buffalo

Buffalo, New York 14214

The Research Foundation of theState University of New York

P.O. Box 7126Albany, New York 12224

January 1972

U.S. DEPARTMENT OFHEALTH, EDUCATION AND WELFARE

Office of EducationBureau of Research

FINAL REPORT

Project No. 7-0581

Grant No. 0EG-2-9-420581-1047-010

THE DEVELOPMENT OF A STATISTICAL EXPERIMENT SIMULATOR

Warren H. ThomasState University of New York at Buffalo

Buffalo, New York 14214

January 1972

The research reported herein was performed pursuant to a grantwith the Office of Education, U.S. Department of Health, Education,and Welfare. Contractors undertaking such projects under Governmentsponsorship are encouraged to express freely their professionaljudgment in the conduct of the project. Points of view or opinionsstated do not, therefore, necessarily represent official Office ofEducation position or policy.

U.S. DEPARTMENT OFHEALTH, EDUCATION AND WELFARE

Office of EducationBureau of Research

ACKNOWLEDGEMENTS

The significant role of Mr. Ronald J. Mogavero in thedevelopment of the program methodology and the early development ofthe computer program is gratefully acknowledged. Similarly,recognition is due to Dr. Subhash C. Narula for his assistance ininterpreting the final results and his enthusiasm for participatingin the extension of this research.

The services of the CDC 6400 computer so essential to thesuccess of this project have been provided by the Computing Centerat the State University of New York at Buffalo.

3

CONTENTS

I.

II.

III.

SUMMARY

INTRODUCTION

A. ObjectiveB. The ModelC. Overview of Report..

DESCRIPTION OF STEXSIM MODEL

..

....

Page

1

2

2

6

10

11

A. Model Design 11

B. Input Specifications 26

C. Output Interpretation 34

IV. EXPERIMENTAL USE OF SIMULATOR 36

A. Description of Experiments 36

B. STEXSIM Results 40

C. Analysis of Results . IP41

V. CONCLUSIONS AND RECOMMENDATIONS . 45

VI. REFERENCES 47

APPENDICES

A. Glossary of Variable Definitions .

B. STEXSIM Program ListingC. Sample Input ListingD. Sample STEXSIM OutputE. Input for Experiments ConductedF. Student Output for Each of Experiments..G. Analysis of Variance Results

ii

485368707583128

LIST OF FIGURES AND TABLES

Page

Figure 1 Overview of Use of STEXSIM 4

Figure 2 Main Program MONITOR 13

Figure 3 Subroutine TRADJ 14

Figure 4 Subroutine LEVSEL 16

Figure 5 Subroutine RTRT 18

Figure 6 Subroutinc RINTER 20

Figure 7 Subroutine AMEAN 21

Figure 8 Subroutine OUTPUT 23

Table 1 Actual Error Standard Deviation 44

iii

I. SUMMARY

A Statistical Experiment Simulator (STEXSIM) has been developedwhich permits one to simulate on a digital computer a wide range ofexperimental environments. As a device to aid in the teaching ofapplied statistics, it provides a means for an instructor to define acompletely crossed factorial model with up to seven fixed or randommain effects, three two-factor interactions, and one three-factorinteraction. A student designs an experiment which probes this modelin order to draw appropriate inferences. STEXSIM reads the designand "conducts" the experiment he has specified providing the resultant"observations" which the student then analyzes.

STEXSIM performs as if it were an actual experimental setup butdoes so very rapidly and cheaply. Accordingly a student canexperience for a number of problems the complete design-expertment-analysis process. This coupling of design and analysis is rarelyachieved in a class in applied statistics. STEXSIM has the valuableadded benefit of the instructor, having defined explicitly theexperimental environment, being better able to interpret results tohis students because he knows the "true" effects.

The STEXSIM model has been programmed in Fortran IV for theCDC 6400 digital computer. Being in Fortran it can be run on nearlyany digital computer. This report discusses in detail the programincluding input specifications and output interpretation. Sufficientdetail is presented to permit one to use the model himself. Further-more the report describes the formulation, execution and analysis of30 "student" experiments run using 7 different "instructor" models.

II. INTRODUCTION

A. OBJECTIVE

The teaching of applied statistics is generally characterizedby the student being first presented with an introduction totheoretical considerations. To reinforce this understanding he isthen given sets of problems to solve using the methodology beingconsidered. Generally he is presented with s3ts of data which he isasked to analyze using the appropriate statistical proccdure. Alltoo often he is not even given the opportunity to select theprocedure, the choice being dictated by the nature of the topiccurrently being covered. Furthermore he is not given the opportunityto design the experiment which would generate the data which heanalyzes. At other times he is asked to design an experiment which,if executed, would permit the making of specified inferences.Unfortunately in this case he is usually denied the opportunity torun the experiment he has designed. The problem with this approachis the lack of coupling of the design phase with the analysis phase.The student is not faced with the complete task of firz.t decidinghow his data should be collected - what variables shoeld becontrolled, how many levels of each, how many observations, etc. -

and then having to analyze his own data once it has beeu gathered.The reasons for this lack of integration are not hard to find forclearly the high cost and excessive time required to accomplish theprocess of setting up and running actual experiments are generallyunacceptable for the usual class. It is recognized that students attimes do gain this experience on one problem in the course of a majorproject or thesis endeavor. However, even in this case his experienceis generally limited to a single problem.

The problem is clear: How can the experiment step in thedesign-experiment-analysis sequence be shorted at an acceptable cost?It has bee.i the objective of this research to search for a solutionto this problem. It is the task of this report to describe thesuccess of the search.

The approach taken has been to explore and exploit the role ofthe digital computer. Through the use of computer simulation,experiments can be modeled in a computer language which then replacesan analogous real-world situation.

Consider first the general role of simulation. Simulation hasbeen used for a variety of other modeling activities in which onerepresents the essence of a real-world system in the form of acomputer model. These include simulations of traffic systems,queueing systems, production scheduling systems, hospital outpatientsystems, etc. The models are developed as computer programs whichare then executed on a digital computer. Because of the highcalculation speeds of the digital computer, it is possible to "mimic"the actions of the real system using these models. Experiments which

evaluate alternative system designs and/or decision parameters can beconceived and tested in a relatively short period of time with neitherthe cost nor the disruption that would be incurred if the real systemitself were used. The extensive literature in this area attests tothe success and acceptance of this approach. A number of universitycourses have been developed to teach simulation as an analysis/synthesis technique.

However, there has been little utilization of simulation as apedagogical device; i.e., the use of simulation to aid in the teachingof some other subject rather than being the subject of instructionitself. The possible exception are management or business games.However, games do not contribute to the task of this research and arenot further considered.

The area in which the pedagogical possibilities of simulation arebeginning to be exploited are in the production-inventory area asillustrated for example by the simulator developed at Case WesternReserve University (ref. 7 ) and the PROS1M simulated developed atAuburn University (ref. 4 and 5 ). Students are presented withsymptoms and data rather than well defined problems. The simulatoris used by the students to diagnose the situation, formulate theproblem, construct appropriate models, organize raw data and developand experimentally test a solution. The purpose of the course inwhich such a simulator is used is to teach production and inventorycontrol, not simulation.

This research has taken an approach similar in philosophy butquite different in detail. A Statistical Experiment Simulator (STEXSIM)has been developed which permits an instructor to structure a problemenvironment and his students to examine this environment by means ofsampling experiments which the students themselves design.

The process is shown graphically in Figure 1. The experimentalenvironment is described to each student who tben decides how hewishes to design an experiment from which he can draw inferences aboutthe system being modeled. His design is entered in the form ofpunched cards to the STEXSIM computer model along with anotherpunched card deck which defines the instructor's model. The studentthen receives output from the model which represents data that hewould have received if he actually had run a real experiment. Hisresults are given to him as a computer listing showing the "obser-vation" resulting for each of the samples he has specified. Ifdesired, the output is also prepared in punched card form which canbe directly entered as data into a standard analysis computerroutine from which he can draw the inferences he desires. Thus thestudent is able to participate in both the design and the analysisphases with STEXSIM providing the vital integrating role.

Furthermore, the model generating the student's data iscompletely under the control of the instructor who can interpret tothe student the nature of his results. This complete knowledge of

3

Figure 1

Overview of Use of STEXSIM

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the "true" model is a feature never present in real worldexperimentation and is therefore one of the more powerful featuresof the STEXSIM approach.

Because these experiments are accomplished in a very shortperiod of time and at low cost, the student can be involved in thecomplete design-experiment-analysis process for a variety of problemsituations. Through this process, it is anticipated that there willbe improvement in both short term and long term retention of basicconcepts and understanding of various statistical methodologies.

5

B. THE MODEL

The STEXSIM computer model is designed to handle problems whichcan be cast in the form of a completely crossed factorial model;i.e., each level of one factor can be combined with all levels ofother factors. This permits use of the various analysis of varianceof cross-classification designs including such incomplete factorialdesigns as Latin square, Craeco-Latin square and other fractionaldesigns. The reader is assumed to be familiar with this area ofexperimental statistics as described for example in Johnson andLeone (ref. 3).

Up to seven main effects each at up to ten levels can beincluded. Three of these main effects (5, 6 and 7) may interactthus providing three possible two-factor interactions (5-6, 5-7 and6-7) and one three-factor interaction (5-6-7). The non-interactingfactors (1, 2, 3 and 4) generally serve the role of blocking factorswhose effects are to be removed from the residual error but whichare not of interest, per se, to the experimenter. However, thereis no reason why any of these four cannot be factors of principleinterest.

To produce a single observation, these main effects and inter-actions combine in a way depending on the instructor's model andstudent's experimental design. The instructor specifies his additivemodel while the student elects to use all or part of this model andspecifies how the treatment levels of the various active factors areto be combined to generate an observation.

For purpose of understanding the approach, consider the basicadditive model if there were only two active factors, A and B.

where g = overall mean

Ai

= incremental effect of ith level of factor A

= incremental effect of jth level of factor BBj

ABij

= incremental effect of interaction of A and Bcorrespondtng to level i of A and j of B

1= residual error associated with theleh observation

Yl = ltb observation of dependent variable y.

Certain commonly made assumptions underlie the philosophy of theSTEXSIM model. If a factor is fixed the sum of the incrementaleffects for that factor must sum to zero. If, for example, factor

6

Ai

A is fixed

r. A = 0all

If the experiment were repeated the same effects would be presentsince these are the only levels of interest.

On the other hand, if a factor is a random one, the variouslevel effects entering a particular experiment are mutuallyindependent random variables each selected from a normal distributionwith expected value zero and variance a'. If the experiment wererepeated a new set of effects would be present. For a particularexperiment, once selected the effects do not change. If forexample B were a random factor, the Bj's would be assumed to berandom variables selected from a normal distribution with mean zeroand variance a2 . However

E B 0all j

for the particular experiment since these are merely samples from alarger population.

Similarly for the two factor interaction, if both A and B arefixed factors, the incremental interaction effects do not changefrom experiment to experiment and

E AB = O.all i,j

On the other hand if either or both of the factors are random, theincremental effects are assumed mutually independent random vari4lesselected from a normal distribution with mean zero and variance a' .

AB

To each observation is added a term representing the residualerror el associated with the lth observation. It accounts for thevariability not otherwise accounted for by main effects and theirinteractions. Each is assumed to be a selection of a mutuallyindependent normally distributed random variable with mean zero andvariance a'

While the assumptions of whether a factor is fixed or randomhas a significant effect on the analysis of an experiment, as far asSTEXSIM is concerned, the only difference is in the manner in whichthe incremental effects are determined. STEXSIM's role is togenerate "observations" each of which is comprised of the additiveeffects described above. When generating en observation STEXSIMneeds to know only the incremental effect of each level of eachactive factor and interaction, but at that time is indifferent asto the source of those effects. These were defined earlier in theexecution of the experiment in one of two way. If factor is fixed,

7

the incremental effects are defined explicitly by the instructorfor each active level. If it is random the instructor specifiesinstead the standard deviation of the normal distribution (mean zero)from which incremental effects are sampled. This selection is done

once per experiment remaining constant throughout that experiment

once selected.

Similarly the incremental effects of an interaction of two orthree factors all of which are fixed are specified explicitly by

the instructor. If any of the factors are random, the instructorspecifies instead the standard deviation of the normal distributionfrom which the selection is made.

Note carefully that the specification of incremental effectsis the most significant feature of the STEXSIM approach. In "real

world" experimentation these effects are not subject to theselection of anyone but rather are inherently present to beestimated and interpreted but not to be manipulated. In STEXSIMhowever they are all fully under the control of the instructor.

Consider now the full capability of STEXSIM. As describedearlier an instructor can specify as active up to seven main effects(1,2,...,7) each of up to 10 levels (not necessarily the same foreach factor). Furthermore two-factor interactions 5-6, 5-7 and 6-7will be assumed present if both factors of the pair are active.Similarly the 5-6-7 three-way interaction will be active if thesethree factors are each active. Each of the seven factors declaredas active must be further declared as fixed or random. If fixedthe specific incremental treatment effects must be specified for all

levels; if random, the standard deviation for the normal distributionfrom which the effects are to be sampled must be given. For theactive interactions, specific incremental effects must be given iffixed; a standard deviation, if random or mixed.

In addition the instructor specifies the overall mean and thestandard deviation of the normal distribution from which the residualerror is to be selected.

A student specifies which factors he wishes to include and thetreatment level of each comprising each observation. Each observa-

tion is f;omputed from the additive model:

yl overall mean

+ E (effects of specified level of each active main effect)

+ E (effects of any active two factor interaction)

+ Li

(contribution from three factor interaction if active)

8

In the event that a ntudent has ignored a factor that actuallyAis active, STUMM will generate random sntections of levels of that

factor for each observation of the student. This occurs for examplewhen a student ignores a blocking factor ehereby confounding thatfactor's effect with the error term. The student would observe aninflated error term. This is analogous to what happens in actualexperimentation when an important factor is omitted from a design.

Once an experiment has been "run," STEXSIM transfers control toa report generator routine which provides extensive output to thestudent and his instructor describing the experiment that has beencompleted.

C. cramEw OF REPORT

Section III describes in detail the Trusrm model including thefunctions of various computer subroutines, how to input informationto the model and how to interpret the output generated by the model.Section IV presents a demonstration of the use of STEXSIM for sevendifferent "instructor" models and a total of 30 "student" experimentaldesigns using these models. The results of these experiments areanalyzed and discussed. Section V provides a summary of conclusionsfor this project and points the way towards the future researchpresently being planned.

The appendices contain a listing of the STEXSIM computerprogram plus detailed input and output for each of the experimentsand results of the analyses of variance.

a

III. DESCRIPTION OF STEXSIM MODEL

A. MODEL DESIGN

The basic STEXSIM model is composed of a main program MONITORwhich calls on any of six subroutines and two functions in the courseof executing each student's experimental design. The entire model iswritten in the Fortran IV programming language for execution on theCDC 6400 computer at the State University of New York at Buffalo.

It is the objective of this section to describe in general foreach of the several routines, its function, the conditions under whichit is called and the information communicated to and returned fromthe routine.Appendix A summarizes the definition of each key variablewhile Appendix B provides a complete Fortran 17V program listing. Flowcharts are provided for MONITOR and each subroutine.

1. Main ProBram MONITOR

a. Purpose: MONITOR provides overall control of the executionof STEXSIM. It causes an instructor's model to be readfollowed by the specified number of student "experiments."For each such experiment a variety of experiment definitiontasks are accomplished after which the requisite number ofobservations are generated for transmission to the OUTPUTprogram. All input to any phase of STEXSIM is via MONITOR.Similarly, any subroutine is called only by MONITOR, neverany other subroutine. Therefore MONITOR is central to thesequence of execution of STEXSIM.

b- 11011:

From punched cards: See input specifications in Section IIIB.

c-

Since all subroutines are called by MONITOR, see the inputspecifications for each such subroutine.

d. Procedure: The general sequence of activity is that theinstructor's model is read in (the contents for which arespecified in Section IIIB) followed by a set of studentexperiments (contents also specified in Section IIIB).Depending on the nature of the experiments, subroutinesLEVSEL, RTRT, RINTER may be called. TRADJ will then beenlled for each experiment. Finally for each observationrequested AMEAN will be called to create the deterministiccomponent of the observation. Once the experiment has been

executed the results are punched and printed by subroutineOUTPUT. When the last student's experiment has beencompleted, a new instructor model, if any, is read.Figure 2 shows a flow chart of the logic flow in MONITORwhile the program can be found in Appendix B .

2. Subroutine TRADJ

a. Ptrpose: Subroutine TRADJ is called by MONITOR exactly once

for each student experiment. When a student requests for afixed factor a fewer number of levels than provided by theinstructor, an adjustment is made of the overall mean and

various treatment effects in order to insure a zero sum of

the "true" effects of the treatments included by thestudent. This in no way affects the value of the dependentvariable, y, that is generated but is provided to theinstructor in his detailed output solely in order that he

might have information as to the exact values of mean and

treatment effects being estimated by the student.

b. Input:

By argument: FMU

by common: IACT(7),IFLAG(7),LI(7),LS(7),AI(7,10),LEV(I,K),BI(3,10,10),CI(10,10,10)

c. Ouqut:

By argument: IOUT,FMSS

By common: AS(7,10)0S(3,10,10),CS(10,10,10)

d. Procedure: The general logic is described in the flow chartof Figure 3 . An adjustment of the overall mean and incre-mental main factor treatment effects .;.s made when the factoris fixed and the student requests fewer levels than providedby the instructor. Similarly for the possible two factorinteractions an adjustment is made when both factorsentering the interaction are fixed and active and the studentrequests for one or both a number of levels less than

provided by the instructor. In like manner an adjustment ismade for the three factor interaction if required. If for

any fixed active factor the student maximum level (LS(I))exceeds the instructor level (LI(I)), the variable IOUT isset equal to 2 and an error return occurs. Upon return toMONITOR this will cause the termination of the execution ofthe particular student experiment in which it occurred.

3. Subroutine LEVSEL

a. Purpose: Subroutine LEVSEL is called by MONITOR whenever a

12

Figure 2

Maim Program MONITOR

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Figure 3

Subroutine TRADJ

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factor (fixod or random),specified by the instructor asactive, is declared inactive by ehe student. For eachobservation of the student the subroutine will assign foreach such factor a level selected randomly from theinterval 1 to the number of levels specified by theinstructor. This selection will not be known to the studentbut will bu printed for the instructor. As whenever anexperimenter fails to include in his design a relevantfactor, this selection will not be measurable by the studentbut rather contributes to the residual mean square in hisanalysis.

b. Input:

By argument: J,NRUN

By common: LI(7),LEV(7,10)

C. Output:

By argument: none

By common: IW(200,7),LEV(7,10),LS(7)

d. Procedure: For factor J for which the subroutine is enteredan equally probable random selection is made from the set ofinteger values, 1,2,...,LI(J). This selection made oncefor each of the NRUN observations requested by the studentis entered into IW(200,7) which contains the treatment levelsfor each of 7 main effects for each of the NRUN 200)observations. An error message is printed if for some reasona level selection is not successful; the level is set at 10and execution continues. The seed number for the randomnumber generator used in this subroutine is defined withinand used exclusively for this subroutine. Figure 4contains a flow chart for this subroutine.

4. Subroutine RTRT

a. Purpose: For every main factor declared random by theinstructor, subroutine RTRT is called by MONITOR to selectthe treatment effects which are used in the student'sexperiment. These effects remain constant for the durationof a student's experiment. A new student's experimentwill, however, receive a new (and presumably different)selection of treatment effects. The standard deviation ofthe normal distribution from which the selection is made isspecified in ehe instructor's model. Subroutine RTRT isentered whether or not fhe student has declared ehe factoractive. In the latter case LEVSEL would have first beenentered.

15

.ZO

Figure 4

Subroutine LEVSEL

21 16

b. Input:

By argument: J

By common: LI(7),STD(J),FLIM(11,2)

C. Output:

By argument: none

By common: AI(7,10)

d. Procedure: One selection is made for each of the LI(J)active levels of factor J. Each selection is made randomlyfrom a normal distribution with mean zero and standarddeviation, STD(J). Any sample not within the minimum andmaximum specified by the instructor (Kum(J,l) and KLIM(J,2))is rejected and another selection made. In the event that anac%;eptable sample is not generated in 1000 trials an errormessage is printed and execution returned to MONITOR. Theseed number for the random number generator used in RTRT isdefined within and used exclusively for this subroutine.Figure 5 contains a flow chart for this routine.

5. Subroutine RINAR

a. Purpose: Subroutine RINTER is called by MONITOR for eachactive two factor interaction (5-6,5-7,6-7) and the threefactor interaction (5-6-7) if any of the factors are random,i.e., it is entered for mixed and random models. Its

function is identical to that of RTRT except the number oftreatment effects selected equals the product of the numberof levels of each factor involved in the particular inter-action.

b. Input:

By argument: K

By common: LI(7),STD(J),FLIM(11,2)

c. Output:

By argument: none

By common: BI(3,10,10),CI(10,10,10)

d. Procedure: K determines the interaction being considered.

Figure 5

Subroutine RTRT

Do

I 114

STD OILV: DO)

18

.23

MAtct W6wSe 4.-gc-re rJ

CS A

opioovriciALs

interaction

8 5-6

9 5-7

10 6-7

11 5-6-/

For the two factor interaction I-J(Km8,9,10),LI(/)*LI(J)selections are made from a normal distribution with meanzero and standard deviation STO(K). For the three factorinteraction (Kpl1),LI(5)*LI(6)*LI(7) selections are madefrom a normal distribution with STD(11). As in RTRT aselection is rejected if it does not fall within the rangespecified by the instructor (KLIM(K,1) to KLIM(K,2)). The

seed number for the random number generator used In RINTERis defined within and used exclusively for this subroutine.The flow chart for this subroutine can be found inFigure 6 .

6. Subroutine AMEAN

a. Purpose: Subroutine AMEAN is called by MONITOR once for eachof the NRUN obsnwations requested by the student. This

routine generates the portion of each dependent variablebefore the error component is added. It adds to the overallmean the specific treatment effects for the levels of each

factor that comprise each observation (specified by studentor generated in LEVSEL).

b. Input:

By argument: L(observation index),FMU

By common: IACT(7),IW(200,7),AI(7,10),BI(3,10,10),CI(10,10,10)

c. Output:

By argument: FMS

By common: none

d. Procedure: This subroutine proceeds by first setting FMSequal to the overall mean, FMU, and then adding to it theappropriate incremental treatment effects of each activemain effect factor and active interaction. The flow chart

is shown in Figure 7 .

7. Subroutine OUTPUT

a. Purpose: Subroutine OUTPUT is called by MONITOR after allrequested observations are generated in order to print out

19

Figure 6

Subroutine R1NTER

,25 20

Figure 7

Subroutine AMEAN

DO Fait eAcHMAW

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results and, if requested, to punch out a card deck of

experimental results.

b. Input:

By argument:

By common:

C. Output: (not

By argument:

By common:

NST,NRUN,FMIJ,FMSS

PUNSW,YD(200) $ IWI (200,7) ,NAME(80) ,ISW,TW(200,7),IACT(7),IFLAG(7),LI(7),INCLD(7),KEY(7),LS(7),LEV(70.0),AI(70.0),BI(30.00.0),CI(l0,10,10),SIGMA,AS(70.0)

including punched and printed output)

none

none

d. Procedure: No calculations are made in this subroutine.Rather it is devoted exclusively to the punching and printingof results for a single student's experiment. Punching iscontrolled by the first data card of the instructor's model.If it contained the word PUNCH, punching is accomplished; ifany other alphanumeric quantity, punching is bypassed. Thepunched deck with one card per observation can be used bythe student as data input to a computer analysis routine.One section is printed to be gtven to the student showingfor each requested observation, the factor levels requestedand the resultant dependent variable. Levels selected byLEVSEL for acttve factors ignored by student are not shown.A second section is printed for the instructor listing thesame information prepared for the student plus extensiveinformation for the instructor as to various modelconditions entering into the generation of the student'sobservations including factors selected by LEVSEL, treatmenteffects for active fixed and random factors, etc. Theoutput format is described in detail in Sectian IIIC. A flowchart of this subroutine is in Figure 8 .

8. Function FNORM

a. purpose: Function FNORM provides a single random selectionfrom a normal distribution with mean zero and standarddeviation SIGMA utilizing as the seed variable NSEED. Itis called for each observation by MONITOR in order to providethe residual error component. It is also called by RTRT andRINTER to provide selections of treatment efftnts for randomfactors and random and mixed interactions.

22

:41

Figure 8

Subroutine OUTPUT

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V

IA A I rut Pito

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aro, (A

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28 ; ;23

b. kaat:

By argument: SIGMA,NSEED

By common: none

C. Output:

By function name: FNORM

By argument: NSEED

By common: none

d. Procedure: The method usedvariates is that attributedNo flow chart is required.in Appendix B .

9. Function RND:_

for the generation of normalto Box and Muller (ref. 1 ).The program is listed however

a. yurpose: Function RND provides a sample from a distributionuniformly distributed on the interval 0 to 1.0. It iscalled whenever a random number is required either directly(as in LEVSEL) or for transformation to another variate ofinterest (as FNORM).

b. Input:

By argument: NSEED

By common: none

c. Output:

By function name: RND

By argument:

By common:

NSEED

none

d. Procedure: The method used is the commonly used multi-

plicative congruential method (as discussed for example inNaylar et al, ref. 6 ). NSEED is multiplied by a constantto provide an integer value which is then scaled by 2-48 inorder to provide a value in the unit interval. The integerresult of this multiplication becomes the new value ofNSEED which is returned to the calling routine. In this wayindependent random number streams can be provided to each ofany number of calling routines.

24

CAUTION: This routine is machine dependent as are all pseudorandom number generators in use today. This particularroutine was developed by the principle investigator for theCDC 6400 computer at the State University of New York atBuffalo. Hence it will operate satisfactorily only on thismachine which, although having 60 bit word, is effectively a48 bit one because of ehe manner in which fixed pointmultiplications are accomplished. Therefore, this routinemust be replaced by one appropriate for the local implementationof STEXSIM.

B. INPUT SPECIFICATIONS

Input to STEXSIM includes a set of cards (Set A) provided by theinstructor to define the statistical model and to specify certainother run defining variables. This set is followed by one set (Set B)for each student's experimental design to be run utilizing thestatistical model of Set A. Up to 99 student designs can be runsequentially for a given model. Any number of models may be stackedto run sequentially. Each Set A will be followed by as many (s 99)student designs (Set B) as desired. Any model of up to 7 fixed orrandom factors each with up to 10 levels may be defined in card Set A.The STEXSIM computer model itself need never be altered; all changesare made via data cards. Reference to the sample inpUt listing inAppendix C should help clarify the specifications below.1. PUNCH CONTROL

To provide control over the punching of output the first datacard must contain either of the following words commencing in cardcolumn 1

PUNCHNO PUNCH

In the case of PUNCH, each student's output will be provided in punchedcard as well as printed form. If NO PUNCH, only printed output willbe provided. An appropriate message is printed on the output sheetsso that the student will know whether or not he should expect punchedoutput. A single punch control card controls punching for the entirerun of STEXSIM, i.e. it cannot be changed from one model to anotherexecuted in a single computer run.

2. INSTRUCTOR SET A

For each model, the instrucLor provides the following set ofcards in the order presented.

Card 1 - Model definition card

There must be exactly one card type 1 containing the followinginfornation.

a. Columns 1 to 7 specify

Column

which factors are active.

Factor1 1

2 23

4 45 56 67 7

26

In each column a

1 denotes an active factor and a2 denotes an inactive factor.

These are read with 711 format into IACT(I),I=1,7.

b. Columns 8 to 14 specify whether each factor is fixed orrandom.

Column Factor8 1

9 2

10 311 412 5

13 6

14 7

In each column enter a

1 if the corresponding factor is fixed2 if it is random or if it is not active.

These are read under 711 format into IFLAG(I),I=1,7.

c. Columns 15 to 28 specify the number of levels of each of theactive factors.

Columns

Each factor can have a maximum of 10 levels.

Factor15-16 1

17-18 2

19-20 3

21-22 423-24 525-26 627-28 7

The integer number of levels should be right justified within theappropriate two column field. For inactive factors blanks or anynumeric quantity may be specified.

These are read in 712 format into LI(I),I=1,7.

d. In columns 29 to 38 the overall mean is entered. Thisquantity is read into variable FMU using an F10.4 format.If the decimal point is punched in the card, the field mayfall anywhere within columns 29 to 38. Otherwise the F10.4format must be strictly adhered to.

e. Card columns 39-40 specify how many student designs (Sets B)follow this Set A. The quantity must be integer and rightjustified. (It is read with 12 format into NSTUD).

The information on this card defines which of card types 3

27

through 8 will next be read.

Card type 2 - Fixed main effect

There will be one card type 3 for each active main effect factorwhich is fixed. These cards are arranged in increasing order offactor index I (I = 1,2,..,7). Within a card, the incremental effectsfor that factor are entered in 10F8.4 format.

Columns Effects for level1-8 1

9-16 2

17-24 3

25-32 433-40 5

41-48 6

49-56 7

57-64 865-72 973-80 10

If the decimal point is punched, entries may be anywhere within theappropriate 8 column field. Otherwise, the F8.4 format must bestrictly adhered to.

These are read into AI(I,J),3=1,LI(I)

Statistical theory requires

LI(I)E AI(I,J) = 0 for all IJ=1

Card type 3 - Fixed two factor interaction

There will be one set of cards type 3 for each interaction of twofixed main effect factors. Since Factors 5, 6 and 7 are the onlyfactors which may interact, the only two factor interactions possibleare 5-6, 5-7 and 6-7. STEXSIM will read sets of type 4 cards wheneverboth main effects of each of these three possibilities is active. Evenif one of these interaction effects is not desired, if the two factors(5, 6 or 7) making it up are active, type 4 cards will be read inwhich case zeroes must be entered.

For interaction 1,3 (I,J=5,6,7;IM provide one card for each level offactor I. On each card enter in 10F8.4 format the incremental effectscorresponding to each of the levels of factor J. Hence, there will beLI(I) cards each with LI(J) entries for interaction I,J.

This is repeated for each of the interactions 5-6, 5-7, and 6-7 inthat order when active. Note that the summation over levels of I fora particular level of J must equal one as must the summation overlevels of J for a particular level of I.

28

"AS

This data is read into BUIC,143,1,4),L4.1,LI(J);L3=1,LI(I)where

IC = 1 if 1=5, JE12 " 1.5, J.7

J.7

Card type 4 - Fixed three factor interaction

There will be at most one fixed three factor interaction which occursonly when factors 5, 6 and 7 are each active and fixed. Each entry onthe data cards is the incremental effect corresponding to eachcombination of levels of factors 5, 6 and 7. There must be one cardfor each combination of levels of factors 5 and 6. Lettimg L5 denotelevel of factor 5 and L6 levels of factor 6, these cards ara in orderof L6 indexing within index L5 (i.e. 1-1, 1-2, 1-3, 2-1, 2-2 etc.).There will be LI(5)*LI(6) data cards each containing LI(7) entries.Each such entry represents the increment effect corresponding to theL7'th effect of factor 7, L5'th of 5 and Leth of 6. This data mustbe in F8.4 format.

This data is read into CI(L1,L2,L3),L3=1,LI(7)L1=1,LT(S) and1.2=1,11I(6).

Statistical theory requires zero summation over any index of CI foreaeh combination of all levels of the other two.

STEKSIN will read LI(5)*LI(6) data cards.

Card type 5 Random main effect

There will be one card type 5 for each random main effect I,1=1,...,7. Each contains three quantities.

Column Content1-8 FLIM(I,1)9-16 FLIM(I,2)17-24 STD(I)

read in 3F8.4 format.

STD(I) is the standard deviatian corresponding to factor I. Theseare used at the time of selecting dae set of treatment effects fcm aparticular student's experimental design. The effects, for as manylevels as requested by the student, are selected trom a normaldistribution with expected value zero and standard deviation STD(I).

FLIM(I,1) is the lowest allowable value of eaeh treatment effect forfactor I while FLIM(I,2) is the upper limit. Any selection from thenormal distribution which does not fall within these inclusive limitsis discarded. This provides a means for preventing extreme values fromcontaminating an experiment.

29

These cards are to be in order of index I (1,2,...,7).

Card tzati. - Random or mixed two factor interaction

One card must be provided for each active two factor interactionwhere both factors are random (random model) or where one is fixed

and one random (mixed model). The content and format is identi

to Chat of card type 5; namely

Column1-8

9-1617-24

read in 3F8.4 format where

ContentFLIM(I,1)

. FLIM(I,2)STD(I)

I = 8 if factor 5 and 6 both active and at least one is random

I = 9 " " 5 If 7 II II II II 11 11 9 II

I = 10 " " 6 " 7 " II II 9 II II 9 I1

These cards, if present, are to be in the above order.

Card type 7 - Random or mixed three factor interaction

There will be exactly one card of type 7 if and only if factors 5, 6

and 7 are all active mnd at least one is random. The format is

identical to card types 5 and 6 with I=11.

Card 8 -

There mus

Error definition card

t be exactly one card type 8.

a. In column 1-8 in F8.4 format the error standard deviation(SIGMA) is punched. In arriving at a particular observatianrequested by a student, to Che sum of various incrementaladditive effects (main and interaction), there is added avariate selected from o normal distribution with mean zeroand standard deviation, SIGMA.

b. Column 9-16 contain the seed number for the r,ndam numbergenerator which generates the error deviates. This quantity

is read into NSEED. Since it is read in I10 format this

quantity should be right justified.

The occurrence of this card denotes the end of the set ofcards defining the instructor's model (Set A). Following

this are NSTUD sets of Set B defining eaeh student'sexperimental design.

3. STUDENT SET 11

Each student's oxperimental design is comprised of the followingcards.

Card 1 - Identification

The first card of each student Set B is an identification card. Allinformation in columns 1-80 is printed on the output reports and ispunched in the corresponding punched output deck to provide identifi-cation information. Exactly one card must be provided.

Card 2 - Desi n definition card

There will be exactly one card type 2 defining the nature of thestudent's design.

a. Columns 1 to 7 specify which factors are acttve.

Column Factor1 1.

2 2

3 3

4 4

5 5

6 6

7 7

In each column a

1 denotes a factor included in the student's design2 denotes a factor dhat is not included.

These are read with 711 format into INCLD(I),I=1,7.

b. Columns 8 to 14 specify whether the student deems eaeh matneffect factor active or random.

Column Factor8 1

9 2

10 3

11 4

12 5

13 6

7

Enter in each column a

1 if the corresponding factor is considered fixed2 if the factor is assumed random or if it is not active.

These are read in 711 format into KEY(I),I=1,7. Note that thisvariable is used solely to print out the student's assumption butdoes not affect the execution of the model in any way.

31.

c. Enter right justified in columns 15-19 the number ofobservations which are requested. This is read in 14format into variable NRUN. NRUN must not exceed 200.

Card type 3 - Factor level definition

There will be one card for each mein effect factor acttvely enteringthe student's design. There is one card for each factor used by thestudent whether or not that factor is defined by ehe instructor asactive. These are to be ordered in sequence of increasing factoridentification 1,1=1,7.

Column 1-2 contains (in 12 format) the number of levels of thecorresponding factor I which is read into LS(I). The next LS(I) twodigit columns contain the identification of each of these ISMlevels. This defines the levels which will be encountered on theobservation definition cards (type 4). These entries must be rightjustified.

Column Identification of level3-4 1

5-6 2

7-8 3

9-10 4

11-12 5

13-14 6

15-16 7

17-18 8

19-20 9

21-22 10

Only the first LS(I) levels should be defined.These are read into LEV(I,J),J=1,LS(I).

If student specifies more levels than does the instructor(LS(I) > LI(T)) and if the instructor defines factor I as fixed, anerror will be generated and the execution of this student's designwill be aborted.

Card type 4 - Observation definition card

There must be NRUN (specified on card 2) observation definition cards.Each card deftnes for each observation the levels of each of thefactors deemed active by the

Column

student.

Levels for factor1-2 1

3-4 2

5-6 3

7-8 49-10 5

11-12 6

13-14 7

32

These are read in 712 format (and hence must be right justified)into variable

IW1(L,I) for 1=1,7 andipl,NRUN

IW1(L,I) 5: LS(1)

One observation of the dependent variable is generated by STEXSEMfor each observation requested by a definition card. Theseobservations are generated from the levels of tbe independentvariables (factors) requested on that card. These cards should bein the sequence in which dhe student wishes to obtain hisobservations. This is the point at which randomization should enter.There must be exactly NRUN type 4 cards.

3 3

.3s

C. OUTPUT INTERPRETATION

Upon completion of execution of each student "experiment"STEXStM produces two sets of output, one set for the student andone for his instructor.

1. OUTPUT FOR STUDENT

The student is provided with a printout showirg for eachobservation he has requested the levels of each of the factors he hasdeclared active (this is taken directly from the student's inputdeck) and the resultant observation generated by STEXSIM. His outputsheet will be headed by a label containing the information in thestudent's identification card (card 1). Appendix D1 contains atypical such listing. This listing includes explanatory comments.In this case the error variance is set equal to zero so that one canobserve the additive nature of the model.

If requested by the instructor's PUNCH control card, the sameinformation is provided in punched card form. The statement PUNCHEDOUTPUT SPECIFIED at the end of the printed output will alert thestudent to the existence of a punched deck. This deck is headed by

one card containing Ehe identification card contents and a secondwith a sequence number. Each experimental observation is on a single

card in the following

Col

format.

Content

observationlevel lor factor 1

Format

1-1011-14

F10.414

15-18 ft ft ft 2 14

19-22 If 11 II 3 14

23-26 If 11 11 4 14

27-30 e u e 5 14

31-34 u e u 6 14

35-38 u ft fl 7 14

These cards can be arranged in any desired order to satisfyinput specifications for any analysis routine Ehat might be usedto ccaduct the final analysis of variance of this data.

It should be noted that the student obtains information onlyas to the levels used of factors he has defined as active. Levelsgenerated by LEVSEL for ignored active factors are given only tothe instructor.

2. OUTPUT FOR INSTRUCTOR

The instructor is provided with an identical copy of theinformation provided to the student. In addition he receivesextensive additional information as to the exact model undeclyingthe experimental results generated for the student. A typical suchoutput annoted with explanatory comments is included as Appendix D2.

34

In the event that Ow student has ignored an active factor, a

second listing provides the instructor with complete knowledge of

which levels of each factor enter in the calculation of each

observation including those selected by LEVSEL.

Next for each of the 7 factors the instructor's deftnition as to

which are active; if active, whether fixed or random and the number

of levels is printed. This is followed by the comparable information

from the student's design. The student's specification of fixed/

random in no way affects the execution of STRUM but is provided

merely for information for the instructor.

Following these, the overall mean as specified by ehe

instructor is printed along with a "student value" which is the

overall mean corrected (by TRADJ) for treatment levels of fixed

factors which have not been used. This would be the "true" value

being estimated by the particular student.

The incremental treatment effects for active main factors and

all active interactions are printed next. For fixed main effects orfixed interactions these are ehe specific values entered by dhe

instructor and would be the same for any student using ehe

particular model. However, for random main effects or random ormixed interactions these are the results of the random selection

made in RTRT or RINTER. While they remain constant for the durationof the student's experiment, a new selection is made for the

experiment of the next student.

The standard deviation for the residual error component is next

printed. It is followed by a listing of the adjusted treatment

effects for each of rho seven main factors. These will differ from

the values specified by the instructor if a student has used fewer

levels of a fixed active factor than are provided by the instructor.

This Ajustment (accomplished in TRADJ) is compensated in the

"student value" of the overall mean printed earlier.

The purpose of this added information for dhe instructor is toassist him in interpreting to the student the model underlying the

generation of the observations he receives. This is the type ofinformation never available in real world experimentation and is,

therefore, one of the most valuable aspects of the STEXSIM approach

to teaching experimental statistics.

35

IV. EXPERIMENTAL USE OF SIMULATOR

A. DESCRIPTION OF EXPERIMENTS

Tn order to test the model and demonstrate its versatility, 7

different "instructor" models have been formulated. These have been

tested by running several "student" experimental designs for each

instructor model. A total of 30 experiments have been executed.

These are identified in this section. The input for each instructor

model and student design are listed in Appendix E along with the

STEXSIM results for each and an analysis of variance run on the

resultant generated data in Appendices E and F respectively.

1. MODEL 1: To test a non-interacting two factor fixed model, factor

1 is active, fixed with 5 levels while factor 2 is active, fixed

with 4 levels.

a. EXPERIMENT 1A: The student specifies the same model as the

instructor with one observation per cell for a total of 20

observations.

b. EXPERIMENT 1B: The student again matches the instructor'smodel but with 40 observations in order to show howreplication improves the power of design by providing ad-

ditional residual degrees of freedom (40 observations).

c. EXPERIMENT 1C: This experiment is the same as 13 exceptthree observations per cell are requested (60 observations).

d. EXPERIMENT 1D: In this design the student requests 5 levels

of factor 1 but uses 4 levels of factor 3 (which is inactive)

and ignores active factor 2. STEXSIM will generate random

selection of levels of factor 2. There is one observation

per cell (20 observations).

e. EXPERIMENT 1E: The student inlevels of factor 1, 2 and 3 tofewer levels than instructor.

this design specifies threedemonstrate that he may specifyFactor 3 will not cantribute.

One observation per cell is requested (27 observations).

f. EXPERIMENT 1F: Factors 1 and 2 are4 levels are requested of factors 5randomly select levels of factors 1observation (16 observations)

ignored conpletely whileend 6. STEXSIM willand 2 for elich

2. MODEL 2: Instructor model 2 provides a test of a fixed two factor

interacting experimental situation. Factor 5 is fixed with 6

levels while factor 6 is fixed at 4 levels. All other factors are

inactive.

36

a. EXPERIMENT 2A: The student specifies the same model as theinstructor with one observation per cell (24 observations).

b. EXPERIMENT 213: Same as experiment 2A except two observationsper cell tn order to make a direct main effects test (48observations).

c. EXPERIMENT 2C: Same experiment as 2A except threeobservations per cell (22 observations).

d. EXPERIMENT 2D: Same as 2A except four observations per cellto demonstrate improved power of design which has morereplications (96 observations).

e. EXPERIMENT 2E: Student ignores factor 6 while using only 4levels of factor 5. Student runs a one-way design withfive observations per treatment. STEXSIM generates levelsof factor 6 (20 observations).

3. MODEL 3: Model 3 demonstrates the role of blocking in reducingthe error means square in order to improve the precision of thetest. To accomplish this model 2 is used with dhe addition ofblocking factor 1 being entered as a random factor.

a. EXPERIMENT 3A: The student ignores factor 1 (blockingfactor) using two observations per cell of each of the 24treatment combinations of 6 levels of factor 5 and 4 offactor 6 (48 observations).

b. EXPERIMENT 38: In this design, blocking factor 1 isutilized at two levels. There is one observation per eachof the 48 cells (2 x 24) which is equivalent to partitioningthe odo observations per cell of experiment 3A into onefrom level 1 and one fvom level 2 of factor 1 (48observations).

4. MODEL 4: This model provides a test of STEXSLM in simulating afixed fhree factor interaction experimental situation. Each offactors 5, 6 and 7 is fixed at 3 levels each. Interactions 5-6,5-7, 6-7 and 5-6-7 are each defined.

a. EXPERIMENT 4A: The student's design matdhes the instructor'smodel with one observation per cell. The three factorinteraction must be assumed zero since it cannot be separatedfrom the error mean square (27 observations).

b. EXPERIMENT 41: This experiment also matdhes dhe instructor'smodel but utilizes two observations per cell. The presenceof three factor interaction can now be tested sincereplication provides a separate error measure (54observations).

37

le42

c. EXPERIMENT 4C: The student in this design assumes factor1 (at 2 levels), 6 (at 3) and 7 (at 3) rather than 5, 6 and

active. There are two observations per treatmentcombination (36 observations).

d. EXPERIMENT 41): Factors 5, 6 and 7 are each consideredactive but only two levels of each are utilized, threeobservations per cell (24 observations).

e. EXPERIMENT 4E: The student calls factor 5 random and 6 and7 fixed to show that it is the instructor's specificationof random/fixed, not the student's which affects the mannerin which STEXSIM generates data, 2 observations per cell(54 observations),

f. EXPERIMENT 4F: Same as experiment 41) except one observationper cell (27 observations).

5. MODEL 5: Irstructor model 5 tests a two factor random interacttngmodel. Factor 5 is active at 5 levels and factor 7 at 4 levels.Both factors are random.

a. EXPERIMENT 5A: The student matches the instructor's modelwith one observation per cell (20 observations).

b. EXPERIMENT 5B: Same as experiment 5A but with tmaobservations per cell (40 observations),

c. EXPERIMENT 5C: In this design the student ignores factors5 and 7 using instead factors I (at 5 levels) and 3 (at 4levels) with two observations per cell (40 observations).

d. EXPERIMENT 51): The student calls factor 5 fixed and 7random. Be uses 3 levels of factor 5 and 3 of 7 with twoobservations per cell (18 observations).

e. EXPERIMENT 5E: In this experiment the student ignoresfactor 7 and uses only 4 levels of factor 5 with 4observations of each level (20 observations).

6. MODEL 6: A daree factor interacting mixed model is tested byspecifying factors 5 and 7 as fixed at 3 levels each and factor 6randomoilso at 3 levels. TWo factor and three factor interactionsare all specified.

a. EXPERIMENT 6A: The student's design matches the instructor'smodel with two observations per cell (54 observations).

b. EKPERIMENT 6B: The student calls all factors random each atthree levels with two observations per cell (54 observations).

38

7. MODEL 7: Model 7 provides a demonstration of the effect ofblocking in accounting for sources of variation. Blocking factor1, 2 and 3 are defined as random while factors 5 and 6 each at3 levels are fixed and interacting are the factors of interest.

a. EXPERIMENT 7A: In this experiment the student ignores theblocking factors specifying 8 observations per cell of thefactor 5 by factor 6 complete factorial model (72observations).

b. EXPERIMENT 7B: Blocking factor I is considered at 2 levelswith 4 observations per cell (72 observations).

c. EXPERIMENT 7C: Blocking factors 1 and 2 are each considered(2 levels each) with 2 observations per cell (72 observatices).

c. EXPERIMENT 70: All three blocking factors, each at twolevels are included in the design with one observation percell (72 observations).

39

B. STEXSIM RESULTS

Each of the 30 experiments described in the previous section

have been executed by the STEXSIM model. The input in Appendix E

when run produced the results in Appendix F. In order to conserve

space only the student output is shown. For each, however, the

instructor output described in Section TIM was provided. Sufficient

input detail is shown in Appendix E to permit one to replicate each

of these experiments. It is important to note, however, that because

of different random number generators on different computers the

specific results would be different as indeed they are with the

SUM/Buffalo computer when a different seed number is used.

The purpose of each of these 30 experiments was to testdifferent conditions under which STEXSIM might be required to

function. In each case STEXSIM accomplished specifically what it

was designed to accomplish thus demonstrating its ability to cope

with the wide range of problems for which it might be required to

function.

40

C. ANALYSIS OF RESULTS

The role of STEXSIM was completed by the generation of theresults described in the previous section; i.e. the generation of"data" from the 30 different experiments. However, for the sake ofcompleteness and to demonstrate the full sequence of activities inthe use of the simulator, an analysis of variance was run for eachof the 30 experiments.

The program used for the analysis was BMDO2V, Analysis ofVariance for Factorial Design - developed at the Health SciencesComputing Facility, UCLA. It is documented in reference 2 . Theinput to BMDO2V for each experiment was the punched card deckprovided by STEXSIM. The deck, as is the usual case, had to besorted into the sequence required by the analysis program. Thisactivity is exactly that which would be followed by an actualstudent using STEXSIM.

The Analysis uf Variance Table for each experiment is includedin Appendix G. Hence, even if one did not wish to use the simulatorthis report provides at least the data for 30 different completefactorial problems with the appropriate analysis which he could usefor student problems, text examples, etc.

Careful review of these analyses reveals in several instancesresults which are counter intuitive, where significance wasexpected it was not found while where it should not be present itdid indeed appear. This should not be considered a weakness of theSTEXSIM model and its approach but rather is a reflection of thesensitivity of the model's performance to certain key inputparameterJ. One of the factors surely is the random numbergenerator itself. Many systems simulation studies have witnessed thecontributory effect of this generator to the variability of responsevariables. The others are the various values of treatment andinteraction effects and the magnitude of the error variance. Inaddition the natural variability inherent in any experiment createsunanticipated results at times simply because of the type I andtype II statistical error. The magnitude of unanticipated resultsexceeds that which would normally be expected.

Research is currently under way to examine carefully theeffect of various parameters on model response. The basic modelused for this study is STEXSIM exactly as described in this rcport.

Let us consider briefly the results of each analysis.

1. Model 1: The results of experiment lA are as would beanticipated with both active main effc ts shown to bestatistically significant at the .01 level. The level ofsignificance is surprisingly high however. In experiments 1Band 1C, however, ir (40. h the experiment of 1A is replicatedtwice and three tile, espectively, the observed error variance

41

("within replicates") is unusually high causing significanceof factor 2 only in experiment lB and no significance in 1C.ID produced anticipated results with no significance as theresult of the residual variance being inflated by the omissionof active factor 2 from the design. Reasonable results wereobtained in lE with the finding of significance for the activefactors and not for the extraneous factor 3 which was inactive.A spurious interaction weared when it should not have beenpresent. 1F produced ag anticipated no significance of the twofactors included in the design since both were inacttve factors.

2. Model 2: Experiment 2A produced reasonable results with bothmain effects being significant. However in 2B, 2C and 2D in

which 2A is replicated 2, 3 and 4 times respectively,surprisingly, no significance WAS found primarily because of anexcessively large error variance estimate. This result iscomparable to that of IB and 1C and is the subject of currentinvestigation. 2E however performed as expected with signifi-cance of the only active factor included in the design observed

by the contribution to error of the ignored other activefactor.

3. Model 3: The two experiments using model 3 gave precisely thepredicted results. In 3A the blocking factor is ignored therebypreventing the experimenter from observing the significance ofthe two active factors of interest. In 313, on the other hand,the blocking factor is included in the design thereby reducingdramatically the residual variance. Both main effects ofinterest and their interaction were found to be highlysignificant.

4. Model 4: In experiment 4A significance was found for each ofthe three main effects. Ilmever, no significance was observedfor their two way interactions primarily because the threefactor interaction is confounded with the error and henceprovides an error estimate that is inflated. In 4B where it hadbeen anticipated that the three factor interaction could beseparately tested, the error variance is excessively large soChat all tests for significance were negative except factorC which has the greatest effect on the model. The inflatederror of 413 is the same phenomenon observed in 1B, 1C, 2B, 2C

and 2D in which replication occurred. Experiment 2C gavereasoncble results except for a very high level of significancefound for factor 1 which in fact was declared to be inactive.4D yielded disappointing results primarily because of aninflated error term (3 replicates in this experiment). 4E withreplication gives inadequate results although 4F withoutreplication pcovides a significant result for all activefactors with the exception of the 5-6-7 interaction whichcannot be separated from the error.

5. Model 5: Model 5 gives a test of a two factor random interacting

42

47.

model. Experiment 5A without replication provided a significanttest for factor 5 but not for 6. Since a random model, thefact that the two way interaction is confounded with error is ofno significance. Factor 6 wtile active in the model has onlyminor effect so Chat its lack of significance is not surprising.5B, however, with replication surprisingly failed to showsignificance for any factor or interaction. In 5C the studentignores the active factors and includes two factors which areinacttve. As wuld be anticipated, no significance was found.5D with replication showed no significance of any factlr.Ignoring one of the active factors in 5E precluded a significancetest on the other factor included in the experiment as would beexpected.

6. Model 6: In both 6A and 68 which are identical except for thatin 6B the student declares all three factors fixed when in factfactor 6 is random, the student finds that the 5-6 interaction issignificant in 6A whereas in 6B, although the 5-6 interaction issignificant, he fails to detect it because of his improper model.No other factors are found significant.

7. Model 7: Model 7 behaved exactly as predicted. In 7A none ofthe three blocking factors are included in the design therebyobscuring the test on the two factors of interest (5 and 6).Similarly in 7B with one blocking factor included, ehe maineffects 5 and 6 and their interaction still are not found to besignificant. Two blocking factors are included in 7C whichprovides a significant test on main effects 5 and 6 but not ontheir interaction. 7D on the other hand yields significance forfactors 5, 6 and their interaction as well as significance forthe three blocking factors (although their test is not a matterof interest). In proceeding from 7A, 7B, 7C to 7D ehe residualvariance is decreased each time as would be expected. In 7Dnearly all the total variance is accounted for.

The results of the analysis of this set of 30 experiments leadsto the conclusion that in general the results of the analysis ofvariance were as anticipated with the majot exception that withreplication the error variance in nearly all cases unexpectedlyincreased dramatically thereby obscuring most tests of significance.This phenomenon is currently being investigated. Further, there isan apparent relationship between the predictability of results andthe magnitude of the error variance componeat. These are listed forreference in Table I . The factfhat Models 3, 5, 6, and 7 seemedto behave best (except for the replication problem) leads to thetentative conciusion that the smaller the variance the better theresults. This is a reasonable conclusion for as the contributian ofthe error variance approaches or exceeds that of a main effect, thetwo are likely to become confounded. This phenomenon is also beinginvestigated further.

43

Table

Actual Error Standard Deviation

Model SIGMA

1 0.750

2 1.250

3 0.005

4 0.250

5 0.150

6 0.001

7 0.010

44

V. CONCLUSIONS AND RECOMMENDATIONS

The Statistical Experiment Simulator (STEXSIM) has beendesigned, developed and tested. This report has described theseaspects of the model in sufficient detail as to permit someone elseto utilizt the model for his own uso.

The model was conceived originally as a teaching device inwhich the capabilities of the digital computer are exploited to permitthe integration of the design and analysis phases of statisticaltraining. It has been structured to permit an instructor to specifya statistical model which then generates "experimental" results foreach student according to the student's experimental design. Innearly all ways it is for the student an experience analogous tocollecting actual data in a real world experiment with two majorbenefits not attainable in real world experimentation. First, becan run an experiment quickly and at negligible cost therebypermitting many design experiences. Secondly, his instructor hascomplete knowledge of the underlying additive model which hasgenerated the student's data. This is invaluable in itterpretingresults but is never available in real world experimentation.

While highly successful in accomplishing this original designgoal, a number of other secondary benefits have become evident asthe model development has evolved. Foremost among these is the roleof STEXSIM as a demonstration device. An instructor in a course inexperimental design could use the model to demonstrate certainconcepts he might be covering without the student actually having tosubmit a design of his own. Experiment 7 is a good example of bowan instructor might demonstrate the role of blocking in improvingthe power of a design. Beyond its demonstration role STEXSIM isalready establishing a place as a research tool and as a generatorof standard "text book" problems.

To test the STEXSIM model seven "instructor" models have beenformulated each of which has been used to generate data for fromtwO to six "student" vNperimental designs. In total 30 differentexperiments have been run and analyzed in order to test as manyaspects of STEXSIM as possible. These have each been described inprevious sections. Each of these experiments were completefactorial designs with equal cell sizes. This wras done so as toutilize a particular analysis routine. However, there is nothinginherent in STEXSIM which requires the use of a completely balanceddesign. STEXSIM generates an "observation" for a single specificationof various treatment combinations to be controlled for thatobservation. Therefore the flexibility of STEXSIM permits anyexperiment which has an underlying factorial model. It can be usedfor fractional designs, Latin Squares, Graeco-Latim Squares, etc.Furthermore it can aid in the study of the handling of unequal cellsizes or missing observations.

The analysis of these 30 experiments pointed out certain

45

.z .50

problems in the selection of parameLer values to be used in themodel. These center primarily on the relationship of the magnitudeof the error variance to the magnitude of incremental treatuenteffects. Difficulties were particularly evident in replicateddesigns in which treatment effects are becoming confounded with theerror term. The problem quite clearly is with parameter selectionand not with the STEXSIM model. Accordingly, research is currently

underway on parameter selection.

Further research is recommended and is currently planned toextend the STEXSIM model to handle unequal variances, non-normalityand other designs for which a diffetant model structure is neededas nested designs for example. In addition it is planned to add atime dependent factor which will contribute an effect to anobservation proportional to place of that observation in the sequenceof samples in an experiment. This will permit the explicitinclusion of the effect of randomization. If a student failed torandomizeothis time dependent effect (with proper parameter values)will be confounded with a possible main effect perhaps giving afalse indication of significance of that main effect. Withrandomization the time factor can be confounded with the error.With blocking and randomization he should be able to remove it fromerror and mein effect thereby providing a correct test forsignificance.

The concept of STEXSIM is supportive of the manner in whichexperimental rtatistics is taught in an applied discipline (asengineering,psychology, education, for example). In these areas astudent generally gains understanding of concepts primarily throughexperience, both personal and vicariously through demonstration. He

also learns appropriate theory but yet there remains the philosophyof learning by doing. This is contrasted to the learning ofstatistics from a theoretical point of view in which understandingof concepts arises through mathematical processes rather thanexperience. Both forms of teaching are appropriate but it should berecognized that they each utilize different methodologies fordifferent audiences. STEXSIM's role is clearly in the area of

applied statistics.

The term Computer Aidedin the area of programmed insapproach of STEXSIM is a newshould be exploited.

Instruction (CAI) has evolved primarilytruction. It is believed that theand powerful form of CAI and one which

46

VI. REFERENCES

1. Box, G.E.P. and Muller, M. E. "A Note on the Generation ofNormal Deviates," Annals of Mathematical Statistics, MIK (1958),610-611.

2. Dixon, W. J. (ed.) BMD, Biomedical Computer Programs, HealthSciences Computing Facility, School of Medicine, University ofCalifornia, Los Angeles (Rev 1965).

3. Johnson, N. L. and Leone, F. C. Statistics and ExperimentalIn. Engineerins and the plosical Sciences. Vol. 2.

John Wiley and Sons, 1964.

4. Mize, J. H. PROSIM V Admdnistrator's Manual: Production System.Simulator, Prentice-Hall, 1971.

5. Mize, J. H. Production System Simulator (PROSIMA1 A User'sManual, Prentice-Hall, 1971.

6. Naylor, T. H., Balintfy, J. L., Burdick, D. S., Chu, K. ComputtrSimulation yechniques, John Wiley and Sons, 1966.

7. Porter, J. C., Sasieni, M. Wr., Marks, E. S. and Ackoff, R. L."The Use of Simulation as a Pedagogical Device," ManagementScience, Vol. 12, No. 6, Feb. 1966, 170-179.

47

APPENDIX A

GLOSSARY OF VARIABLE DEFINITIONS

48

VARIABLE DEFINITION1

1. First defined in instructor input section of MONITOR

IACT(I) =

IFLAG(I) =

LI(I) =

FNU =

NSTUD =

AI(I,J) =

BI(IC,L3,L4):

1 if factor I is active in model2 if factor I is inactive

1 if factor I is fixed in model2 if factor I is random or not used

number of active levels of factor I

overall mean

number of students for whom input designs(Set B) are pravided

additive intremental effect of Jth level offactor I

matrix of incremental 2 way interaction effectsof interaction IC where

IC = 1 for interaction 5-62 " II 5-73 II

6-7L3 = levels of first factorL4 . " " second factor

CI(L1,L2,L3): matrix of incremental 3 way (5-6-7) interactioneffects

Ll = level of factor 5L2 = level of factor 6L3 = level of factor 7

IN(K) = 1 if interaction IC is active and has a random component0 if interaction K is inactive or if active is fixed

where K = 8 refers to 5-6 interactionrs 9 " 5-7= 10 " " 6-7 iv

= 11 " " 5-6-7 "

NST = identification of student currently beingprocessed

49

FLIM(I,1) = lower limit on random effect for factor I

FLIM(1,2) a upper "

STD(I)

ft ft tt I, It

.= standard deviation of random effects componentfor factorI (effect selected fromN(0,STD(I)2)

where I = 1,...,7 for main effects I= 8 for 5-6 interaction= 9 " 5-7 ft

= 10 " 6-7 ft

= 11 " 5-6-7 "

SIGMA =

NSEED =

PUNSW =

standard deviation of error component (errorselected from N(0,SIGMA2)

random number generator seed

contents of first three columns of punchcontrol card (PUN for punching, anything else forno punching)

2. First defined in student input section of MONITOR

NAME

INCLD(I)

KEY(I)

stores alphanumeric contents of student'sidentification card

= 1 if factor I is deemed active by student2 u t It n not active by student

= 1 if factor I is assumed fixed by student2 u ft ft ft ft random " "

NRUN = number of observations requested by student

LS(I) = number of different levels of factor I usedby student

LEV(I,L) = identification of Lth level of factor I(L LS(I))

IW1(L,I) = level of factor T included in observationrequest L

= 0 if factor is not deemed active by student

IW(L,I) = level of factor I used to generate observationL (includes model generated levels when studentfails to use all active factors in addition toIW1(I,J)

= 0 if factor is not active nor deemed active bystudent

50

IA(1) 1 I I factor 1 1:4 fixed active factor used bystudent

2 if factor I is fixed active factor not usedby student

3 if factor T is random active factor used bystudent

4 if factor T is random active factor not usedby student

5 if factor I is not an active factor

ISW: a printing control switch

0 if student does not ignore any active factor1 if student has ignored any active factor

YD(L) = Lth observation of dependent variable

3. First defined in TRADJ

FMSS: adjusted mean equal to FMU compensated forstudent not requesttng all levels of each fixedfactor

AS(I,J): similar to AI(I,J) except adjusted for any levelsof fixed factor I which are not included instudent's design

BS(IC,L3,L4): similar to BI(IC,L3,L4) except adjusted for anylevels of fixed two interacting factors notincluded in student's design

CS(L1,L2,L3): similar to C1(L1,L2,L3) except adjusted for anylevels of fixed three interacting factors notincluded in student's design

IOUT 1 if no errors encountered2 if LS(I) > LI(I) for any fixed main effect

I (to abort execution of student's model)

ADELTA(I) adjustment needed for each level of maineffect I

BDELTA(IJ) = adjustment needed for eadh cell of followingtwo factor interactions

IJ = 1 5-6. 2 5-7= 3 6-7

CDELTA . adjustment needed for each treatment combinationof 5-6-7 three way tnteraction

51

.56

4. First defined in subroutine AMEAN

FMS = observation of dependent variable beforeerror has been added

All other variables are defined and ased locally within the varioussubroutines.

52

.57

APPENDIX B

STEXSIM PROGRAM LISTING

53

..58

PROGRAM MONITOR (INRU1,CUTPLT,FLNCM,TAPE7=FUNCH,TARESeINPUT)

COMMON/INTGR, IACT(7) ,IFLAC(?) ,L1(7) ,Tsw,Ih(11),tNcLr(7),1KEY(7) ,LEV(7,10) ,L5.(7) ,tis1(:on,7),TA(7 ) ,I14(zGao.),NAkE(ee)

COMmON/RZEL/ A1(7,10) 01(3,10,10) ,C/(10,10,10) ,AS(7,10),01(11,10,1U) IOS110,10,10) O'LIM(11,2),STC(11),ACELTA(7),2tIDELTA(3) ,COELTA ,OUT(1(114) 0g100),YD(200),RUNSW,SIGMA

INSTRUCTOR INPUT CAI,' SECTION) STATEMENTS 101117

RCAD SWIrCH TO CONTRCL FLNC),INGREAL) 105,PUNSW

105 FONMAT(A3)9999 CONTINUE

ISWn0READ InT,IFLAG,L1 netEs ANC GENERAL MEAN

READ 101,(IACT(J),J*197),(TFLAGIO,J=1,7),(LI(J),J21,7),FPUINSTLC161 FORMAT (711,71197I2,R10.4,I2)

IF(EDF,5)5E0,'351550 CALL EXIT55/ CONTINUE

REAC AI,BIICI TABLESDO 400 I:1,7DO 400 J=1,10

400 AI(I,J)=0.0DO 401 1%1,10DO 401 J=1,10DO 40i 01,3

401 BI(K,I,J)21.0DO 402 I'41,10DO 402 J%1,1000 402 01,13

402 CI(I,J1104:0.)IKST READ AI TABLE,1.t,,MA1N tFFFCTI1

DO 10? L41,7L1411ACT(L)GO TO (103,102),L1

/03 OIFLAG(L)GO TO (213,1)2)0

213 M4LI(L)Rr;AO 1w4,(AI(L,J),J21,M)

104 FONMAT (10Fis4)102 CON1INUE

PRINT 100,CIA(;1(J),J=1,7),(1F1AG(J),Jz1,?),(LI(J),4=4,7),FPLINSILC/06 FORMAT (1111,711,711,712,1-10.4,12)

MAC BI TABLE, I.E., TWC WAY iNTERACTIONS

on 116 Li=516Nt,L14.1

DO 110 L11,/I%fACT(L1)*IACI(12)!VINT 99, 1.19L2,1ACT(L1),TACI((2),I5

99 FOR1AT(I5)IF(IS..211/111.10,110

111IR(IFLAG(L1).NhelsCF.IFLt6(1.2).NE.1) GC IC 210

ii-.CL1.L2j5)10)9107,108106 IC4/

GO TO 109

54

0

107 IC:7(.0 70 191

/08 IC:"!

11:9

CO 1?1 1.3=101c-RINr gi, 1.11L2rIAC7(1.1),IACT(1.2),IS,H1012

98 For,MAT(7/8)REAC 1041(4I(IC,L3,14),1A=1,142)

121 CONTINUE110 CONTINUE

REAC CI TAAE,I.E., *THREE WAY INTERACTIONIF(IACT(5)*IACT(E)*IACT(7)2)112,1140/14

112 IF1IFLAG(5)4IFLAG(6)'1FLAG(;).NE.1) GO TO 11(eNI=LI(5)NE?r-LI(6)

N3=1I(7)DO 113 L1=101100 113 L2111,N2READ 104,(CI(L111.20.3),C3=1,N3)

113 CONTINUEFEAC 1-AN004 EFFECTS FACTOR CA7A

114 DO 117 J=1,7K=IACT(J)GO TO (116,1/1),K

116 K=IFLAG(J)GO TO (1119115),K

115 READ 104,(FLIM(J,K),K=1,2),STC(J)117 CONTINUE

DO 315 K=8,11315 I4(K)=0

READ TWO WAY INTERACTION IF EI7HEF FACTOR IS RANDCMCO 311. L1=5,6N=LifiDO 31C 1.2=14,7!F(IAC1(L1)*IACT(L2).NE.1) GC 7C 310IF(IFLAG(1.1).EO,I.ANC.IFLAGIL2).EC.1) GO TO 310IF11.1*1.2-35) 36,407,304

306 IC=8GU TO 309

30/ IC=9GO TO 309

308 10=10309 IN(IC)=/

READ 1v40FLIN(IC,K),k?1,2),S7CUC)310 CJNTINUE

VAY VAFIANCE CCPFCNENTIi:(1ACTO)-4y14OT(C)3TAL7(712) 312,314,4/4

312 IrtIFLAG(5)*IFLAt(l:)4IFIAG(7).EC.1) CO TO 314in4,(FLIN(li 00,41(n1,2),SIC411)

/07:AC 120,SIG1AO'UCC

120 FORMAT (W8.4,,Y0)

STUCENT 0.TA INPL1 SECTION

/r00 c3r4;T:z1,NITUDfe:r0/2191(MAlE(I)9141,80)

210 FOVAT (JOAO20.,(INI:LO(J),..1:1,7),(KEY(4)04117),NRUN

P-1(11.)'nt

314 CONTINUE

55

4

201 FORMAT (7/1,7/1,15)INPUT P.OMBER LEVELS ANC ACTLAL LEVELS FOS FACTORS LSED00 202 K=1,:'ISaINCLO(K)GO TO (204,212),IS

204 READ 203,M,(LI,V(X,J),J104)LS ( =ti

203 FORMAT 112,1012)202 CONTINUE

/NPUT SET OF EXPER. CCNC. FCR OESERVATIONS

READ 205,WW1(I,J),J=1,7),I=1,NRUN)205 FORMAT ( 712)

00 f.23 I=1,NRUNDO 124 Jii,7IF (IW1(I1.1).E0.0)/W1(I0J)v0

123 CONTINUECONSTRUCT IA(J) TABLE FROM SILDENT DATA00 1 Ja107LrIACT(J)GO TO 12031,L

3 VW/m.5CO TO 1

2 L=IFLAG(.1)GO TO (415),L

4 IA(J)=INCLO(J)GO TO 1

5 TA(J)=2+INCLO(J)1 CONTINUEGENERATE OMITTE0 CM: CCNSTRLCT Asons,cs Tames00 20 Mi = 1,20000 24 M2 = 1,7IWCM102).= 0

20 CONTINUE00 10 J21,7K1=IA(J)DO 15 I=10NRUN

15 1W(I,J)=/141.(I,J)GO TO (611,8,9,10),X1FIxEn, AOTtVE FACTOR USED BY E[UOENT

6 GO TO 10FIXED, ACTIVE FACTOR, NCT USEC FY STUENTCALL LEVSEL(JORLN)1501GO 70 10RANDOM, ACTI11:. FACTCR USTL EY :ILCENTr,ENERAlE TRLATMENT ErFECTS FOS FA(TCR J

8 PALI. PTRT(J)1,1 TO 10RANDOM, ACTUE FAC;C NC USE/ EY SILLCNT

9 CALL LkVSEL(J,NRUN)

CALL PTRT(J)GO TO /0

10 CONTINUEGENERATE LFHGTS FOP IN1LRACTI0N(3 IF gAN0CM OR MIXEC MCGEL00 '.:AG KLtd,11.

(IN(K).NC.1) GO TO 510CALL RINTrR(K)

510 CONTINUE

4

-

r 4

CALL TRA1JCI0UT,FpUtFrSS)GO 10 (118,)99),IOL1

COMPUlE EMPE4ICAL CiT,.t FCR WERIPENT

118 DO 11 L=101kUNCALL AWAN(LIFMU,FF5)YO(L)-zrii;*RNOPM(SI(YAIWikED)

11 CONTItiECALL OUTPUT ( MST,(ALN,FMU,FeSS)999 COM-INV.

GO TO 9999ENO

SUBROUTINE TRA0J(I0LT,F14U,FMSS)

COMMON/ISTGR/ /ACT(7) fIFLAG(7) ILI(?) ,ISWII/N(11),INCLC(7),1kEY(7),ILEV(7910) 1LS(7) )I%1(200,7),IA(7 ) 9IW(2000),NAME(80)COMMON/REEL/ AI(7,1() g21(3,14,10) ,CI(10,10,10) gAS(7,10),18S(3110,10) pCS(10,109113),FLIM(11,2),ST0(11),ADELTA(7), .2BOELTA(3) ICJELTA 9CLI(1(910)

0(10J)00(200),PUKSW,SIGMAfN.) 10U I:117DO 101 J:1,11)

100 ASCI,J)=.J.0DO 101 1=1,1000 101 J=1,1000 1%11 K=1,3

101 8S(K,I,J)=0.0DO 102 I=1,1J00 102 J=1,10DO 102 K=1,13

102 C!3(I,J,K)=0.4

ADJUST MAIN .:EFFECT TREATe.ENTS

FMSS=FMUIOUT=1001 I=1,7

IF(IACT(I)*IFLAG(I)-2) 24,1IF(LI(I).LS(I)) 3,415

3 RRINT89IIOUT2

8 FOTIMAT(' FACTOR 4,1:',* NC. LEVELS LSE0 IS TOO HIGP4)GO TO 14 AOLLTA(I)=0.4

N=LitI)DO 7 K=1,14

AS(I0()=A1(I,K)7 CONTINUE:

GO TO 1.

9 N=LS(I)FN=NSUM=0.0006 K-AINK1=LF.V(t,K)r.UM-5UM,4I(I0(1)

6

A1)ELT1 (1)=c;U1/FN

.62

57

144461..."

EmSsm. FMSS * APELTAtI)00 9K1,!LEV(1,10AS(1,104AI(I,K1)...A0ELTA(1)

9 CONTINUE/ CONTINUEGO TO (20,62),1001

ADJUST 2...NAY INTERACTION TERMS

20 00 21 I1w5,6IltI1+1CO 21 1231II?IF(11,012-35) 33,34,3!

33 /J=1GO 70 22

34 IJ=2GO TO 22

35 IJ=322 IF(IACT(I.1)*IACT(12)*IFLAG(/1)*IFLAG(I2)..2) 2.3,21,2123 I3=1I(I1).LS(I1)

IF(I3) 24,25,2525 Nir-LS(I1)26 Ir(LI(I2)-LS(I2)) 27,2812927 PR/NT8,I2

/OUT22GO TO 21

24 PRINT8o/tIOUT*2GO TO 26

28 IF(I3) 21,3692936 N21:LS(I2)

00 30 K13$1,14100 30 K2=1,N2noCLTA(td):10,0*OS(IJIKI,(2)30I(IJIKI,K2)

:4 CONTINUEOu TO 21

29 NZgLS(I2)SUM-:0.0RoN14N200 31 K1=1,111DO 31 K2=1,NZK3-7LVVII191(1)K4gLEV(I2,1(2)FUM=SUM+OI(IJ,K30(4)

!I CONTINUEHOUTA(IJ)=SUM/FNrmss m FMSS * EICELlA(IJ)

00 .32 K1=1,N100 Z!! K2=10210.1.EV(Iill(1)K4.11V (Ie042)OglIJ,K1,K2)30ICIJ)143,100-0CE4TAMA

??. NNtINUEit CoNTINUE

60 To 040,60,100AAJwir 3-wAY INTEPALTIONS

44 !I

(do

4,

4

0

:

da,

dW

15=7

IC=PA.TIIi)vIACT(1?)*1AC1t11)IB=D;LAC(I1),IFLA'AtZ)*IFLACtI.3)IrtIC'11:n 41,62072

42. IF(LI(11)-LS(I1)) 4243,i,442 PRINT 15,11

IOU1=ZGC TO 62

43 IA0J=1GO TO 45

41' IADJ:12GO TO 45

41; IF (If -4.' ) 1st tiie oil4h Pk!IN1

1001GO 10

47 IA0J=2GO TO 48

48 IF(LI(I3)LS(.13))49,S19SL49 PRINT 8,13

100=2 .

GO TO 62SO 1ADJ:.1251 N1=LS(I1)

N2-111.S(I2)

N3=IS( I3)GO TO (52053)0/%0J

52 CDELTA=0.0DO 54 It1,N100 54 J=102DO 54 K=5.03CS(19J,K)=C1(I,J,K)

54 CONTINLEGO TO 62

53 FN=Ni'N2*N3SUM=11,0DO

1,;i1

"4

K6=IEv(I5,K3)SUM=SUM+CI(K4,K50(6)

55 CONTINUECOUITAUM/FNFMSS 7 EN;S CCFLTA

00 .56 KI=1,11100 r..)6 et:!:101200 56 1%3:41.05

EV(II.,K1)K5=.1.EV(I,K2)1(511LZVCI30(3)

CS(K110,10)=CI(1(4,RS,KE).CCELTA56 CONTINUE62 RETURN

END

SUOROUTINC LZ10,11. (j,NPLN)

59

.64

"Ana ..es

COMMOM/rMTGR, TACT(?) OFLAC(7) 10(7) IMitIN(11),INCLCM,1KE1(7) pLEV(T,111) ILS(7) 01h1(200,7),IA(7 ) 11W(200,7),NAME(80)DIMENSION ISEL(10),FR(10)DATA LSEED/9199/

C CLEAR USE COUNTER00 i Kz1,/13

1 ISEL(K)*1C FORM CUMULAlIVE DISTRIEUTICN

KLIM=LI(J)FACT%1.00FLOAT(KLIM)00 2 K.119KLIti

2 FR(K)=FACT.FLOAT(K)DO 3 L*11NRUN

C MAKE SELECTIONXR=RNO(LSEEP)DO 10 LEVEL:4.91CIF(KR.LE,FR(LEVEL)) GC TO 2C

10 CONTINUEPRINT*100

100 FORMAT (1)(1*FAILURE 7C MAKE SELECTICK IN LEVSEL4)LEVEL * 10

20 IW(L,J) 11 LEVEL3 ISEL(LEVEL)*2

NLEV*0DO 30 01,10IisISEL(K)GO TO (30,31),Il

31 NLEV2NLZ.V4iLEV(J,NLEV)=K

30 CONTINUELS(J)=NLEVRETURNENO

SUBROUTINE PTR1(..1)

COMMON/INTGR/ IAC7(7) $11-LAC(7) pLI(7) II5NIIN(11),INCLD(7),1KFY(7) pLEV(7,10) ILS(7) 9/t.1(100,7),IA(? )

COMMON/REEL/ A1(7,10) ,E1(311t;p1(1) ICI(10,10,111) OS(7,10),ieS(3,10,1(J) ,CS(10,11,10) ,FLIP(11,2),STC(11),ACELIA(7),2SOELTA(3) ICOELTA IOUT(1(piG) 0(100)00(200),FUNSW,SIGMA

DATA LSEED/1111/K'LI(J)ST210(J)LOWIrFLI1(,111)HIGH'FLIM(J,,!)DO 1 LlIt0(DO 2 II141,10UUEF = FNORM t,LSEEC)IF(FroLT.LOW.OR.EF.GTOIDH)GC IC 2GI 10 it

2 CONTINUEPRINT 1.01,J

101 FORMAT(' FAILURE TO SELECT RANDOM FACTOR IN RUT FCR Je,05)M:TURN

11 AMJIL)=EF1 CONTINUE

60

a.

ki TORNttIO

alpTL:UTINE PINiFU(K)

DOMMON/INTGR/ 1ACT(7) 1,1FLAC(1) ,L1(7) ,TSW,/h(11),INCLC(7),1KEY(7) IILEV(7,1u) ,LS(7) 111.1(20077),1A(7 ) 11111(200,7),NAME(80)COMMON/REEL/ Ali ,V) tfiCIIIC110) ,O1(10,1C110) IAS(7110)111PS(.,10,10) ,(;(*),10,/0)1FLIM(1112),SIC(11),ACELIA(7),ZOOELTA(3) ,C0:LiA ,C111(11.11C) 0(100)00(200),PUNSW,SIG1'A

CATA LSEE0/71117/

LON=FLIM(K11)HIGH = FLIM(K12)ST=STO(K)GO TO (1,111,1,1)1,1,80,10,11)01 RETURN

8 M1=5H2=6IC=1GO TO 80

9 Ml=bW-;/

" Iti fin

10 M176M2=7IC=3

80 LI=LIIM1)L2=LI(M2)DO 51 I=1,L100 81 J=1,12DO 82 11=1,1000EF=FN0RM(STILSEE0)IF(EF.LT.LOW.OR.EFeLihIGF)GO TO 82GO TO 95

82 CONTINUEPRINT 101,K

101 FORNAT (' FAILUke TC SELUCI RANCE!' FACTCA IN PINT2R FOP Wy15)P7TURN95 BI(IC,I,J)=EF81 CONTINUE

RETURN11 LT=II(5)

L:=LI(5)LA:t1Ii7)00 441 1.11,11DO "000 "0 MCK-1,1300 12 n=tpuoEF=Tf-N0Q4(ST$1.21,E0)

IF(0-..T.T.LOW.OP.C.F.1.T.H1(4.)C0 TO S2CO r0 93ci2 CONTINUE

Prerta 10111(F;;TURN

13 CI(I,J,KKK)=F90 CON1INUE

.66

61

4

A

1 1, CHANGES /N MEAN CUE IC 2ND CRCER INTERACTICNS

RCTURNENO

SUBROUTINE AMEANUOPL,FMS)

COMMONPNTGR/ IACT(7) ,IFLAC(7) ,1I(7) 91SW,IMIA,INCLC(7),tKEY(7) ,LEV(711L) IILS(7) 0.1.1(2000)9/A(7 ) ,114(0,7),NAME(e0)COMMON/REEL/ AI(7,1b) 1E1(3,10010) ICIC10,1000) ,A(7,10),1US(1110115) ,US(10,10,10) ,FLIM(1192).STU(11),ACELTA(7),200ELTA(3) 9COELTA ,CUT(1(liC) 0(100),Y0(200),PLNEN,SICHA

CHANGES IN MEAN CUE IC MAIN EFFECTS

FMS=FMUCO i It1,7LLtIACT(I)GO TO 12,1),LL

2 II= IW(L0I)FMS=FMS4AI(1III)CONTINUE

CHANCES IN MEAN OLE 10 1ST CNCER INTEFACTIONS

DO 3 125,611=14.100 3 JsI107IF(I*J35)4016

4 IJt1GO TO 7

5 IJ112GO TO 7

6 IJ=37 tF (IAC1U)4IACT(J)2)B93038

L2t1W(LIJ)FNS'FMS4.aI(IJ0.1,42)

3 CONTINUE

411111

IF (IACT(5)*IACT(C)*10C1(7).-.2) (3,10,11)9 1.1.2IW(L15)

L2aIR(LI6)L3=714(107)FMSzrMSI.CI(L19L;!,L3)

10 Rt.:TURN

ENO

4.

SUMROUTINE CUTPUT(NSTOFLNIFhL,FNSS)

COMMON/INTGR/ IACT(7) gIFLAC(7) ILI(?) ,TSW,Ih(ti),INCLC(7),1KEY(7) ,LEV(ll1U) 10(7) ,I4,1(2000),IA(7 ) lOW(217017),NAPE(80)COMMON/REEL/ AI(/110) IEI(3,1G,10) lCic11'l10,1n) OS47,10),InC(3,10,10) IL:F(111,10,10) ,FLIM(1112),Sit;(11),ITCLIA(7),2BOLLTA(3) ,CJiJrA ,CL1(11.)1C) ,Y(100)0C(200),PUN2INIEICMA.CIKNSION ICWIE(134)UATA IASK/1H./IIELANg/1M /,IFLUS/1HAWUNIZMPLN/

62

.67

4

a.

PUNCH SE1MENT FOR GENERATED EAU

IF (PUNi4.NE.PUN) (.0 TO 999DO 71 J1=1,80

71 1CC(J)=Ib1USPUNCH 721(ICODE(.),J11980

72 FnPMAT (A('A1)PUNCH 729(NA4E(I),I=1,8C)PUNCH 73,MST

73 FORMAT (I10)PUNCH 709(YO(L),(IW1(19.1),J=1,7),L=1,NRUN)

70 FORMAT ( (F10.4,7I4))999 CONTINUE

OUTPUT SEGMENT FCR GENERA7EL CATA; Th0 COPIES

PRIHT RUN IDENTIFIFFDO 81 Il=1,61)IF (NAME(IB).NE.IELANK) CC 7C 82

81 CONTINUEI1=1

82 DO 83 1=1,80IE=81-1IF (NAME(IE).NE.IELANK) GO IC 84

83 CONTINUEIE=80

84 IE=IEf4PROVIOE TWO COPIES00 64 K=1,2PRINT 101

101 FORMAT (1Hi)00 SI: I=104

80 ICCUE(I)=IBLANK00 e6

86 ICW7E(1)=IASKPPIN1 1031(IlOCF(I)021,64)

103 FORMAT(3/X,84A1)DO 87 In104

87 ICO0E(1)':I9LANKICOCE( I1)=TASKTr:CnTAIE)--zTASKPPINT 1113,(ICOLE(1),I=1,0)00 Ad L=1,30

8d icf.Cv.(If:!)-INAMI:(I)P;u:,E(14)=IASK

PRINT ..7.7),NST,(IC0CL(1),1=1,84)63 FOE:1AT (1H 93X)4STUCENT NU1EER*II5,6)(04A1)

00 m.1) I.:10)489 r;fli,E(7)=IDLANK

IM;E(I1)=IA3KICFAAI7)=IA3KPRINT 1:131(ICOCE(I),I=1,84)DO 90

90 TO((I)=IASPRINT 133,(IGOCr(1),I=1,84)P.ZINT 112

102 FnRVAT(///)PRINT 69

60 FCaPAT (.5)(1*F1'CT:R LEVELS49/12)(9403SERVATICN 1 2

63

1/2 A.Alraosiao.. *A. A ...AAA.

1 3 4 600 61 L=1,NRUNPRINT 62, 1,Y0(1),(I141(10),J=1,7)

62 FORMAT (6X,I41F10.4,7(Ie92X))ei coNTNue

IF(FUNSW.NE.PUN) GO 1C 102PRINT 300

30.1 FORMAT (1HU14PUNCPEE CUTIUT SFECIFIF.C*)GO TO 64

302 PRINT 30/301 FORMAT 11H01'NO FLNDMEC LUTFLIvT64 CONTINUE

7419/1)

PRINT FACTORS USEC INCLIAINC TMCSF GENERATED BY FCCEL

IF(ISW.EnsOT GO TC El65 FORMAT (1110,5X,4FACICFS USEC EY MCCCL IF CIFFERENT')

PRINT 65PRINT 6000 E6 Lt1,NRUN

66 PRINT 62tL,YOTLT,(IVN(L,J),J=1,7)ISW20

PRINT INSTRUCTOR DATA; FACTCRS INVOLVED

6? PRINT 530530 FORMAT (//p5X0*INSTRUCTCR I

PRINT 531531 FORMAT T5X,' FACTOR tCT1VE

DO 20 J=1,7I*IACT(J)GO TO (21,22)11

21 I=IFLAG(J)GO TO (23,24),I

23 MINT 532.,J,LI(J)532 FORMAT (101,//f4X,* YES

GO TO ZOV, PRINT 5331j1LI(J)

533 FORMAT (1UX,I104X,* Yr.3GO TO 20

22 PRINT 534,d5'24 rORMAT (10XII1,4X,* fq:*)

GO TO ZO20 CONTINUE

140 p FACTCRS INVOLVEC40/)

G PRINT STUDENT DATA, FACTCRS USEC

TYPE NC. LEVELS *I/ )

FIXED 49EXIII2)

RANOCM *pfX,12)

PRINT 535tilt; rORMAT ( //f5X)*SIUCEIkT INPLI FPCTCPS U:EC4,//)

PR/NT ti366,56 FORMAT CiX.* FACTOR USCC TYFC NC. LEVELS

11-EVELS USEO*,/)00 Jzil?13INCLC(J)r,0 TO (2612(),I

26 IAKEY(J)GO TO (28,20,1

ZO MlLS(J)MINT 5371.1.W.:(J).(1.V(,..10,111")

riA ijiMAT YES v.6X,I216X.10I;)(,O TO 25

64

/

a wist...1)53,,J,Lso),(LEut.,K)02101)

538 FOKMAT (1LX,I1.4X99 YES RthCCM 9.EX.I2.EX.1015)u0 f0

27 PRTNT 514 .J539 FO;IMAT (10X,I114419 NO9)

GO TO 2525 CONTINUE3J PRINT 54015MU.FMSS

540 FORMAT (//,5A1904ERALL 11%ERtGE*1//,10,4INSIRLC1G5 YALLE4010.201/.10X.+STUOENT VALUE 9,F1C.29//)

PRINT INSTRUCTOR INFLI, *AI9 MAIN EFFECTS

PRINT 550550 FORMAT (5X.4INSTRUCTCP INPUT4./p5X,YELCCK1KG ANC PAIN EFFECTS41/1)

PRINT 551551 POPMAT (5X,4 FACTOR NO. LEVELS TRT. EFFECTS40/)

DO 40 1=1)7K=IADT(I)GO TO (41,40).K

41 Ni=LI(I)PIZINT 55211.11,(A1(19J),J1:11M1)

552 FORMAT (10X,I1,10X,12,8N,10F8.3)40 CONTINUE

PRINr INSTRUCTOR INPUT, +819 TWO..NAY INTERACTIONS

PRINT 553553 FORMATT//5WINSTRUCTER INPL7*/5X0M0 WAY INTERACTION EFFECTS4)

CO 42 Ii=5,L,II=I1+100 42IF(TAGTTI1)*IAIW(I2).2)48,42,42

48 IF(I1"q2.-:!5)43,44,4543 IJ=1,

GO TO 4644 Li=2

GO TO 4645 IJ=546 M1=LIII1)

M2=:LI(I2)PRINT 554,11912

554 FO!!OAT(11-014.4P.CTGR*059/g5X,4COLIMNS.FACTCPs)15,//)PRINT 555

555 FOr...HAT T5X.* TRT. EFFECTS40//)00 47 I-1101PRINT 556,IIWAIJ,I.,1).J=102)

556 FORf'AT ()X0/154.16F4.3)47 CONTINUC42 CONTINUE

PYINT INSTRUCTOR INFO, 9CIf TNFEEWAY INTERACT/Ch

PRINr 557557 FOPMAT t//0WINSTi-ITTO. IN'ILT9p/15X;*3.AY INTERACTICh EFFECTS*)

IF(IAGT(3)"14CT(6)+IACT(1)-..W.:0,5315.!50 Ni-ILITO

.N?tl/(6)N3411(7)DO 5e It11.01

65

PRINT 5C51I6sa FORMAT(IMWLEVEL CF FACTCR 5 IS4051/0)

PRINT 559559 FORMAT (5x)* FACTCR 6 NC, LEVFLS TRT. EFFEC1S4,/,

15X) LEVEL FACTCR 741//)00 52 Jni,M2PRINT 5601.1,43,(CIEI,J0)0(s102)

560 FORMAT C9X,Iiplux,I1,10X910F8.J)52 CONTINW:53 CONTINUE

PRINT 561,S1GMA561 FORMAT i1M(195X114SIGYA 2 4,F10111)

OUTPUT MAIN EFFECTSI/ASt TAELE

00 19 P1pi0an 19 J11010OUT(I,J)=0.0

19 CONTINUECO 1 1=1,1KIIIACT(I)GO TO (211),K

2 MillLS(I)00 i J21,M1KinLEV(tpul)OUT(I,K1)=AS(I0J)

1 CONTINUEPRINT 501

501 FORMAT1RO5Xt.1LOCKING EFFECTS ANC MAIN EFFECTS4',//g4 INCREPENITAL ADJUSTED TREATMENT EFFECT540//)PRINT 502

502 FORMAT (4 LEVEL*,FACTOR 1 2 2 4

1 7 a 9 104)00 3 1=1,7PPINT 503,Ip(OUT(194),J21,10

503 FORMAT (7X,1294X110,0.4)3 CONTINUE

RCTURNEND

FUNCTION RNP(1'.X.F.11)()AN% K/305175/8125/ISCALE/0.3:21126E14/NSEC0 zNSEE0+KRNO=FLUAT(NSfXD) OSCALERETURNENC

FUNCTION FNOR1(ICVAWEE0)C CO.iPuTUS NORMAL 0) VIATE! 1 IH ?FAN nRo AN0 STANCARC CEVIATICN SIGMA

DATA K/0/,T1401,1/4.2832/lr (K.E0.1)G0 TO 1

. FACTimSCIRT(-2.0*AtOC(PNC(NSEEC)))FAOT2:7w0PI*RN1)(NSEE0)Z=FACTi'sIN(FACT)GO TO 2

66

.71

...A.M.A....

val

v s n Mr1331,441

Cs: rate. 0.

;,

I

--..ilar.....,,emm

.~111gpmgm

as 11.",I:

r. pISP

MP'

11.1C

I ""111"

.°)

IP 01410 Cit

r-

APPENDIX C

SAMPLE INPUT LISTING

The standard deviation for the error component was set to zero

for this sample experiment so that one may reconstruct each

observation from the various increment effects which are included in

order to check the execution of the STEXSIM model.

Iv

,c-f

sece

.1-

1ea

sel r

a-ci

s-W

Lic

vvil

Aiw

a-

,

00

le-

Aee

cis,

ar'

-1,

U

+ 3

s+

1"

rgto

-te

St-

e vg

-/.1

P't,

"t r

ON

eira

-4-

t

e.

I"'"

4

t a"

+.

+ 1

. C+

3C

+ 1

C-e

r.se

t-42

19fe

d

,co

,kk

:\if

,11.

1#*

St, )

4'44

(0-4

' eew

\Of

,-jk

14.9

.,#;f

rets

--44

,44

vugt

Kr

100.

0/

SA

MV

.E P

FC

ELE

P

--4

)7)

514.

..44

4,,

g, S

-4 -

iti

r4.

a--z

i)4

4.-c

5 3

3Se

-evs

PIX

FCW

ITH

ST

UC

EN

T IG

NO

RIN

G F

AC

TC

R

a.

41k.

40,

4-8.

slic

.41

1 5+

ILe.

C.C

.t do

*3

LI,

...13

.8I

ac.

gcw

-L.,.

.L

t.t-s

fl.f

et-c

k.s

1111

111o

;4..L

4la

.aft

_e-

(.12

4-c.

,-A

sk

1144

1.1%

cAo

14%

-s

APPENDIX D

SAMPLE STEXSIM OUTPUT

I. Output for student2. Output for instructor

70

iY

,.11

t-0

itr 0

toe.

,

STUDENT NUMBER

.......s\

.****A**.************

**

* SAMPLE PROBLEM

MIXED

WITH STUDENT 77

'

IGN0f-IVG FACTOR 7

*y

*:5

443.

4144

6,41

44,4

4444

411.

****

****

****

****

4.11

6Arr

erge

raili

.***

4"4"

1"04

"*.,4

110.

4111

411*

..1

FA

CT

OR

LE

VE

LSOBSERVATION

12

34

67

4.II

97.1232

o0

2102.5677

o4.

20

3101.3256

00

3

4103.5114

0

5.

102.5914

00

0-

20

6102.2074

00

00

30

7105.2749

00

00

10

8106.1484

90

00

72

0

=1

105.6081

00

00

33

0

UNCHED OUTPUT

1

4(4,04

-V0,41,-1

low

.frel

v4-1

-64

c. s

eacl

dis

)31

%A

.1...

A

STUdENT NUMBER

*41141/440411-41408POW11141414.401141viiIPIPP4044111$41.040411.111,4141411411,111144PAPP4414**44,40441.410;

1.* SAMPLE PROBLEM. MIXED

WITH STUDENT IGNORING-FACTOR 7 ,

*.

IVO

411

141.

346

41t

414

341

141

6IP

* 41

.41-

1111

641.

41,4

1-11

8114

6441

4164

1114

6116

1141

1461

1141

1141

1*46

4044

64i4

641-

11 1

11

OBSERVATION

12

197.1232

2102.5677

o3

181.3256

4103.5114

0a

5102.5914

-06

182.2074

7106.2749

08

106.1484

a9

105.6081

NO PUNCHED OUTPUT

FACTORS USED BY

40UEL IF

OBSERVATION

1

197.1232

2102.5677

3101.3256

4103.5114

5102.5914

6102.2874

7106.2749'

8106.1484'

9105..6081

DIFFERENT

2

INSTRUCTOR INPUT t FkgTORS INVOLVED

FACTOR

ACT:4E

FACTOR LEVELS

34

56

a1 2 3

02 2

22

33

1a

32

0a

3

FACTOR LEVELS

3

a

56

02

a3

2 22

23

a3

1.

32

33

TYPE

NO.- LEVELS

1NO

2NO

3NO

4NO

5YES

FIXij

3

6YES

R4NDON

3

7YES

FIXED

3

STUDENT INPUT t FACTORS USED

FACTOR

USED

x-v:

11-N

rvtA

,,;%

TYPE

NO. LEVELS

LEVELS USED

. o0

,

Coe

4ov

Sluo

dwar

l0 Fo

g-sr

c.1

o 'T

vcu

u g M

K-T

or 7

st..e

.ver

.4s-

reD

ei L

awsa

L.

NO

2NO

3NO

4NO

YES

FIXED

31

23

6YES

RANDOM

31

23

NO

OVERALL AVERAGE

INSTRUCTOR VALUE

STUDENT VALUE

INSTRUCTOR INPUT.:

BLOCKING ANO WAIN EFFECTS

100.

00

Fe-

&Iv

o/ c

ia.L

.

4usi

suJi

3

10 O

. 0 0

koc)..A4

f 2

L.+

11.4

,44

44ek

Ii14

4

FACTOR

NOf. LEVELS

TRT. EFFECTS

WI%

Yol

aAVledg.

eft..

.As

63 3 3

+3.000

2.364

+1.000

0.000

1.012

0.000

3.0

00 035

1000

INSTRUCTOR I44PUT

TWO WAY INTERACTION EFFECTS

ROWSFACTOR

5C OLUMNS...F ACTOR

6

ROW

le,

TRT.

EFFEpSe

tr.+

gt,4

ii"114(

Vrine4r

i//

,//f

.065

.033

e113

+.101

0275

.457

+.316

.035

1.242

ROVSFACTOR

5COLUNNSFACTOR

X,

ROW

TRT. EFFECTS

1+2.000

2s-

1 00

03

3.000

+1.000

0.00)

1.000

ROWSFACTOR

6COLUPINSFACTOR

7

ROW

NT. EFFECTS

144

6012

.141

.063

.1116

3.000

1.000

+4.000

3

.7

.1 I.

'01

Lw+

ie4

Pav4v.)

3eac

-S 1

ts*

1v 4a

tea itrit-r- (rv,..10.4.4.44-r31

Secf

t.4.4

.414

140

1.44

in.0

06,-

ICA

1044

4-')

474

0144

,4 -

ere-

Cto6Lell.

Sete-ski

1.3.1

Ave., V6rP14.4 $0..7!

11, n

ow.

4a4.

1,sr

- 7

sim

it.e.

..L

Aki

t.*1.

441

&si

tJL

'1.-

CIM

POliv

4140

040L

.

01«s

e. r

'.01+

47

elga

viS

thr'

C*-

7

8.1.

.."Ja

41te

trsi

ii4)

,Z.

itL.s

4wki

iA-4

0, w

at.

imm

ihm

...--

a-Ir

.= 0

.,

-;;J

3...134

...WO

.003

INSTRUCTOR INPUT

3WAY INTERACTION EFFECTS

LEVEL OF FACTOR 5 IS

1

XX

FACTOR 6

NO. LEVELS

TRT. EFFECTS

LEVEL

FACTOR 7

1/

13

.549

.360

23

.164

....517

33

:.529

.....434

LEVEL OF FACTOR 5 IS

FACTOR 6

NOILEVELS

TRT. EFFECTS

LEVEL

FACTOR 7

1:3

e392

.142

23

.197

.030

3.153

.612

LEVEL OF FACTOR 5 IS

3

FACTOR 6

LEVEL

NO. LEVELS

FACTOR 7

TRT. EFFECTS

13

.183

.238

23

.040

.279

33

.466

0458

SIGMA =

BLOCKING EFFECTS ANO MAIN EFFECTS

INCREMENTAL ADJUSTED TREATMENT EFFECTS

.223

.541

.356

.588

.

.677

.168

....246

.959

Ttir

dot.

4A-4

3

ere.

.wis

..1...

A41

131:

Rc.

.k.

G00

birriA

rco

di

#

!.

045

...10....ote.),

14.41.4

Tietelul"

P)k,J.I.Jovilitp..4

,....... +16,0,1a.64,4

S in

:C.4

-A

/O

ak6%

ra%

A A

i-ei

e....

..A...

r-...

..4 7

LEVEL

FACTOR

12

34

56

7a

1

9. 11

01

0.0003

V.0000

0.01100

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

2na

noo.

onoo

o.oc

aoch

omp

0.00

00pa

wn

0.00

000.

0000

Dau

m0.

0000

30.0000

0.0000

0.0000

0.0000

0.0400

0.0000

0.0000

0.0000

8.0000

8.4000

40.0000

0.0000

0.000P

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

53.0000

0.0000

3.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

60.

0000

0.00

000.

0000

0.00

0000

000

0.00

000.

0000

.0.

0000

0.00

0000

0000

7...1.0000

0.0000

1.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

APPENDIX E

INPUT FOR EXPERIMENTS CONDUCTED

In order to conserve space only the first five observationspecifications arc included for each of the 30 experiments. Theremaining observations are identical in format. The exact numericalvalue for each can be obtained from the corresponding output listingof Appendix F. The instructor's model and student's design otherwiseare exactly as when the experiments were conducted.

PUNCH

11222221122222 5 4

-4.8

-2.8

0.0

-13.0

8.0

+3.0

0.75

533

40.0

+2.0

+10.0

6NODEL

440

ExP-1A

STUDENT SPEVIFIES SANE MODEL

AS INST.

11222221122222

20

5 1 2 3 4 5

ONE OBSERVATION PER CE1.1.

S.*

41

23

4

42

12 3

54

Z3

ExP-113

STUDENT SPECIFIES SANE MODEL

AS INST.

Two OBSERVATION PER

CV-L.

11222221122222

40

5 1 2' 3 4 5

4 I 2 3 4

1 .1

1, 1 7

1 2

1 3 4

EtP-iC

STUDENT SPECIFIES SAME MODEL

AS INST.

THREE OBURVATIONS PER

CELL

11222221122222

60

51

23

4S

42

34

4i

31.

1 1 i

2 2

ExP-10

STUDENT SPECIFIES LEVELS OF 1,

NONE OF 2, 4 OF 3

12122221212222

26

i2

34

5

41.2

34

44

2 52

.

41

14

ExP-1E

STUDENT SPECIFIES 3 LEVELSOF 1,2,3

11122221112222

27

31

35

31

23

31

35

11

i

113

1 1 5

1.2 1

1 2 3

ExP-1F

STuDENT IGNORES FACTORS 1

ANO 2 BUT SPECIFIES 4 LEVELS

OF 5 AND 6

22221122222112

16

42 3 4

4 1 2 3 4

1 1

1 2

1 3

1 4

2 1

22221122222112

6 4

55.0

5MODEL 2

' , ,10e

6.0

3.0

+5.0

+7.0

+700

1!

:.

3.0

0.0

0.0

.3.0

t

+3.0

0.0

0.0

3.0

i-2.0

-1.0

+1.0

+2.0

an

0.0

Bea 0.0

OS

Oa

1.0

+2.0

2.0

+1.0

't

+2.3

0.0

+1.0

3.0

t2.0

1.0

0.0

+3.0

1.25

533

EXP 24

STUDENT MATCHES INSTRUCTOR LEVELS

1 OBS. PER CELi.

22221122222112

24

..

r.

6 1 2 3 4 5 6

4 1 2 3 4 1 1

1 2

1 3

1 4

2 1

EXP. 2 B STUDENT MATCHES INSTRUCTOR

2 OBS. PER CELL

22221122222112

48

6 1 2 3 4 5 6

4 1 2 3 4 1 1

1 2 3

1 4

2 1

EXP. 2C

STUDENT MATCHES INSTRUCTOR

22221122222112

72

6 1 2 3 4 5 6

4 1 2 3 4 -1

1

1 2

1 3

1 4

11

3 OBS PER CELL

EXP, 2 0

STUDENT MATCHES INSTRUCTOR

4 OBS. PER CELL

22221122222112

96

6 1 2 3 4 5 6

4 1 2 3 4 1 1

1 2

1 3

1 4

1 I

EVP. n

STUOENT USES ONLY 4 LEVELS OF 5 AND IGNORES

65 OBS

22221222222122

20

4 1 2 3 4 1

1 1

1222112222211210

6 4

-55.0

2

10.

6.0

3100

+5.0

+7.0

.7,0

-3.0

2.0

0.0

*3.0

+3.0

0.0

0.0

-3.0

-2.0

-1.0

.1.0

2.0

0.0

0.0

0.0

0.0

1.0

+2.3

2.0

+1.0

+2.0

0.0

+1.0

3.0

2.G

1.0

0.0

+3.0

.7.0

+700

2.0

0.005

533

MODEL 3

---

ExP 3A --FIxED TWO FACTOR WITH BLOCKING FACTORWHICH IS IGNORED BV ST4. 4 OBS6

22221122222112

40

.:

61

34

56

41

2.3

4I

-1

I2

13

14

21

EXO 34 - STUDENT USES BLOCKING = = 2 BLOCKING LEVELS - 1 085 PER

CELL'

12221122222112

48

2 6 4 1 1 1 1

1 1 1

2 2 23 34 4 6 4 6 2 5

5 2 2 1 1 3

6

222.21112222111

3 3 3

125.0

6MODEL 4

3.0

0.8

+3.0

10.0

5.0

.15.0

1.0

2.0

+3.8.

1.0

0.0

*up

.2.0

.+1.0

3.0

1.0

1.0

+2.0

1.0

0.0

+1.0

+2.0

+1.0

3.0

1.0

1.0

.2.0

100

0.0

+1.0

+200

+1.0

t

1.0

+2.0

+3.0

0.0

3.0

t

0.0

0.0

0.0

300

0.0

+3.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.

3.0

0.0

+3.0

0.0

0.0

0.0

+3.0

0.0

3.0

0.25

533

EXP. 4A

FIXED THREE NAT - STUDENT MATCHES INST. LEVELS - ONE OBS,

PER CELL

22221112222111

27

3 1 2 3

..

I

3 1 2 3

3 1 2 3

1 2 3

1 3 1

1 3 2

3 2 2

1 3 3

EXP. 48

FIXED THREE WAY

TWO OBS. PER CEL1-..

22221/12222111

54

3 1 2 3

3 1 2 3

3123

1 1 1

1 1 2

/ 1 1 3

1 2 1

1 2 2

1.

;

EXP.

FIXED THREE MAY ...STUDENT IGNORES F",r42TCP 5 ANDUSES 2 LEVELS C: 12 OBS

12222111222211

36

2 12

3 1 2 3

3 12 3

i 1

11 2

11 3

12 1

12 2

EXP 40. THREE WAY FIXED

STUDENT USES ONLY '

..EVELS OF EACH FACTOR

3 OBS.

222211/2222111

24

2 1 3

2 1 3

2 1 3

1 1 1

1 1 3

1 3 1

1 3 3

3 1 1

EXP 4E. THREE WAY FIXED

STUDENT CALLS FACTZP.i 5 RANDOM

TWO OBS

22221112222211

54

3 1 2 3

3 1 2 3

3 1 2 3

1 1 1

1 1 2

1 1 3

1 2 1

1 2 2

EXP 4F

FIXED THREE WAY

STUDENT CALLS FAC3CMOR 5 RANDOM- ONE OBS. PER

CELL

22221112222211

27

3 / 2 3

3 1 2 3

3 1 2 3

1 2 3

1 3 1

1 3 2

3 2 2

*61.

0,44

.! 1

41/1

1&-,

A tl

itt.

& :

Saa

bI40

.44h

1 3 3

2222121222222210101010051004

20.0

-10.0

+10.0

2.5

-1.0

+1.6

0.5

-5.0

+5.0

1.5

MODEL 3

0.015

533

ExP SA -TWO wAY RANO0N - STUDENT mATCHES

INSTRUCTOR - ONE OBS. PER 044

22221212222222

20

5 I 2 3 4 5

4 i 2 3 4 1

1;

t

12

13

14

:2

1

EV. 58 - TwO wAY RANDON - STUDENT MATCHES

INSTRUCTOR

TWO OBS. PESPCkLL

22221212222222

40

5 1;2 3 4 5

41.2 3 4 4

41

22

1

42

;4

1

EXP. SC - TwO wAY RANDOM - STOT. USES FACTORS

1 AND 3 RATHER THAN 5 AND 7

12122222222222

2C

52 3

45

4 1

2 34

IL

;

13

14

ExP.

50

TwO WAY RANOOM - STOT. CALLS FACTOR 5 FUE0 - 3 LEVELSEACHi 2 OBS.

22221212222122

14

3135

4

3 1 2 3

11

i

12

12

13

I

LIP. 5E-

RANDOm TWO wAy - STD. IGNORES FACTOR 7 AND USES 4 LEVELScF 6. 4 OBS.

22221222222222

16

4 1 2 3 4 2 3 4

22221112222121

3 3 3

100.0

2MO6EL 6

3.0

0.0

+3.0

1.0

0.0

+see

2.0

1.0

+3.0

1.0

0.0

+1.0

..3.0

+1.0

4.0

5.0

+5.0

+1.25

5.0

+5.0

+0.5

5.0

+5.0

0.0

5.0

+5.0

01.0

0.001

533

EXP 6A

MIXED THREE WAY STOT MATCHES INST. MODEL

2 OBSERVATION;

22221112222121

54

3 1 2 3

3 1 2 3

3 1 2 3

1 1

11

1 2

13

1 2

11

2 2

EXP. 68

MIXED THREE WAY WHICH STUDENT CALLS .177AFE

TWO OBSERVATIVMS

22221112222111

54

8 1 2 3

8 1 2 3

:3 1 2 3

1 1

1I

211

31

2 1

1 2

2

11121122222112101010

3 3

3.0

00

75.0

4MODEL NUNBER 7

.CO

+2.0.

+2.0

4.0

2.0

1.0

+3.0

*4.0

0.0

+1.0

+8.0

+1.0

4.0

5.0

+5.0

+1.5

5.0

+5.0

+1.5

5.0

+5.0

+1.5

0.01

533

EXP. 7A

STUDENT IGNORES BLOCKING (0 OBSERVATIZUSS,

22221122222112

72

3 1 2 3

3 1 2 3

1 1

1 2

1 3

2 1

2 2

EXP. 78

STUDENT CONSIDERS ONLY BLOCKING FACTOR,- 1 14 OBS.)

12221122222112

72

2 i 2

3 i 2 3

3 1

23

11

11

21

1 3

12

11

2 2

EXP. 7C

STUDENT CONSIDERS BLOCKING FACTORS 1.A110 2 42 OBS.)

11221122222112

72

_

ii

'

2 1 2

2 i 2

3 / 2 3

3 1 2 3

1 1

1 1

11 2

1 i

1 3

2 i

1 1

2 2

EXP. 70 - STUOENT CONSIDERS

ALL THREE BLOCKING FACTORS (1 IBIO

11121122222112

72

2i

2

21

22

12

3/

23

3i

23

1/1

11

11 1 i

CD

1 1

112

11.3

12 1

12 2.

I.

t.

FILMED FROM BEST AVAILABLE COPY

APPENDIX F

STUDENT OUTPUT FOR EACH OF EXPERIMENTS

In order to present more information to the reader withoutincreasing the number of pages in this report, the output included inthis Appendix is that printed for the instructor. Everything afterthe phrase PUNCHED OUTPUT SPECIFIED would not be printed on thestudent's copy. The reader in this way can see a portion of theinstructor's output whenever the listing of observations terminateabove the end of a particular sheet.

83

L'Se

4

els

...***4.***411414i-faii4PWWWW,4441~M*4114411MIPMW*41***441.4.404P44411441141****4-041141AMP*4114144,44,4140

STUDENT NUMBER

1EXP-1A STUDENT SPECIFIES SANE MODEL AS INST.

ONE OBSERVATION PER CELL

le% el*

. , 2 340

4 5 6 7

O3SERVATI3N

4i.53aa

37.7429

454491

53.1345

43451L9

33,7IL3

44.9,25

a5t.t9i?.,

S43.22iS

12

1.2.65i:1

11

5f;.445

12

23.4g33

13

3-:.17:5

14

39.:a61

...,

._

23.S5C3

16

44.15..6

17

7561425

13

45.1+54

7:

77.-.:'a

iN

iii.0

4.4-

11.*

****

4114

,4*4

****

****

40.1

.4.2

044,

4***

4.4.

4.0.

041,

4***

*445

.1,4

,411

4.40

41-W

9.44

1.**

4.4.

44,4

1-41

4446

4.4.

4.4.

4414

.4.4

.

FACTOR LEVELS

i2

34

56

42

0i

00

12

00

06

43

00

40

54

09

40

23

50

06

13

60

00

14

C0

06

44

03

00

32

02

0G

33

00

00

34

00

00

41

a0

a0

51

69

0G

22

00

00

11

P. .

00

0

52

C0

0E

2i

0a

0A

24

00

20

53

E0

3C.

31

00

00

PUN:PlE2 3JTF--T SzEC:FIE0

INSTRUCTOR INPUT $ FACTORS INVOLVED

FACTOR

CTIIiE

TYPE

NO. LEVELS

Y=S

FIXED

5

YE.5

FIXED

4NO n:NONO

STUENT INPjT

FACT3RS USED

FAS4TOk

USED

TYPE

NO. LEVELS

LEVELS USED

. aYES

FIX:-"D

2YES

FIXED

3NO

4NO

51

23

4

41.

23

4

6 9 0 0 8 C 6 0 C 6 0 8 it t 0 0 0 0 4 0

prua

taA

dk.-

k-

5

STUDENT NUMBER

2EXPJ.B

STUDENT SPECIFIES SAME MODEL AS INST.

TWO OBSERVATION

CELL

FACTOR LE/ELS

035ERVATION

1.

23

45

67

122.2566

11

o3

05

C9

73,1689

11

0a

GG

t3

37,5244

12

ts,

10

at

436.9119

1)

5a

3U

tt

533.933v

13

C3

35

c6 , , i

4 ).2,;3?.

43.092d

46.3475

, 1 1

3 4 4

0 0 0

. 3 3

a a 0

6 c a

C c c9

:::i.i.272

21

00

04

G1C

25.35-'9

21

03

4C

CII

4 --,

37.467

33.5:29

..) 2

2 2c C;

, :.

a a4 ra

C r.1.!

:',.9-76

.6

C0

f4

..A.:1344

23

0. .

ac

b15

47.1563

24

0C

05

a15

45.31.i1

24

03

0c

c17

23.7131

31

ca

0c

eta

27.2541

31

00

o0

a19

33.2335

32

e. .

a0

,st.

2C

33,9111

3,

6. .

414

L11

43,149..

33

.t!

C0

5C

99

41..0574

33

0.

ca

iJ

23

43.9355

34

03

0C

C24

49.8574

34

03

00

c25

23.8672

41

30

00

026

27.7649

41

a0

35

c27

41.1473

42

53

00

023

42,5254

42

63

05

Gzg

43.5

110

43

Z3

3C

C3:3

45.3303

43

03

06

031

51.4905

44

0G

00

432

51.3282

44

00

00

C33

30.8972

51

00

a5

034

31.0747

51

00

00

035

44.8186

52

C0

00

036

43.7341

52

aa

a0

037

46.6124

53

00

d0

038

46.2469

53

00

40

G39

54.1939

54

08

00

04C

54.0434

54

00

00

PUNCHED OUTPUT SPECIFIED

,

* * ** 4.

...1 4* ...I ** la 4* C.) *** QC141 *

* a. ** ** 4o *z ** a ** H ** P ** olIt ** ** ni ** La ** VI ** M * P la c2 0 0 es .2 &a 4.3 42 ea CS 4.1 ca C2 CD C4 C7 41 12 CA 4..1 La ..2 cm Ll C2 0 Ca 42 43 c.0 Ca 42 Ca 42 4=1 0 0 ..) ca 42 4.2 4_1 47 #.4 42 42

* 0 *** la ** 141 ** Cle *2: ** lo, ** ** ** U * .0 ,I3 c3 4.1 4to 4,3 %. oo o3 o ca co v,o cm co co ea o co cl ,3 ...I co .3 el3 co co Ls . .s .4 ea ci to 44 0 0 Co ca C4 Ca C) na I= 0 1.2 0

* **z *

* H *

*d *

LU * 1.11 es coo 43 42 Ca CM C2 ra CS es cs 441 Ca Ca C:1 Ca 42 eS eS #.4 ea 411 42 C2 40 42 C2 C2 0 42.ca 42 C2 Ca 0 CS Ca Ca C7 42 C7 ea C2 C3 Ca CM

0 *0 $E *

*LU *

*In *

III, *U) In .2 IIS c3 CO Co o ea CI ca 0 CO 0 0 c3 C2 co ca o CI O co co Ca 0 0 0 ca CD CS 0 0 o.2 ca Co co ca Co Co ez co o Co o CD 0 42 C1 0LU .aH * ILI

IL * :0H * la* * ....I

* LU *0. * lY* CI

* * Mm.* H * t . ) f o l C2 Ø Ø I D 42 Ca ...a C3 0 12 Ca ea ta u2 Ca C$ CM 42 42 ca 42 0 ca 47 ca 42 C2 0 4.4 0 CM ca CM 0 42 42 42 42 0 C2 C7 C2 0 C3 CM 0

2 * 04

Iii * U.0 II,

H *Ifl *

**

t.) *14 44 * Al 44 44 44 .4 04 4 v4 .2 4 24 AI Al ed to Nt oo to oo 4 44 CI 4 0.1 Al Al ...1. 4 44 NI .4 04 v4 AJ AJ .2 PO .2 P2 .4 CO .2 04 P2 PI 0%1 .4 .4

I ** a. *

W* la 4lit ** * * *

le)

4

MMIgliplilp.

24 4 ha .1 44 04 44 UN lA OU 44 UN 44 Ti PI PI .2 in .1 UN UN PO C4 0.1 UN 4 AJ P7 ha 44 4 44 UN .2 14 to, 04 ha 42 141 04 .4 4 UN

41. AM v4 v4 co nn v1 ,to c.) 0 ua to) t.) at% 01 #.1 43 04 .41 cIO 4 00 MP Cr, 1%- 41 elf oca to Pa ,t PI LA 4

la .4 UN P) 4t. Al P. f t. IA in #.2 al Cn NJ n 4 t. #'4 41 UN k0 t4) NI 4.) NJ .4 NJ 43 .4 fII)')I)\tflJq-4tAPi to 11.4 dM PI IA 24 INN P. 4, 14-. 22 PI all ,f1 1.2 AN itl .1 2 .2 IA .4 4-2 na .4 #4) 1.4 ft f!lt p. ..e 4) a) .1 Cn .1 14 4 UN 4

0.. n7 .4 .2 UM III 00 fil CA Pc PJ .2 444 44 IT% t44 ..1 hj t fl fo) ILA mi ,4 (J.1, "de ath. 4 Ki un tt) fil UN on re) 411 et) ir ,0 .1-4 P. ON (.1% .1' Phi (13 AO r! 1 «41 LP Pi en to PI ,r4 in Ai IT v-4

NJ 04 Cy 04 Pa .1 Po tO 04 PI PI PI -t t -t P) 1 t (*) bl km -t to ,t 44 4 0.1 4 CI UN

AJ INa .2 UN 4) 0% 42 MC' .4 04 122 4 UN 4.1 P. crl Li . 44 Pa .2 UN 4) P. #0 CP r.a .4 iv Pa .2 IA 4) P. 00 cr Ca .4 INJ Ca I LA 4) P.

e4 44 .4 41 44 N oi Ao Al Al Al AJ t45 rn re) M V) 14) rn ,t 4

C t C

86

I.

4849

51;

5157

5354

55 56

57

5559

62

39.1796

24.6478

4).5172

42.9939

33.5711

35.7567

46.fl6i

26.8.157

47.C546

36.3325

46.0756

52.2364

51.74-36

3 2 .. :-. 7 .. 2 2 _ 1.. -

2 3 2 2 2 3 1 4 2 4 4 4

a 0 a C o 0 0 0

0 0 a a a a 3 a a 3 C a

2 a 3 f. 3 3 a a a

a Li a le I. 0 a a a

là

C. a

PUND,tED OUTP'JT

INSTRUCTOR INPUT

FACT:S r4VOLVED

FA

CT

1'S

vc:

YFS

3NI

5 7

STUDENT INPJT

JSE0

NO. LiF.ELS

5 4

FACTOR

USE3

NO.

LEVELS

LEVELS USED

1ys

51

23

I.

52

YE

SF:AE:

41

23

4NJ

4NO

5NO

6NO

7NO

OVERALL AVERAGE

INSTRUCTOR VALjE

40.0th

STUDENT VALUE

40.00

INSTRUCTOR INPUT

BLOCKING ANO MAIN EFFECTS

FACTOR

NO, LEVELS

TRT. EFFECTS

25

4.00

0 2.

400

0.00

02.

040

4.06

04

13.000

3.400

3.000

10.000

* **0

*******

***

:****M***************

4M*

*****************

* *

N%

.

40

M

M4A144

w4WCOt...

0 PI4U.

N

u2 00 CS= us 00 04.3 0 43 Ca cv el %a es co t.3 us

,

43 0 0 0 C3 0 c4 CS CS 02 C2 CS 0 45 0 0 0 -1 0 0

es es clic% CS cal 12 0 020 CI 0 la 0 0 cl CS 0 2 2

VS CS C2 CI CS C2 PA CS es C2 43 0 CS 43 C2 f4 L2 CS es 12

4 hO 04 .4 4 PI Od 04 v* 04 01 A 4 A Pe, re 4 A 4 C4

.

CI CS CS ra - vt C2 C2 CI VZ vs CSC, Cs ex C5 CI Mel

Pe.

4)

US

N4..,

UJ3.W...1

Wele..

C3 Ol4u.

UI AI

42 CS 0 S CM C3 C3 Co 414 IQ is %.3 UV C.5 ,45 C3 14 CJ C2

1.14.14-ommes400.a4.m,..1caacomcsmcv

0 0 CS CJ 0 C2 CM CS C, C5 1'1 r2 0 cs .75 C5 ci Oft

ocbocammcsanomczocagnocamal

4 tiq c4 A 0 rg, 04 Cu -1 N NI 1.4 4 el 0) PI 0 v4 0

T4 ft, 4 P1 4 4 MI ,4 .4 ft) CQ r4 4 PO Pt ,r ri 4 4

qp4 4 CU UN 4 A MN 4 '4 141 07 CU C4 PO 4 ,4 PO r4 M NJ .t CO M 4 1.4 :# r4 M SI NI c4 CU PI st r4 NI T4

4 r:10

at I 4

( I Li

/-4 q 2-

W M .4.411M.OMWNW.:-14t0.12MMt,sw 1) M .0.1P....0MM.API.ohN-stO,W ..i $44,11.1M/410$MN,OMtIMWau..aNAMIii0 W rtn..%mi.siiMM.OtimrNtl011 ,ft clOr,M.410ttr)(0.2.CMNwN2M,1 0 0 (.1.1k0.40tto,/it.tMp...fr-r4

w mck,N4r,wm44,0(,..m4,4r..yl,$) w 4 No)^,44:,.c4.4enp,,,,,,If.P ul

10 ...,.... 0Or144-4Nelmw4p-mw0M t-- n ,o1440-rormtNNtitiN"0 *****41, CA4Mt4M4NM4mM14t44N4hi.t 7.) NA.m.l.ttil4MP)7mN444.rcqtrA

..- 0 0 0z 1- W114

n 0O ,44VM4004Mk0N404"t, 0 0. .4v4m4mwr-coMc4.4mmlowt.-W(7"= r4r4e4,1r4r4r4v4r44 c) #4,140.-1Ao44.4,4t.-

Cl at

4nC(41:;)CU

88

is-oaaaaaaaaipaaaaaliwasta..aasaaemearniaeaafaivpasa.

STUDENT NUN3ER

5* ExP-1E

STUDENT SPECIFIES 3 LEVELS OF

1,2,3

1 2 3 4 5 6 7 8 9

42 -..

....'

131415

16

1713

1q

4. ,4,21

22

23'4

2526

27

OBSERVATION

21.7109

22.2372

23.85:1

37.4495

36.1438

35.2639

39.65C1

37.568;

3a.4037

26.1*&?

27 . 445

39.1997

39.V.24

39.5339

44.:798

42.3912

43.5E-3

..1.34;t3

31.9

7531.3365

45.8937

43.6610

43.2373

48.3223

47.1836

47.0g00

1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 a 5 .1. 5 5 5 5 5 5 5

2 1 1 1 Z 2 2 3 3 3 2 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3

FACTOR LEVELS

3.

4

10

33

5a

I0

30

5a

13

a0

50

1a

33

.

5a

10

3a

50

10

3a

50

10

38

50

10

30

50

1a

30

50

4 56

30

60

aC

.

0C

1C

30

3U

aa

0G

aa

0:.

a.4 v

3r

ac

ac

44.

ac

aa ...

3,

00

ac

aa

ak

0L

aa

0I,

0G

7 8 C 0 C c 0 a C 0 c ts c 6 a c a c C. c i

. a c LI C a 0 C

PUNCHED OUTPUT SPECIFIED

INSTRUCTOR INPUT

FACTORS INVOLVED

FACTOR

ACTIVE

TYPE

NO. LEVELS

1YES

FIXED

52

YES

FIXED

43

NO

4NO

5NO

.

6NO

7NO

STUDENT INPUT

9 FACTORS Wt..:

-

STUDENT NUMBER

6EX91F 'STUDENT IGNORES FA:TORS 1

AND 2 BUT SP_CIFIES 4 LEVELS OF 5

ANC

4,464414,441.416.844**41.4.4.4411.41.44.0444***

:ACT3R LEVELS

33SEIAT13

12

35

67

152.2256

aa

II

C

245.3E

oe

a1

2e

51.23.34

13

G

4r:

aa

14

G

5"3.17,175

aa

a2

1G

6a

a2

2Z

.

737.94:7

02

3C

541.5553

fta

aa

24

C

935.6322

31

C

40

518 573r;

aa

32

e

14

31..1690

ao

a3

33

C

12

72..1277

3a

34

I:

13

42.1:,-4

aa

a4

16

14

45.i64t

42

0

15

40.7449

a4

3C

16

44.6337

aa

.a

44

a

..."

-

FA:T:kS .,SE: 37 klf..::EL

IF

"1.;'FERENT

FACT3R LEVELS

aSERVATION

12

34

56

7

5.2256

44

00

-.:

45.93n6

14

a0

12

C

351.2-1!!4

34

00

13

C

441.7168

42

00

14

C

524.3375

41

00

21,

0

654.7:

54

00

22

0

737.4907

22

Ca

23

C

641.6i58

33

00

24

0

-1

35.E326:

12

r 00

31

0

i:

51573a

44

a.

o3

2n 4.

11

16.-1593

12

4a

33

0

12

23.7277

11

0a

34

0

13

42.1544

49

00

41

0

14

45.3641

53

00

42

0

15

437449

23

00

43

C

16

44.6357

43

G0

44

a

INSTRUCTOR INPUT 2 FACTORS INVOLVED

FACT:A

ACTIVE

TYPE

NO. LEVELS

.ot

,1U

:11.

4ga

,

4,4114#414194*******49444,0.49.***441**4444-414#4441414.44414444,444*4444444444.

STUDENT kUM3ER

141'EXP 2A

STUCENT MATCHES INSTRUCTOk LEVELS

I OBS. PER CELL

4114444*44411444/44,44,04******44144,44044.************444******4$44**/#441444.

08SERIITICN

12

FACTOR LEVELS

34

7

,41

144.3'34

0V

04A

11

0w

12

04i1

345.7,:::,

00

00

13

04

.i3s5.7

0a

00

14

05

45.5i.,±

0C

00

21

0ts

64,...7-:.

00

0a

22

r 47

...:1.2.:72

0il

00

23

ft

.....

.... - -

0C

0C

24

0a

r.:

;,.=:,

,41

:4a.z7,..a.

oG

ar.

/0

=...

r:.

- -

r ...

00

32

0ii

52.7:

r Jr v

00

33

0.0.

12

-...:E5

J0

00

34

13

54

67...;.:

Gr 4

0G

41

014

!;:ai:-:

30

03

42

C...

5::.:::

C0

03

43

018

G.T.2577

00

00

44

0MD

17

E1.2375

00

0C

51

018

663.31

00

0C

53

it)

8,

IIII

19

6:

2.2423

00

00

52

0 0.

20

63.:6-7:3

00

00

54

0II.

21

55.7i::,

00

00

61

022

61.2S15

00

00

62

023

64.5+.7

00

03

63

024

06.5156

00

00

64

0

1 t41

i

PUNCHED OUTPUT S2ECIFIED

IKSTRUCTOR :NPUT

FACTORS INVOLVEC

FACTOR

ACTIVE

TYPE

NO. LEVELS

1NO

2NO

3RD

4NO

5YES

FIXED

6YES

FIXE0

NO

STUDENT INPUT

9 FACTORS USED

6 4

FACTOR

USED

' TYPE

NO. LEVELS

LEVELS USED

.11,

0,1,

41*.

tllW

ith

=4 * 40 * *

4* 1%. s... Ira ti 6.3 .2 1..a .4 .:s ...3 4 44 kA %.3 ...) 4 .4 .4 Aa , .1 411 1.4 .4 tza %2 Ca .2 0 4.4 4.3 si.) 42 C.1 %.2 C4 ..a 4 ,...a ;:* a to .3 ,.4 ',-:1 0 .3 ta 44.44-J #

t'sq* ...-1 ** iiJ ** C--V *

re *# 1 sl ** 13. 4.* ** * 011. V14 ** len *# 0 *41 * 21!* (\I 4. t!?* #

* # .* * s

* DI # UN r4 irl r4 I-4 (NJ (N1 N N JO V) PI PO 4 4' 4 4 si, IA tA tr1 10 411 ID t0 1-4 .-I s-4 1 (N1 N N !NJ 00 44) 41. In 4 4 ...t 4 UN UN 44.1 LA %el NO NO4. 0 it

1-4. *C.2 it

* ** AI ** I-* VI *7 4.. t...4 *

* VI 4 43 cm ta C.) Es 0 4 4) .a a 4,= 4A) ta .?.4 1'2 42 CI, 41 42 42 ri 42 CI r3 fr3 C3 !,2 43 CS = CI CA I* CS a C3 afotootsio4o.arnoc3U$ * -I

* Iti 4 141

# I: * 7** C-.1 * 111

* 1,... * -..1

** r *

* IY* A4. 14.. * 1...* 7 4. L) 44) La IVI 0 s= 4) 42 la ell (2 C4 lr4 (21 .4 44 4:J 12 C3 0 4:3 4..) cl sU ca CA 0 ca r., 11 t-'4 .2 4.2 Li C2 C3 CS 4:3 4...) 43 CI4 C.3 14 C4 47,1 (=a ca ca.4.3* to * a

CI Lt.4**

'n1-vs

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(NJ

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4.1.'" `AI `44 41 44) .1' If% tr' P.. t ,C3 I 144 P. I' It% I tr) LIN II .ts 44 4-1 Ai 44 44. 4 tm 14.1 .(1 .() 0,4)

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(24ttl

.4 01 try 4 IIN %CI 144.4, 41 1 44 413 In 4 IA tt 0% .4 4\1 141 -4, th kg, it (r. el 14 (0 P(1 'L. I. al 01 s (I) 34) .1 ,0.4 *4 a4 v4 41 144 1 1 11 1%4 01 1\1 0.1 CM 0.1 NJ les to, 4.42 1.(4 Iv, tql 1.1) - 4 4 4 4

%4', 111111,111111111192

48

E5.425C

13

PUNCHED OUTP.IT SoECIFIED

INSCRUCT:z InPUT * FACTORS INVOLVED

FACTO;

ACTIVF

TYPE

NO. LEVELS

4NO

7NO

3

NO

5YES

FIXED_

5YES

FIXED

7ND

STUIEN-

,FACTOR:. USED

6 4

FAST2

jSEO

TYPE

NO. LEVELS

LEVELS USEO

I:E;AGE

FIxED

FIXED

v4LJE

c"..,::

55.41

INSMSTD? INPUT

SLOCKI-,S INS HAIN EFFECTS

6 4

FACT3R

NO. LEVELS

TRT. EFFECTS

5 6

23

45

62

34

6-1a.coo

-3.41

5.000

7.010

7.000

40.(loo

3.:;*

3.140

INSTRUDTD

INPUT

TWO wAY INTE1ACTION EFFECTS

ROWSFACTOR

5COLUNNSFACTOR

6

ROW

TRT. EFFECTS

134400

0.030

0.020 3.000

...41

a11

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...11

1.0.

11,0

th-

,..4.

41,0

atos

4,41

4,-

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* 14 it ...J

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101

4 4 4

- -

.32b

46

62.4208

PUNChE0 OUTPUT SPECIFIED

INSTR=TOR INP;;T # FZCTORS

INVOLVEC

FACTOR

ACTIVE

TYPE

C. LEVELS

111i

.i

YES

RAgOOM

10

;2 3

NO NO

.06

4NC

5YF.S

FIxrD

6

6YES

FIXED

4

7NO

5

.

STUDENT INPUT

FACTOR

FACTORS USED

USEC

TYPE

NO. LEVELS

LEVELS USED

1YES

RANCOR

21

2

;2

N3

3NO

4NO

1111

%

5YES

FIXE3

61

23

45

6

I-1

6YES

FIXED

41

23

4

7tiII

Ise

CIERALL AVERAGE

11STP.JcICA' vALuE

55.Ct

STEsT n&LUE

55.00

INSTRUCTOR ZNPUT

ELOCXING ANC MAIN EFFECTS

FACTOR

NO. LEvELS

TR% EFFECTS

110

1.151

.413

1.716

.629

.142

1.202

1.252

.181

56

.3.000

5.000

1.000

7.000

64

-343GO

0.300

0.460

3.000

IhSTRU:TCR 2:3PT

TmC

AY INTER:tCTION EFFECTS

R0i1SFACTOR

5CCLUMNS--FACTOR

6

ROW

TR% EFFECTS

.2SE

4

a

4.4.****44.***4444.4**4464444*********44+04444444.4**444**444-4444.4444444**444*-AA,44.

STUDENT NUM3ER

1ExF. 4A

FI.XED THREE WAY

STUDENT hATCHES INST. LEVELS

ONE M. PER CELL

4.+**404444**444444.44444444444444444444444*4444444444444444444444444444.4144444444*

FACTOR LEVELS

DESERjATION

12

34

56

7

117.::a27

, .i.

00

12

3

00

13

1

4t;

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01

32

11S.7415

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146.937J

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2

10S.4293

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00

11

2

116.0309

00

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12

2

PUNCHED .ot:TPUT SPECIFIED

INSTRJCTOR INPUT

9 FACTORS INVOLVEC

FACTOR

ACTIVE

TYPE

NO. LEVELS

1NO

2NO

3NO

4NO

5YES

6YES

7YES

-FIXED

3FIXED

3

F/XED

3

STU1ENT rom , FACTORS USED

;

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119.6863

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53

141.3716

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54

149.1324

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PLNCHED OJTPUT SPECIFIE3

INSTR'-3TCR INPUT

,FACTORS INI/CLVED

FACTn

ACTIVE

TYPE

NO. LEVELS

0 0 0 0 17, 0 0

0 0 0 e 0 0 0

3 3 3 .1 3 3 3

1 2 2 2 3 3 3

3 1 2 3 1 2 3

4t4

0

3rO NO

5YES

FIXED

3

0F/y.Ee'

3

7YES

IX

3

5T;,:7 :INPUT

1;.:TCRS .;;EC

FAZ7Z:t

TYPE

NO. LEVELS

LEvELS USED

7

'o=7.

31

2

YF:

F.4:xED

31

7v,-

FIxEC

31

23

:%3TRJCTOR vALuE

STJ:ENT

INSTR.=C7CR INPUT

ELCC<I'LS AND MA:N EFFECTS

125.rle

125.30

FC:724

NO. LEJELS

TRT. EFFECTS

53

e3

73

1INSTEMOR I1PUT

;

-

MO *AY INTERACTUN EFFECTS

13

I

., 4

ROWSFACTOR

5

0911

111

-3.000

0.000

3.000

-10.000

-5.000

15.000

1.000 2.900

3.000

_11

109

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'F 1":7FFERENT

1FACTOR LEVELS

6

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INSTRUCTOR INPUT

FACTORS rontotAme

itAiih

mt

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1.2 *

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,FAZT3RS IN,JCLYEC

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INSTRUCTR lJE

STJOENT vALuE

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TYPE

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LEvELs USED

FIXEC

3i

27

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31

23

F1XEC

3i

23

&...00KI4; ANC MAD. EFFECTS

i06.LC

140.C4

FACTOR

NO. LEVELS

TRT. EFFECTS

53

63

73

IhSTRUCTOR INPUT

Tito WAY INTERACTION EFFECTS

RONS -FACTOR

5

-3.000

0.044

3.400

2.364

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-1.0116

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1.000

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FACT3R

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TYPE

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tO tID YES

FIXE3

3

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FACT:P.

US1C

TYPE

NO. LEVELS

LEVELS LSEC

4 5 6 7

N3YES

YES

YES

FIXEC

FIXEC

FIXES

3 3 3

- . . .

2 2 2

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OVER;.LL AVE;AGE

Li3TRLiC7OR VALUE

STJCENT VALUE

IXST;UCTCR INP:JT

ELOCKIV.i AND MAIN EFFECTS

1LIT:J.00

100-C9

FACTOR

No. LEVELS

TRT0 EFFECTS

53

3.000

0.300

3.00a

63

..f1S0

.093

.261

73

.1.300

0,J04

1.440

INSTRUCTOR INPUT

TWO WAY INTERACTION EFFECTS

ROWSFACTOR

13 1

2 23

31

32

33

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APPENDIX G

ANALYSIS OF VARIANCE RESULTS

On each printout variables are numbered sequentially from 1

by the ENDO2V program. The factors to which each correspond are

written on the sheet.

The common scheme for indicating significance is adhered to.

A single * denotes an effect significant at the ot= 0.05 level while

a double ** indicates significance at a 0.01.

128

133

PR33'..EM NO. LA

NUMBER OF VARIABLES

2NLMBER OF REPLICATES

1

VARIABLE

NO. OF LEVELS

15

pi...A.,

24

2.

GRAND

40.02d51

c)

SOjR:E OF

DZGREES OF

SUMS OF

MEAN

VARIATION

FRECj3 4

SQUARES

SQUARES

...

14

132.53478

33.13373

*0

23

1345.26619

448.42873

/6-10

RESDUAL

12

.24678

.43723

...

TOTA..

19

1483.08775

i

.t I

-.

...ki

kti,.

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. K..7

alp

01.

4.-.

W01

014

11iti

i

PR53LE1 NO. 13

NU33ER Lc."

VARIA3:_iS

2Nul3ER

REP,A.43ATES

2

VARIAaLE

NO. OF LEVELS

5Fite-mpir.f

24

Sa

Z

GR4N3 MEAN

39. 93045

SOUR:E 3F

V4RIATION

DEGREES OF

suis aF

MEAN

SZ6J4T<LS

SQUARES

1ft

07.05713

16.75432

23

1.04!0.77/3,7

312.25i12

*12

12

3,7382

.2972

WITHIN

RE°L.I.-, TES

20

1;44.1015i

97.2093o

TOTA.

39

3041.,:i.di

PROBLE1 NO. lp

hit.)48F.R OFVARIA3LE5

2NU48ER OF RE?LICATS

3

VARIABLE

NO. OF LE11-S FArwm

2.

..

z.

GRAND MEAN

39.95636

SOUROE OF

VARIATION

.DEGREES OF

FREE034

SUMS OF

MEAN

SQUARES

SWARES

14

42.61727

10.65429

23

445.53920

106.51303

12

12

6.15092

'

.51256

WITHINRLPLIATES

40

4167.74712

104.19368

TOTAL

59

4662.0543U

0

PROS...EN NG. 10

NUM3ER OF VARIASLES

2NUM3ER OF REPLICATES

1

VARIABLE

2

NO. OF LEVELS

5p

c-ru

rf...

4

C)

GRA;t1D MEAN

40.75142

t.-13 V

SOJ

OF

C)

VAiI4TIJA

Oii."GREES OF

FRilE031

SUMS OF

SQUARES

MEAN

SQUARES

14

2i7.

5867

874

0336

702

3114.26408

38.08803

RESIDUAL

12

1320.63578

110.05298

TOTA.,

19

1732.4864

;

^

PROBLE.M NC.

KO13ER OF VARIA3LES

3

NUMBiR 3F REPLICATES

1

C) 0

VARIABLE

1 3

NO. OF LEVELS

3 3 3

2. 3

GRANO MiAN

36.68437

SOUR:E 3F

OEEES OF

SUMS OF

MEAN

Vib:*kRIA.TION

FREEDOM

SLUAR:S

S:tUARES

2321.5:3311

22

1349.95363

fiat

,

HO

32

2.00443

1.33224

12

41.'62283

.40371

13

023

47.533

1.63-D54

it*RESI3UAL

2.7555

.34444

tb

TOTAL.

26

/687.63244

fib

4.4

to)

a ;

4111

1

VIM

PR33Li:A NO. iF

NU4BiR OF 1,1AIABLES

2

ULMER 3F re,EPLICATaS

vARIA3LE

NO, JF LEVE_S

.44

FA4..T764.

24

.

II1P

SOJ

42.22176

OEGRCiS OF

vARIATION

FRaaD)4

13

23

RESI3U1L

9

TOTA.

15

a

SUMS OF

VAN

SuUARES

S1UARES

258.30012

68.1000,,

314.01793

134.6726':.

531.21693

55.69078

1073,53506

A4a

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.403

lq,1

114h

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F-4 P'

PR33LEN UO, 24

NU-.3:17t

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VARIABLE

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0 GRAND MN

0SOUR:E 3F

0VA;CIATION

NO, OF LEVELS

6rA

crw

it6

55.16867

IliGREES OF

FREz:O3M

SU4S OF

SOjARE

MEAN

SQUARES

5115=z,150

2376233:JO

*4-

23

127,0*963

42033a21

RESDUAL

101.16105

6.74407

TOM_

23

-

1414,42517

,11.

4.11

1./.1

. 14

Vra

h7,

1,44

..42

ailm

aa41

11,,P

.:16.

,..,,t

1..

PR:13-LN

Q. 23

-NU13ER OF VARIA3LZS

2

NL;12IR 3F RiPLICATES

2

AO. OFa

FAcrua...4

4

mi;AN

54.52935

DS OF

SU4S OF

MEAN

FREE.)04

SOjARES

SQUA5

15

287.15144

57.43029

23

131.1806?

43.72687

12

15

22.18920

1.47928

wirnL:t

itEPLI3ATES

24

1330.93251

82.95632

TCT1:.

47

2431.51376

:

:

PR33L.7%

NUM3ER

NUM3ER

;Jr

VA=CIA3LLS

2

REPi.IATES

3

VARIAiL.L

N3. OF LEVELS

16

ps.c.That. r

9

GRAN) 4EA4

04,77520

_nGE:-S 3F

SUMS OF

MEAN

ViT

iF301

SaUARES

SQUARES

1 2 12WITMIN R.IPLICALiS

TOT4L

- : 3

1)4871

31.17907

oo,05257

-3,3U94

3.5'4.:)13

3or'.03do3

100.23581

22.3185Z

6.321Ca

i22.b3475

;;J. 20

NUM3iik 3F VAiaABLES

NU13E1

OF kEPLICATS

4

VARI:iBLE

N3. OF LEVii-S

1a

r4

(:

24

S.

4

GRAA) MEAN

54.d3317

ug

SOUR:E 3F

DEGREES OF

SUMS OF

MLAN

VAiIATIJN

FD34

SUUARES

SUUARES

REE

4.21

"sgs

liaN

4ArO

*441

.4,;_

,.!

3441.23S53

63.04711

23

7.50390

2.50130

12

15

25.04970

1.55998

WIMIN

RI--.PLICATES

72

4721.45112

65.57571

TOTAL

95

53.24029

idef

ih'..

4114

,;:l.

PR

Oat

-EA

NO

. 2E

4.

NU

M3E

R O

F V

AR

IA3'

..ES

NU

M3E

R O

FREPLICATLS

VARIABLE

NG

.OF

44

5

'LEVELS

PC

--na

ik. 5

"-.

GR

AN

D M

E4N

1.67

253

4,

t...

0,4EANS

WITHIN

3

16

8s86322

63C.67217

2.95441

39.42951

to

IOTA.

19

639.73543

Ur

.41

.

11.

PRJ3L.EM NO. 3A

Nj43 :k. OF

VARIA3..ES

2MUM3ER 3F

REPLICAL:S

2

VARIABLE

NO. OF LEVELS

16

Fetc.w4t. 5

,4

4

GRAND MEAN

SOJROE OF

OzGKZLS OF

SUMS OF

MEAN

VARIATION

FREED34

SQUARES

SQUARES

2.5

221.10572

44.22114

23

80.81753

28.9392:,

12

15

34.77357

2.31824

WITHIN

RiPLI:ATES

24

2051.76810

85.49034

TOTAL

47

2394.4649i

;

0

a 0

PRO3-=3

33

NU13ER 3F tiARIA3,-t:S

3

NUA3ER 3F REPLICATES

1

43. OF

12

07 3

4Co

EP

GRAND MEm%

54.62933

0S

CJS

FDEGRES OF

S:JIS OF

MEAN

VARIATID

FRH

SQUA-RLS

SOUARiS

11

29.28344

29.2a344

*11

25

2143.51467

428.73293

V-

03

..,

215,3701

71.9157

,II.

12

5.rJ3C3.-3

.03332

13

3.30324

4,033C8

123

15

132.02o6.)

8,80178

sw

RESIDUA-

I.

.00032

.00032

IOTA.

47

2523,80040

,

;s4

law

.

(a)

0

3,13:26'

LF iI.AN3r FJi FA4;TOIAL

mEALT,,

FAOILITY, Ut;LA

PRO3LE4 NO. 4A

NUMSER 3F IAIRIASLES

NU43ER OF Ri!;':.ICATLS

1

1 2 3

GP.ND NL,47:

C)

SOUi:E OF

VARI4TICiN

o

1 2 3 1,

13

23RESIOUAL

TOTAL

!AO

.14

'

7

to.

pA c

.--v

wft

,.

I

125.046Z5

3t.ES 3

2 2 2 4 4 4 a2 6

irz.RSIDN OF 3EC. 13, 1563

OF

SUMS OF

-1

SQUARzS

MEAN

SQUARES

157.02023

78.51010

t*3155.76384

1377.88192

It*119.27643

59.63922

6.59894

ib.399t4

63.58757

15.14589

62.35904-

15.55976

67.97074

8.49'634

3688.57675:

a a13,133_Ev1 NO 43

N'Ima=R 3F

NUYBER OF

VARIA3LE

3

GRAN) MEAN

3itEPLICATES

2

NO. OF LEVE:..S

3FACMWM.

3 37

124.

9534

8

S3JE OF

VIT

INOF

FREE:J)4

22

23

212

413

423

4123

6WITHIN

REPLIUkTiS

27

4TOTAL.

53

4

1:1;

30'0

4,-;

g1W

.

ibf"

MZAN

SQUAR.ES

355.33004

1774;;502

2163.34*77

1081.b7436

6Z3.09223

33.04612

3te3Ja90

9,.57722

43.?289

10.;5/2

2C.837/

5,20339

26.7327

3.34916

4730.45609

175.20215

7445.05274

.1(

oto

PR33LL:1 NJ. 4C

NU-i3ER OF VARIABLES

3

NO13ER OF REPLICATES

vA21A3L:.

AO. OF LEVE-S

2rA

23

.

33

GRAND AEAN

12a.12::72

SOURO:1 OF

DEG-(Ei.S 3=

SUMS JF

%F.J..N

VAkIATION

FRE6034

SQUARES

S:...ARES

11

2841.69666

2841.63566*

22

1530.26918

765.12359o

32

2'33.91.997

126.3b999

*v.

12

2624.67403

312.33705

**.

13

211.6301

5.75150

23

4121.1560

30425916

*123

4143.60618

35.90154

*WITHIN

REPLICATES

id

156.29926

8.58329

TOTAL

3.

5683.23500

out

tirti

4.iii

tirsi

t:ft.

.41

-,;;114

a 4

PROBLEM

U. 43

NU15ER 3F VARIALILS

3NU:43ER OF REPLICAT:"S

3

VARIABLE

2 3

GRAN3 MEAN

NO. OF LEVELS

2 27

129.13052

S3URCE OF

Oi.--GRiE7', OF

SU4S OF

MEAN

VARIATION

FREED34

SQUARES

SQUARES

19.44684

1S.44E6tr

24.

52.22b83

525002580

31

52.5113

52.54119

i2

422905

229j5

13

.02684

23

.07389

.07a09

173

V.,417357

25.17652

REPLIZATES

lb

5052.69671

315.79354

TOTAL

23

5675.21684

Skag

e;40

#4;f

:zai

:*k.

:1:0

,'144

1.46

,AtP

iE.4

A44

4.fi

l,'.4

0.04

.4-6

3t4g

-P01

1,4-

4;.3

,^,

FR33..E.1 NO.

NUNSEK OF ,IARIA3LES

3

Nc.:PLICATES

2C)

e. ..;

13

4

.0

23

4123

bWITHIN RE°LICA1E3

27

-:()

TOTAL

53

VARIABL:'

NO. OF LLIV-S

32

33

124.

9:4

: 3.;.

-

SOUR:E OF

UEG;Cas OF

i/A4I4TI3;i

12

22

37

.1.. 4.,

4

0 0

7

LUIS OF

JtAUS

MEAN

SUUARES

362.26164

181.13082

2143.83106

1071.91553

oSod2737

31,91369

41.34976

10.33744

43.i0124

10.975!2

23.37026

6.84256

22.73601

2.84200

4695.95606

173.92430

7337.23345

44."

tee:

git

PRO

3i.;N

P.(

, 4F

N1J13ER 3F VARIA-6%-ES

3

NUA3ER 3F REPLICATES

VARIABLZ

O.

OF

LEVELS

.

13

;2

3-

4,

33

....

741

.

41P

GRAAF) MiEAN

124.97813

.

4111

.

41.

ASP

'

alp

SOURC; OF

VARIATILN

1 2 3 121323

RESI3UAL

TOTAL

OEGR,IES OF

2 2 9 4 4 6

25

SUAS OF

Si4jARES

156.14463

311:j.51353

139.49189

65,75207

71.;.337J

66.83544

69.24467

3887.0393

MEAN

SQUARES

78.07235

15!03.73576

6.3.745:0

16.43602

17.513-t2

16.706

8.65553

410

AM

.

NO

P

,Si

a"'

""'

;zi

:'

PROS.-EM NO4 54

WISER OF V4RIA3LES

2NtriaiR 3F RiPLI GATES

1.

VARI43LE

tif.'04OF LEVELS

15

c.ro

st,

24

-

GRAN) MiA%

21.5:1415

SOJR

3F

VArZIAT13N

1 2 RESIDUAL

TOTAL

DEGREES OF

SUNIS OF

MEAN

FREE031

SQUARiS

SQUARES

4126434C:1a

31.58502

*-*

36.7.'730

2.2490G

12

34.31t143

2.85557

19

167.47752

J

PR33LcM NO. 53

Nj43ER 3F VARIA3...ES

2

NLA3ik OF kEPLICATES

2

VARIABLi

NO, OF LEVE...S

15

Fort-row. sr-

02

4`-

7

0 GRAN) MEAN

2E453334

SOUR:E OF

0 VARI4TI:JN

rI

4N...

L 2 12

0 WITmIN

T3TAL

0

DEGkE=S OF

SUIS

iF

MEA;;

FRia331

SQJAR,--S

siltittiCS

423.33:,:13

5.51

3.95993

12

32.761

2.fl572

RLICATZ3

20

11,-4.53i;43

5.934C2

33

1754d369::

..74.

6);4

4,44

,430

,13,

444§

6,44

4646

-,

1,1

',AM

!,,

!!!

!-!

4,...

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4g2h

i!--

!!!

-11

0,44

0.4,

s-t

PROBLEm NO.

NU13ER OF VAR.T.L3L.:7S

2

NU4BER 3F RI"-;;;Ti.S

VARI4SLii

:4 C

$3F LZVEL.S

15

rAc-rullu

1

24

_3

GRAND mEAN

23.55632

SOURD.r. OF

DE.SkES OF

SUMS OF

mEAN

vARIkTICAN

FRECO3M

SQUAKLS

SQUARES

14

17.82252

4.43563

23

15.3444,/

5.11483

RESIDuAL

12

b9.72433

5.81036

TOTA_

19

102.89132

--

.3:1

4.11

4.,

Htr

PF39LE..:1

r4;e6

NL43i;.! :F VARIA3.ES

NU13:-R 3F RiPLITS

2

VARIAaLE

AO. OF LEVE,-S

3rA

.7

37

GRAN) MEAN

20.50336

ut

sro

vAaI47.-T

aEGRrLES 3F

FREEa31

SUMS UF

SQUAKES

MEAN

SQUARES

25.71955

2685377

22

1,093

.51421

12

49.25065

2.3141t

WITHIN

REPLICATES

961.59677

6.84409

TOTAL

17

77.60140

13tJ

"

'4

11 ig

41-1

1.:

E'.3

1,6,

41:4

0PROBLEM td4.).

NUMBER 3F VA;::A3LES

NU13ER jF RELI;;ATLS

VARIABLE

N.)

:.:17

Li i:-"L.S

4FA

C. T

VAL.

GRAND M1A4

212.908'1

MEANS

WIT4IN

TOT:.V

3

- :±

'''

46063

31s7o379

Jc, 42942

1,5521

2,64533

,z+

.1ai

d,4 ;

ktiti

,W

4 v

As.

1-a

Us

0 0 0 a 0 0

;--t

1NO. 64

NU;IS:-R OF VARIABLES

3

NUMP2'R OF REPLICATES

2

VA

RIA

BL

E

3

GRANO MEAN

SOUP:1=

-

VARIATION

NO

. OF

LE

VE

LS

3vd

tS"

311

101.38091

7

OEREES OF

SUMS OF

FR1E00.1

.SQUARES

MEAN

SQUARES

282.25594

41.13297

22

5.35874

2467037

32

9.21071

4,5.6:535

12

4107,63906

26.90976

13

417.03797

4.25199

23

4.80000

00000

123

21.93444

.2.74b05

WITHIN

F.::=PLICAT

27

348.13749

,14.745813

TOTAL

53

641.40435

4

:;.;

;:4

;W.

S;

-r-

Mra

-S

.16

01.4

110,

.

a I

111 al it atI141 lii I I I

!CI in:.

Q. z

Aff

01) tiN ' CT) .1) t1 r4 t)

, .4") 01 43I i 4 0 N. r. 44N 11-1

7 .1 t Ps. it\at t a 14 4LI 7, CIN (1 (N1 14')

( 3 (\J ;

Cr) .1 -I-4 Is. In in11. y Pf) .4.1 111 1.0 01 C, LIN

-4 C./ -4 cr to wi111 0:) 41' 1 r) c.) co cJ

Cfl ri L. 1:" CN ..-1,* :1 *..1 r4 ) r .1'I') (1) (\ I all in

NI 1 4.

CN.1 0.1 ar CO is.. (1)(\I LA

CI

I i I i 1

I I a I I I I'I

I 1 4 , I I 4 Iil e I I 4

C '1 V 0" I I4NI tn in iNJ I 4 0

1 1 411 :9 .. 4 "J PO ri ,1-4 (U v-4 3 t'

153

1591

PR33LEM No. 74

WP/3ER C

ARIABLES

NU43ER C

RELICATES

8

VARIABLP

2

:40.

OF

LE

1EL

S3

FVec

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iz.

3.

GRAND MEAN

75.6333

SCJURCE OF

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OF

VARIATION

i2

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712

4

;4ITHIN REPL134TES

63

#T

CT

AL

71

:agl

igiii

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liFita

teir

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o':*

24:4

8-44

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4,...

v.-1

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SUM

S O

FMEAN

SaUARZS

2.15156

1.07578

18,74345

9.37173

22.74763

5.651

1632,63044

26:7CE.42

1726.27308

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