Honors Project

Genta AgajSupervisor: Dr. Brian Bowen

Technical Advisor: Mrika Kotorri

MethodologyBackground Information on Standardized

testsNormality CheckAnalysis of Variance (ANOVA) Test Regression EquationRecommendations and Conclusion

Presentation Outline

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Obtain the State Matura Exam scoresMunicipality Education Directorate (MED) Sample size: 3,267 (out of 5,284)Minitab was used as a statistical software

Methodology

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Any test that is “administered and scored in a

predetermined, standard manner” (Popham, 1999). Standardized test results have a Normal Distribution

The tests are composed out of two sections:1. General section (120 points)2. Concentration-based section (80 points)

Standardized Tests

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9680644832160

Median

Mean

706968676665

1st Q uartile 53.000Median 69.0003rd Q uartile 80.000Maximum 107.000

65.592 66.855

68.000 70.000

17.967 18.860

A -Squared 29.65P-V alue < 0.005

Mean 66.223StDev 18.403V ariance 338.670Skewness -0.511150Kurtosis -0.346412N 3266

Minimum 0.000

A nderson-Darling Normality Test

95% C onfidence Interv al for Mean

95% C onfidence Interv al for Median

95% C onfidence Interv al for StDev95% Confidence Intervals

Summary for Total Points

988470564228

Median

Mean

7069686766

1st Q uartile 54.000Median 69.0003rd Q uartile 80.000Maximum 107.000

65.906 67.142

68.000 70.000

17.543 18.418

A -Squared 29.30P-V alue < 0.005

Mean 66.524StDev 17.970V ariance 322.918Skewness -0.426277Kurtosis -0.616856N 3249

Minimum 17.000

A nderson-Darling Normality Test

95% C onfidence Interv al for Mean

95% C onfidence Interv al for Median

95% C onfidence Interv al for StDev95% Confidence Intervals

Summary for Total (removed outliers)

Normality Check

363024181260

Median

Mean

25.024.524.023.523.0

1st Q uartile 19.000Median 24.0003rd Q uartile 29.000Maximum 39.000

23.042 23.540

24.000 25.000

7.080 7.433

A -Squared 36.97P-V alue < 0.005

Mean 23.291StDev 7.252V ariance 52.596Skewness -0.586443Kurtosis -0.250879N 3260

Minimum 0.000

A nderson-Darling Normality Test

95% C onfidence Interv al for Mean

95% C onfidence Interv al for Median

95% C onfidence Interv al for StDev95% Confidence Intervals

Summary for English

3530252015105

Median

Mean

25.024.524.023.523.0

1st Q uartile 19.000Median 25.0003rd Q uartile 29.000Maximum 39.000

23.184 23.671

24.000 25.000

6.896 7.240

A -Squared 35.64P-V alue < 0.005

Mean 23.427StDev 7.064V ariance 49.895Skewness -0.507360Kurtosis -0.484059N 3240

Minimum 4.000

A nderson-Darling Normality Test

95% C onfidence Interv al for Mean

95% C onfidence Interv al for Median

95% C onfidence Interv al for StDev95% Confidence Intervals

Summary for English (outliers removed)

302520151050

Median

Mean

20.019.519.018.5

1st Q uartile 12.000Median 20.0003rd Q uartile 24.000Maximum 30.000

18.261 18.751

20.000 20.000

6.970 7.316

A -Squared 56.58P-V alue < 0.005

Mean 18.506StDev 7.139V ariance 50.965Skewness -0.416625Kurtosis -0.924102N 3267

Minimum 0.000

A nderson-Darling Normality Test

95% C onfidence Interv al for Mean

95% C onfidence Interv al for Median

95% C onfidence Interv al for StDev95% Confidence Intervals

Summary for Math

Normality Check

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What does it mean for students?What does it mean for universities?Why the distribution is not normal?How to make the distribution normal?

Normality Check – Analysis and Discussion

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Milleniumi i 3te Zeniti Xhevded

DodaSami

Frasheri LuarasiAmericanSchool ofKosova

DonBosko

PrenkJakova

EqremQabej

Universum

HoxheKadri

Prishtina

28Nentori

Mean 90.31 85 79.72 78.88 78.2 77.2 76.97 65.52 65.31 65.27 56.67 46.03

0

20

40

60

80

100

120

Scor

es

School

ANOVA Test on Scores - General Section

Tukey Test Grouping

A A B B B ABC B C B C D D CDE E F

Number of students

26 11 368 866 15 40 220 50 209 15 926 525

Private Yes Yes Yes Yes Yes Yes

General Yes Yes Yes Yes Mixed Yes Mixed Yes Mixed8

Milleniumi i 3te Zeniti Luarasi Xhevded

DodaSami

FrasheriDon

BoskoEqremQabej

Universum

PrenkJakova

AmericanSchool ofKosova

HoxheKadri

Prishtina

28Nentori

Mean 34.962 31.636 29 28.885 28.447 26.4 25.048 24.733 24.5 23.125 21.793 17.678

0

5

10

15

20

25

30

35

40

45

50Sc

ores

in A

lban

ian

School

ANOVA Test on Scores - Albanian Section

Tukey Test Grouping

A ABC BCDEF

B D B D C G F G H

DEFGHI

EFGHI

HI I J

Number of students

26 11 15 364 866 220 209 15 50 40 926 525

Private Yes Yes Yes Yes Yes Yes

General Yes Yes Mixed

Yes Yes Mixed

Yes Mixed

Yes9

Limitation – calculations are done from a sample Focus on ANOVA’s use as a tool instead of the

comparisons The benefit of publishing online ANOVA results:

1. Benefits to students2. Benefits to parents3. Benefits to schools (especially private)4. Benefits to Municipality

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Analysis and Discussion

“School” tested whether being a student in “Xhevded Doda” means performing better;

“Gender” tested whether females perform better than males; “Private/ Public Education” tested whether private schools

have performed better than the public schools; “Average Student per Class” tested whether a larger class size

have higher scores than a smaller class size.

Regression EquationSignificant

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Limitations – too little variables used Coefficient of Determination is 13.8%

Recommendations – add more variables such as: GPA, parental income, parental education, school’s budget per student, the amount of cheating on the test day, etc.

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Recommendations

Normality Check Test the questions beforehand

ANOVA Make the results public

Regression Equation Expand it further

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Conclusion

Work Cited

Constitution of Kosovo. Law No. 04/L-032 on Education.Constitution of Kosovo. Law No. 03/L-018 on Final Exam and State Matura Exam.Bellaqa, Bashkim et al. (2014) “Education Statistics 2012-2013.” Kosovo Agency of Statistics.

Retrieved September 12, 2014.Fletcher, D. (2009, December 11). Standardized Testing. Retrieved September 18, 2014.Hogben, D. (1963). SOME PROPERTIES OF TUKEY'S TEST FOR NON-ADDITIVITY (Order

No. 6405896). Available from ProQuest Dissertations & Theses Full Text. (302128132). Retrieved from http://search.proquest.com.ezproxy.rit.edu/docview/302128132?accountid=108

How important is class size? (2012). Retrieved December 29, 2014, from http://www.greatschools.org/find-a-school/defining-your-ideal/174-class-size.gs?page=all

How to Interpret Your GRE Scores. (n.d.). Retrieved January 15, 2015, from http://www.princetonreview.com/grad/gre-exam-score.aspx

Kucnel, N., & Hezlett, S. (2007). Standardized Tests Predict Graduate Students' Success. ScienceMag, 315(5815).

McDonald, A. et al. (2000). Aptitude Testing for University Entrance: A Literature Review. Retrieved October 3, 2014.

Popham, W. J. (2001). The truth about testing: An educator's call to action. Alexandria,VA: Association for Supervision and Curriculum Development.

Popham, W. J. (1999). Why Standardized Tests Don't Measure Educational Quality. Retrieved September 15, 2014.

Rideau, S. O. (2009). Teachers cheating on standardized achievement tests: Perceived causes and effects. ProQuest, UMI Dissertations Publishing).

Rotberg, I. (2006). Assessment Around the World. Retrieved September 18, 2014.Stigler, S. (2008). Fisher and the 5% level. Chance, 21(4), 12.

doi:http://dx.doi.org/10.1007/s00144-008-0033-3Turner, C. (2014, April 30). U.S. Tests Teens A Lot, But Worldwide, Exam Stakes Are Higher.

Retrieved October 7, 2014.Wenderoth, A., & Moo Sang, B. (2004, January 1). Situational Analysis of Education in Kosovo.

Retrieved October 3, 2014.Worthen, B. R., & Spandel, V. (1991). Putting the Standardized Test Debate in Perspective. Alexandria: Association for Supervision and Curriculum Development.

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