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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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