Master Admission Exam Results Analysis

NARMIN JARCHALOVATAHMINA IMANOVAMURAD MURADOVELMIN IBRAHIMOV ADA

Road Map

Problem description

Hypothesis testing & recommendations

Regression

Concluding remarks

2

Do males perform better than females?

Do students graduating from Russian Sector score more than the Azerbaijani Sector Students?

Are even question banks more difficult than odd?

Which question types are females’ favorite?

Does your educational background affect your test results?

Problem description

3

Methodology

4

Quantitative analysis

Excel program

Level of significance = 0.05

Source: SSAC, 2011 1st tour Master exam results in Logic

Deductive research method

Unit of analysis: master applicant’s result in Logic

Independent variables: student’s gender, language of instruction, educational background, test bank category

Dependent variable: exam results

Limitations

5

Time scope of data

Absence of student-by-student on their university affiliation

Lack of qualitative analysis due to technical character of the paper and time constraints

Goals

To give insight for further research by specialists in educational science

Type 1

Numerical

Y L A D D V 8 7 * 3 4 9 * * * ** * * * * 9 3

+

V=?

Type 2

ProblemsMəhsulun maya dəyərinin 40%-ni xammal qiyməti təşkil edir. Xammal qiyməti 50% artarsa, yeni maya dəyərinin neçə faizini xammal qiyməti təşkil edər?

Type 3

Word pattern arı – neştər; ilan – ?

Type 4

Figures

Type 5

Charts

0

10

hündürlüyü (sm)

zaman (ay)

20 30

40

50

1 2

A

B

Type 6

Numerical pattern 123=9, 96=9, 48=5, 911=?

Type 7

Graphical pattern

+

+ ?

Question types

6

7

Statistics on Gender’s Performance

H0: μm-μf≤0; H1: μm-μf≥0

Males perform better than females

Sample size for each gender

50

Hypothesis test results

F test Do not reject α = 0.05

t test Reject α = 0.05

σ = σ

H0: μm – μf > 0

Hypothesis 1 – Males vs. Females

8

     Test results

t-Test: Two-Sample Assuming Equal Variances

Males Females

Mean 31.5 29.38

Variance 37.68367347 34.81183673

Observations 50 50

Pooled Variance 36.2477551

Hypothesized Mean Difference 0

Df 98

t Stat 1.76061869

P(T<=t) one-tail 0.040711292

t Critical one-tail 1.660551217

P(T<=t) two-tail 0.081422584

t Critical two-tail 1.984467455

REJECT

9

Regression 1 – Role of gender

R2 0.03

50

Y = 33.6 ― 2.1 X

Exam resultGender: Males 1

Females 2

Sample size for each gender

10

Regression 2 – Role of educational background

R2 0.08

Humanities

Y = 26.9 + 1.97

X

Exam resultSpecialty:

Humanities 1Economics 2Technical 3

Identified specialties

Economics Technical

11

Hypothesis 1: Implications

12

Males choose mostly technical courses, because of their future work plans, that’s why they pass logic tests better than females

Males choose technical occupations because they are initially better at math and math-related subjects

Hypothesis 2: Number type questions

H0: μm-μf≥0; H1: μm-μf≤0

Males perform better in number type questions

Sample size for each sector

50

Hypothesis test results

F test Reject α = 0.05 σ ≠ σ

13

Test results

t-Test: Two-Sample Assuming Equal Variances

  MALE FEMALE

Mean 0.446429

0.379286

Variance 0.078925

0.055856

Observations 50 50

Pooled Variance 0.067391

Hypothesized Mean Difference 0

Df 98

t Stat 1.29321

P(T<=t) one-tail 0.099489

t Critical one-tail 1.660551

P(T<=t) two-tail 0.198979

t Critical two-tail 1.984467

 

DON’T REJECT14

Hypothesis 3 – Figure type questions

H0: μm-μf≤0; H1: μm-μf≥0

Females are doing better than males in figure type questions

Sample size for each sector

50

Hypothesis test results

F test Do Not Reject α = 0.05 σ = σ

15

Test results

t-Test: Two-Sample Assuming Unequal Variances

  MALE FEMALE

Mean 0.505714 0.522857

Variance 0.046822 0.047155

Observations 50 50

Hypothesized Mean Difference 0

Df 98

t Stat -0.39542

P(T<=t) one-tail 0.346697

t Critical one-tail 1.660551

P(T<=t) two-tail 0.693394

t Critical two-tail 1.984467  

DON’T REJECT

16

Impl icat ions for hypotheses 2&3

17

These differences might be related to gender differences in reasoning: males are prone to abstract thinking, while females feel more comfortable performing tangible tasks

This problem can be investigated in deep by psychologists and might have far-reaching implications for educational methodology

Hypothesis 4 – Azerbaijani and Russian sectors

H0: μaz-μru≤0; H1:μaz-μru≥0

Azerbaijani Sector performs better than the Russian

Sample size for each sector

50

Hypothesis test results

F test Reject α = 0.05 σ ≠ σ

18

Test results

t-Test: Two-Sample Assuming Unequal Variances

  AZERBAIJANI SECTOR RUSSIAN SECTOR

Mean 30.24 29.08

Variance 29.7779592 31.6669388

Observations 50 50

Hypothesized Mean Difference 0

Df 98

t Stat 1.04640565

P(T<=t) one-tail 0.14897392

t Critical one-tail 1.66055122

P(T<=t) two-tail 0.29794785

t Critical two-tail 1.98446745  

DON’T REJECT

19

Implications

20

Though observed means suggest that Azerbaijani sector performs better, the significance 0f this difference is not very high and doesn’t hold at 5-% level

Relatively low performance of Russian sector might be correlated with lower contest among its students than in Azerbaijani sector; hence allocation of places might be revised

Hypothesis 3 – odd versus even test variants

H0: μ A,C-μ B,D≤0; H1:μA,C-Μb,d≥0

QB “A” and “C” are harder than “B” and “D”

Sample size for each sector

50

Hypothesis test results

F test Do Not Reject α = 0.05 σ = σ

21

Test resultst-Test: Two-Sample Assuming Equal Variances

  EVEN ODD

Mean 29.34 30.68

Variance 42.10653 33.97714

Observations 50 50

Pooled Variance 38.04184

Hypothesized Mean Difference 0

Df 98

t Stat -1.08629

P(T<=t) one-tail 0.140009

t Critical one-tail 1.660551

P(T<=t) two-tail 0.280017 DON’T REJECT22

Hypothesis 5: Implications

23

The difference exists , but it is significant at 10-% level, and it should be examined throughout several years in order to confirm any dependency

In case its existence is established, it may be caused by the difference in the tests’ sequence; if more difficult ones are in the beginning (and the test sequence indeed differs according to a variant), they can take more time and thus students show worse results

OECD education ranking

24

OECD education rankings

On the overall reading scale

On the reading subscalesOn the

mathematics scale

On the science scale

 

Access and retrieve

Integrate and interpret

Reflect and evaluate

Continuous texts

Non-continuous

textsShanghai-China 556 549

558

557 564 539 600 575

Korea 539 542

541

542 538 542 546 538

Azerbaijan 362 361 373 335 362 351 431 373

Kyrgyzstan 314 299 327 300 319 293 331 330

Concluding remarks

25

Introducing quantitative courses for humanitarian students

To check the quality of education at humanitarian universities and learn why their students end up scoring less than their technical counterparts

To develop analytical skills by introducing essay questions into master exams

To analyze gender choices in education

Any questions or comments?

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Thank You for Attention!