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!