Master Admission Exam
Results Analysis
NA RM IN JA RCHA LOVA
TA H MINA I M A NOVA
M U RA D M U RA DOV
E L M IN I B R A H IM OV
A DA
Road Map
Problem description
Hypothesis testing & recommendations
Regression
Concluding remarks
2
Do males perform better than females?
Which question types are females’ favorite?
Do students graduating from Russian Sector score more than the
Azerbaijani Sector Students?
Are even question banks more difficult than odd?
Does your educational background affect your test results?
3
Methodology
Deductive research method
Quantitative analysis
Unit of analysis: master applicant’s result
in Logic
Excel program
Independent variables: student’s gender, language of
instruction, educational background, test bank category
Level of significance = 0.05
Dependent variable: exam results
Source: SSAC, 2011 1st tour Master exam
results in Logic
4
Limitations
Time scope of data
Goals
To give insight for further research
by specialists in educational
science
Absence of student-by-student on
their university affiliation
Lack of qualitative analysis due to technical
character of the paper and time constraints
5
Type 1
Type 2
Numerical
Problems
Type 3
Word pattern
Type 4
Figures
Type 5
Charts
 YLA
DDV
8 7 *
+
34 9 *
* * **
** ** 9 3
Məhsulun maya dəyərinin 40%-ni xammal
qiyməti təşkil edir. Xammal qiyməti 50%
artarsa, yeni maya dəyərinin neçə faizini
xammal qiyməti təşkil edər?
arı – neştər;
ilan – ?
A
hündürlüyü (sm)
50
40
30
20
B
10
0
Type 6
V=?
Numerical pattern
1
2 zaman (ay)
123=9, 96=9, 48=5, 911=?
+
Type 7
Graphical pattern
+
?
6
Statistics on Gender’s Performance
7
H0: μm-μf≤0; H1: μm-μf≥0
Males perform better than females
50
Sample size for each gender
Hypothesis test results
F test
Do not reject
α = 0.05
σ=σ
t test
Reject
α = 0.05
H0: μm – μf > 0
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
Sample size for each gender
50
R2
Y
Exam result
0.03
=
33.6
―
2.1
X
Gender:
Males 1
Females 2
10
Identified specialties
Humanities
Economics
R2
Y
Exam result
Technical
0.08
=
26.9
+
1.97
X
Specialty:
Humanities 1
Economics 2
Technical 3
11
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 mathrelated subjects
12
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
Mean
Variance
Observations
Pooled Variance
Hypothesized Mean Difference
Df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
MALE
FEMALE
0.44642
9
0.07892
5
50
0.06739
1
0
98
1.29321
0.379286
0.055856
50
0.09948
9
1.66055
1
0.19897
9
1.98446
7
DON’T REJECT
14
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
Implications for hypotheses 2&3
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
17
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
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
20
H0: μ A,C-μ B,D≤0; H1:μA,CΜb,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 results
t-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
22
P(T<=t) two-tail
0.280017
DON’T REJECT
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
23
OECD education ranking
OECD education rankings
On the reading subscales
On the overall
reading scale
556
Access and
retrieve
549
Korea
539
542
Azerbaijan
362
361
Kyrgyzstan
314
299
Shanghai-China
Reflect and
evaluate
557
Continuous
texts
564
Noncontinuous
texts
539
542
538
542
546
538
541
373
335
362
351
431
373
327
300
319
293
331
330
Integrate and
interpret
On the
mathematics
On the
scale
science scale
600
575
558
24
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
25
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Thank You for Attention!
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