Page 9 - Azerbaijan State University of Economics

Yadulla Hasanli, Nazim Hajiyev, Gunay Rahimli:Distribution and Analysis of Admission
Scores (In the Case of Azerbaijan

İ
χ2 = ∑ ( − ) 2 (1)
=1

Here, k- is the number of intervals, − observed frequency in the i-th interval, is
İ

expected frequency in the i-th interval and is obtained by multiplicating event’s
theoretical probability (here, the event is that variables are in the i-th interval) by the
number of trials. Probability of variables are in the i-th interval is found as follows:

= ( ) − ( −1 )

To determine if data follows any theoretical distribution using χ2 test, the hypothesis
is constructed as follows (Hein K., 2002):
: the variable is subject to the stated distribution;
0
: the variable is not subject to the stated distribution.
1
Then we compute the value of χ 2 for the random variable using formula

(1). If we choose the distribution law correctly, then χ 2 variable will have

χ2 theoretical distribution, as the number of observations increases.

This is a continuous distribution and this distribution depends on a parameter r
called the degree of freedom: r=k-1-s. Here, k is the number of intervals, s- is the
number of parameters of the distribution law.

There is a table especially designed for χ2 distribution. Using this table, firstly we

find the critic value of χ2 for the given value of the degree of freedom and it is
compared with χ 2 . If χ 2 < χ 2 , then hypothesis, that is, the
0

law of distribution is accepted. Otherwise, the proposed hypothesis is rejected
(Палий И.,2004).

Tested distributions
Most natural and economic processes follow a normal or asymptotic normal
distribution (for these processes, as the number of trials increase, their distribution is
approaching normal distribution). When analysing exam results, checking whether
the results have a normal distribution or not is one of the widely used methods in the
literature (W.Yuan, C.Deng, H. Zhu, J.Li., 2013; Akella, S., Diaz, P. M., & Babu, B.
S., 2017). Therefore, firstly, we will check whether the scores obtained in the
admission exams follow a normal and exponential distribution.

9