Summary CHI-SQUARE DISTRIBUTION BASIC CONCEPTS

22CS301
PROBABILITY, STATISTICS
22EC301 – PROBABILITY,
AND
STATISTICS AND RANDOM PROCESS
QUEUING THEORY
UNIT III
UNIT IV

TESTING OF HYPOTHESIS

1.5. CHI-SQUARE DISTRIBUTION
5.1. BASIC CONCEPTS

5.2. PROBLEMS

, Degrees of freedom= n-1 = 4-1=3
Tabulated  02. 05  7 . 815

H 0 accepted. The experimental results support the theory.



Chi- square test for independence of attributes

The Chi-Square test of independence is used to determine if there is a significant
relationship between two nominal (categorical) variables. The frequency of each category for
one nominal variable is compared across the categories of the second nominal variable. The data
can be displayed in a contingency table where each row represents a category for one variable
and each column represents a category for the other variable.

For example, say a researcher wants to examine the relationship between gender (male
vs. female) and empathy (high vs. low). The chi-square test of independence can be used to
examine this relationship. The null hypothesis for this test is that there is no relationship
between gender and empathy. The alternative hypothesis is that there is a relationship between
gender and empathy (e.g. there are more high-empathy females than high-empathy males).

Let us consider two attributes A and B.A is divided into two classes and B is divided into
two classes. The various cell frequencies can be expressed in the following table known as 2  2
contingency table.

A a b

B c d



a b a+b
c d c+d
a+c b+d N