PRESTIGE

INSTITUTE OF MANAGEMENT , GWALIOR

Submitted by: RAHUL KAPOLIYAMBA-1ST C

Submitted to :PROF. AMRITA SHRIVASTAVA

CHI-SQUARE TEST

What is statistical Hypothesis ? A statistical hypothesis is an

assumption about a population parameter . This assumption may or may not be true . Hypothesis testing refers to the formal procedures used by statisticians to accept or reject statistical hypothesis .

Meaning of chi- square test

A chi square test , also written as x square test ,is any statistical hypothesis test where in the sampling distribution of the test statistic is a chi-squared distribution when the null hypothesis is true . Without other qualification , chi-squared test often is used as short for pearson’s chi-squared test.

The chi-square test is an important test amongst the several tests of significance developed by statisticians.

Is was developed by Karl pearson

in 1900.

Chi is pronounced as Kye

Chi-square test formula

When to use chi-squared ?

Chi –squared is used to examine difference between what you actually find in your study and what you expected to find .look at the list of questions below. If the answer is yes to each question ,a chi-squared test is appropriate

Are you trying to see if there is a difference between what you have found and what would be found in a random pattern?

Is the data gathered organised into a set of categories?

Uses of chi-square test

Chi-square test is one of the most general and simple test . It is applicable to various types of problems. The significance of chi-square test is as follows

1. X2 test helps in testing independence – with the help of Chi-square test, we can find out whether two or more attributes are associated or not .

Cont.

2 Chi-square as a test of goodness of fit- X2 test is also known as test is also known as test of goodness of fit because it enables us to ascertain how well the theoretical distribution ..

Mis use of chi-square test Chi-squared test is one of the most

frequently used statistics . Unfortunately , it is also misused. The most common mistake in the application of chi-square is the violation of independence between measures or events.

1. Small theoretical frequencies2. Neglect of frequencies of non -

occurance

Cont.

3. Failure to equalise the sum of obeserved frequencies and the sum of theoretical , frequencies

4. In correct determination of the number of degrees of freedom .

5. Use of non-frequency data.

Application of X2 -distribution To test the significance of sample

variance To test the independence of

attributes in a contingency table To compare a number of frequency

distributions To test the goodness of fit.