This document discusses the chi-square test, a statistical hypothesis test where the test statistic follows a chi-squared distribution if the null hypothesis is true. It was developed by Karl Pearson in 1900. The chi-square test can be used to examine differences between observed and expected results in a random pattern. It is applicable to testing independence between attributes and goodness of fit to theoretical distributions. Common mistakes in applying the chi-square test include small theoretical frequencies, neglecting non-occurrences, and incorrect determination of degrees of freedom. The chi-square test is used to test significance of sample variance, independence in contingency tables, comparisons of frequency distributions, and goodness of fit.

1. PRESTIGE
INSTITUTE OF MANAGEMENT , GWALIOR
Submitted by:
RAHUL KAPOLIYA
MBA-1ST C
Submitted to :
PROF. AMRITA
SHRIVASTAVA
CHI-SQUARE TEST

2.  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 .

3.  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.

4.  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

6.  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?

7.  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 .

8. 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 ..

9.  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 frequencies
2. Neglect of frequencies of non -occurance

10. 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.

11.  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.