Chi-Square is an important non-parametric test and as such, rigid assumptions are necessary regarding the type of population we require only the degree of freedom for using this test. Non- parametric chi-square test can be used

- As a test of goodness of fit
- As a test of independence

This test was developed by statistician “**Karl Pearson”**.

** As a test of goodness of fit:** Chi – square test enables us to explain how the theoretical distribution fits to the observed data. If the calculated value of the chi-square is less than the table value at a certain level of significance it means that there is no difference between observed and expected frequencies otherwise there is a significant difference between expected and observed frequencies.

* As a test of independence*: the Chi-Square test enables us to explain whether or not two attributes are associated. For example, we may be interested in knowing whether a new medicine is effective in controlling fever or not. The chi-square test will help in deciding this issue. For this first of all we calculate the chi-square value and the value is compared with the table value.

If the calculated value of chi-square is less than the table value at a given level of significance for a given degree of freedom we conclude that the two attributes are independent i.e. medicine is not effective in controlling fever.

We may apply the chi-square test either as a test of goodness of fit or as a test to judge the significance of an association between attributes. Chi-Square is calculated with the help of the following formulae :

\(\chi ^{2}\; \left( \mbox{C}al \right)\; =\; \sum_{}^{}{\frac{\left( O-\mbox{E} \right)^{2}}{\mbox{E}}}\)

Where O = Observed frequency

E = Expected frequency

*D.f = (r-1) (c-1)*

Conditions for the application of the Chi-square test :

- Observations recorded and used are collected on a random basis.
- All the items in the sample must be independent.
- No – group should contain very few items.
- The overall no if items must be greater than 30. i.e. it should normally be at least 50.
- The constraints must be linear