# Chi-square test for Homogeneity

The chi-square test is a non-parametric statistical technique that is used to evaluate the association and homogeneity between categorical variables. The variables should come from two different populations. The method mainly uses frequency counts and checks whether they are distributed evenly across different populations.

In order use the chi square test, contingency tables are involved. A contingency table is a table that shows the distribution of one variable in rows and that of the other in columns. This distribution can either be in percentage or total count. An example of a contingency table is as shown below

The null hypothesis of the chi square test for homogeneity is the proportion from two given populations are equal. For instance using the table above, the hypotheses will be;

### Null hypothesis:

The proportion of women respondents who are unemployed is proportional to men. Similarly, the proportion of women who are employed is equal to that of unemployed men

### Alternative hypothesis:

At least one of the null hypothesis statements is false. The chi square test statistic is usually calculated using the formula

The chi square test statistic for homogeneity is usually associated with (r-1)*(c-1) where r is the total number of rows and c is the total number of columns.

If the P value of the test is less than the significance level, the null hypothesis is rejected. Additionally, if the calculated chi square test statistic is less than the tabulated the null hypothesis is also rejected.

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