The Chi-Squared Test of Association allows the comparison of two attributes (i.e. qualitative variables) in a sample of data to determine if there is any relationship between them.

The idea behind this test is to compare the observed frequencies with the frequencies that would be expected if the null hypothesis of no association / statistical independence were true. By assuming the variables are independent, we can also predict an expected frequency for each cell in the contingency table. If the value of the test statistic for the chi-squared test of association is too large, it indicates a poor agreement between the observed and expected frequencies and the null hypothesis of independence / no association is rejected.

An example where chi-square test can be used
A 3*3 contingency table is given below relate to 830 professional workers living in India towns and cities, who were interviewed during a survey:

If we are interested in finding the relationship between activity status and occupation group (i.e. whether these two attributes are independent or not), we calculate chi square statistic based on the difference between expected frequencies and actual frequencies, and then according to the value we reject/accept our null hypothesis.