WHY NOT CHI-SQUARE?

Previously we used the chi-square test to test the null hypothesis that two categorical variables are independent. If you reject the null hypothesis of independence, what can you say about the two variables ? Can you conclude anything about the strength or nature of their association on the basis of the actual chi-square value? Do large chi-square values indicate strong associations and small values indicate weak ones?

The actual value of the chi-square statistic provides you with little information about the strength and type of association between two variables. In our discussion about the cross-tabulation, we implied that sample size will influence the results and, as a consequence, the chi-square value. If you take a particular cross-tabulation and multiply all cell frequencies by 10, you also increase the value of the chi-square by 10. By increasing the frequency in each cell , you are not in any way changing the nature or strength of the association ” that remains exactly the same. The value of the chi-square statistic depends on the sample size as well as the amount of departure from independence for the two variables. So you cannot compare chi-square values from several studies with different sample sizes. This is one reason why the chi-square statistic is not very useful as a measure of association. Furthermore, since chi-square is based only on expected and observed frequencies, it is possible for many different types of tables to have the same value for the chi-square statistic. Different types of relationships between two variables can result in the same chi-square value. Knowing the chi-square tells you nothing about the nature of the association.