Analysing dependence

If it is concluded that dependence is likely in the table, you should examine carefully the cells of the table where there are the biggest mismatches between the observed and estimated cell counts. This should help you to discover the nature of the dependence.

Examples

The chi-squared test for association is applied to a few real contingency tables below.

In some examples, the value of χ2 is so far into the upper tail of the reference distribution that we are almost certain that the row and column variable are dependent. In others, the value of χ2 is small enough that it could have arisen by chance even if the variables are independent in the underlying population.