Chi-squared test

A chi-squared test rejects a null hypothesis for a statistic whose null distribution is a chi-squared law, exactly or asymptotically. Pearson tests compare observed and expected counts; both goodness-of-fit and chi-squared tests of independence are instances.

For an $r$ by $c$ contingency table, Pearson's sum of squared observed-minus-fitted counts divided by fitted counts is asymptotically ${\chi }_{(r-1)(c-1)}^2$ under independence.