Chi-Square Test: Analysis of Contingency Tables

The original chi-square test, often known as Pearson’s chi-square, dates from papers by Karl Pearson in the earlier 1900s. The test serves both as a ”goodnessof-fit” test, where the data are categorized along one dimension, and as a test for the more common ”contingency table”, in which categorization is across two or more dimensions. Voinov and Nikulin, this volume, discuss the controversy over the correct form for the goodness of fit test. This entry will focus on the lack of agreement about tests on contingency tables. In 2000 the Vermont State legislature approved a bill authorizing civil unions. The vote can be broken down by gender to produce the following table, with the expected frequencies given in parentheses. The expected frequencies are computed as Ri × Cj/N, where Ri and Cj represent row and column marginal totals and N is the grand total.