Chi-Square Test

Definition

A test that is frequently used to detect significant relationships between two variables measured on nominal scales, or to determine whether a distribution differs significantly from expectations. Chi-square tests belong to the class of statistical inferential procedures known as nonparametric or distribution‐free tests.

The chi-square test is a significance test based on chi-square distribution. A chi-square test is most commonly used as a test of homogeneity or a test of independence for contingency table analysis, and as a goodness-of-fit test for analysis of observed frequency distribution. Chi-square test statistic can be calculated as the sum of the squared differences between observed and expected frequencies, $\sum {\left({O-E} \right)^2/E}$ , where O is the observed frequency and E is the expected frequency. Statistic produced by this test follow a chi-squared distribution, with $(r-1)\;(c-1)$ degrees of freedom for a contingency table analysis and $r-1$...