Reference Work Entry

Encyclopedia of Public Health

pp 112-113

Chi-Square Test


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 ...

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