The chi-square test is used for categorical data. There are three situations in which one can use the chi-square test: to test for independence, for equality of proportions, and for goodness of fit. The test statistic and the expected values for the first two cases are identical, but the hypotheses and sampling situations are distinctly different. For the goodness-of-fit situation, the test statistic and expected values are similar but not identical, and the hypotheses and sampling situation are also different from the other cases. The first two cases are presented first. All data tables were created by the author for this entry.

Test for Independence

Situation. One has a single random sample, and this sample is cross-categorized by two variables each with 2 or more categories. The ...

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