When the marginal frequencies are random for one variable and fixed for the other,the analytical procedures are identical but the test is referred to as the chi-square test of heterogeneity.

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When the marginal frequencies are random for one variable and fixed for the other, the analytical procedures are not identical and the test is referred to as the chi-square test of independence. The chi-square test of heterogeneity is used when comparing the distribution of a categorical variable across different groups or categories.

When the Marginal Frequencies Are Random for One Variable and Fixed