Explain how the chi-square independence test is different from the chi-square homogeneity of proportions test.

Use this information about the homogeneity of proportions test. Another chi-square test that involves a contingency table is the homogeneity of proportions test. This test is used to determine whether several proportions are equal when samples are taken from different populations. Before the populations are sampled and the contingency table is made, the sample sizes are determined. After randomly sampling different populations, you can test whether the proportion of elements in a category is the same for each population using the same guidelines as the chi-square independence test. The null and alternative hypotheses are always some variation of these statements.
\(H_{0}\) : The proportions are equal.
\(H_{a}\) : At least one of the proportions is different from the others.

Performing a homogeneity of proportions test requires that the observed frequencies be obtained using a random sample, and each expected frequency must be greater than or equal to 5 .