In a study comparing responses from 6th graders and 12th graders to a question with three possible answers, which test is appropriate to compare the distributions across the two independent groups?

In a study comparing responses from 6th graders and 12th graders to a question with three possible answers, which test is appropriate to compare the distributions across the two independent groups?

• A. Chi-square test of homogeneity
• B. Chi-square test of independence
• C. 2-proportion z-test
• D. ANOVA

Answer: (A)

When you want to know if the way people choose among several categorical options is the same across two independent groups, you use a chi-square test of homogeneity. Here, the outcome is categorical with three possible answers and there are two independent groups (6th graders and 12th graders). You’d organize the data in a 2-by-3 contingency table: rows for the two groups and columns for the three answer choices, filling in the counts. The null hypothesis is that the distribution of responses across the three categories is identical in both groups; the alternative is that at least one category has a different proportion in the groups. This test checks whether the overall pattern of responses is the same across the two populations. Why not the other tests? A 2-proportion z-test only compares one category at a time and isn’t suitable for comparing distributions across three categories without multiple tests. ANOVA is for comparing means of a continuous variable across groups, not for categorical outcomes. A chi-square test of independence is used to assess association between two categorical variables within a single sample; here the focus is on comparing distributions between two separate groups, which is captured by the homogeneity test.

When you want to know if the way people choose among several categorical options is the same across two independent groups, you use a chi-square test of homogeneity. Here, the outcome is categorical with three possible answers and there are two independent groups (6th graders and 12th graders). You’d organize the data in a 2-by-3 contingency table: rows for the two groups and columns for the three answer choices, filling in the counts.

The null hypothesis is that the distribution of responses across the three categories is identical in both groups; the alternative is that at least one category has a different proportion in the groups. This test checks whether the overall pattern of responses is the same across the two populations.

Why not the other tests? A 2-proportion z-test only compares one category at a time and isn’t suitable for comparing distributions across three categories without multiple tests. ANOVA is for comparing means of a continuous variable across groups, not for categorical outcomes. A chi-square test of independence is used to assess association between two categorical variables within a single sample; here the focus is on comparing distributions between two separate groups, which is captured by the homogeneity test.