In a chi-square test of homogeneity with multiple groups and a single categorical variable, which statement is the null hypothesis?

In a chi-square test of homogeneity with multiple groups and a single categorical variable, which statement is the null hypothesis?

• A. The distributions differ across groups.
• B. The distributions are the same across groups.
• C. The means of the groups are equal.
• D. The totals are equal across groups.

Answer: (B)

The main idea being tested is whether the categorical outcomes are distributed the same way across different groups. In a chi-square test of homogeneity, the null hypothesis states that there is no difference in the distribution of the categories among the groups—that is, each group has the same proportions for each category. If this is true, the observed counts will align with what we’d expect based on the overall category proportions across all groups. Why this is the best answer: saying the distributions are the same across groups directly captures the absence of any association between group membership and category outcomes, which is exactly what the test assesses. Why the other statements don’t fit: a statement about the means of groups isn’t relevant here because the data are categorical, not numeric measurements. The idea that totals are equal across groups is not required—the groups can have different sizes, and the test accounts for that. Saying the distributions differ across groups would describe the alternative hypothesis, not the null.

The main idea being tested is whether the categorical outcomes are distributed the same way across different groups. In a chi-square test of homogeneity, the null hypothesis states that there is no difference in the distribution of the categories among the groups—that is, each group has the same proportions for each category. If this is true, the observed counts will align with what we’d expect based on the overall category proportions across all groups.

Why this is the best answer: saying the distributions are the same across groups directly captures the absence of any association between group membership and category outcomes, which is exactly what the test assesses.

Why the other statements don’t fit: a statement about the means of groups isn’t relevant here because the data are categorical, not numeric measurements. The idea that totals are equal across groups is not required—the groups can have different sizes, and the test accounts for that. Saying the distributions differ across groups would describe the alternative hypothesis, not the null.