In a trial comparing two drugs, patient outcomes are categorized as 'improved', 'no change', or 'worsened'. Which test evaluates whether the distribution of outcomes is the same across the two drugs?

In a trial comparing two drugs, patient outcomes are categorized as 'improved', 'no change', or 'worsened'. Which test evaluates whether the distribution of outcomes is the same across the two drugs?

• A. Chi-square test of homogeneity with 2 degrees of freedom
• B. Chi-square test of independence with 6 degrees of freedom
• C. Fisher's exact test
• D. Z-test for proportions

Answer: (A)

The situation is about whether the distribution of an outcome across categories is the same in two different groups. With two drugs and three possible outcomes, you have a 2-by-3 contingency table, and the question asks if the proportions across the three outcomes are identical for both drugs. The chi-square test of homogeneity is designed for this exact scenario: it tests whether different populations (the two drugs) share the same distribution of a categorical variable (the outcomes). The degrees of freedom for this table are (rows − 1) × (columns − 1) = (2 − 1) × (3 − 1) = 2, which matches the given option. Fisher's exact test is typically used for small samples and is most common with a 2-by-2 table, so it’s not the standard choice here. A Z-test for proportions compares two binary proportions, which doesn’t capture the full three-category distribution. The test of independence would also assess association between drug and outcome in a 2-by-3 table and leads to the same conclusion in this setup, but the homogeneity framing is the most direct way to state the question.

The situation is about whether the distribution of an outcome across categories is the same in two different groups. With two drugs and three possible outcomes, you have a 2-by-3 contingency table, and the question asks if the proportions across the three outcomes are identical for both drugs. The chi-square test of homogeneity is designed for this exact scenario: it tests whether different populations (the two drugs) share the same distribution of a categorical variable (the outcomes). The degrees of freedom for this table are (rows − 1) × (columns − 1) = (2 − 1) × (3 − 1) = 2, which matches the given option.

Fisher's exact test is typically used for small samples and is most common with a 2-by-2 table, so it’s not the standard choice here. A Z-test for proportions compares two binary proportions, which doesn’t capture the full three-category distribution. The test of independence would also assess association between drug and outcome in a 2-by-3 table and leads to the same conclusion in this setup, but the homogeneity framing is the most direct way to state the question.