Two groups: homeopathic vs placebo; pain response categorized into four levels. Which test compares the distributions of responses between the two groups?

Two groups: homeopathic vs placebo; pain response categorized into four levels. Which test compares the distributions of responses between the two groups?

• A. Chi-square test of homogeneity with 3 degrees of freedom
• B. Chi-square test of independence with 3 degrees of freedom
• C. Linear regression
• D. Multinomial logistic regression

Answer: (A)

When you want to know if the pattern of four-category pain responses is the same across two independent groups, you compare distributions using a chi-square test of homogeneity. Here the data form a 2-by-4 contingency table (two groups by four response levels). The null hypothesis is that the distribution of responses is identical in both groups, so any differences are due to sampling variation. The chi-square statistic measures how much the observed counts deviate from what would be expected if the distributions were the same. The degrees of freedom come from multiplying the number of categories minus one by the number of groups minus one: (2−1) × (4−1) = 3. So a test with 3 degrees of freedom is appropriate. Why not linear regression? That’s for a continuous outcome, not a four-category categorical one. Multinomial logistic regression could model the outcome as a function of group, but for simply testing whether the distributions differ between the two groups, the chi-square test of homogeneity gives a direct and standard assessment.

When you want to know if the pattern of four-category pain responses is the same across two independent groups, you compare distributions using a chi-square test of homogeneity. Here the data form a 2-by-4 contingency table (two groups by four response levels). The null hypothesis is that the distribution of responses is identical in both groups, so any differences are due to sampling variation. The chi-square statistic measures how much the observed counts deviate from what would be expected if the distributions were the same.

The degrees of freedom come from multiplying the number of categories minus one by the number of groups minus one: (2−1) × (4−1) = 3. So a test with 3 degrees of freedom is appropriate.

Why not linear regression? That’s for a continuous outcome, not a four-category categorical one. Multinomial logistic regression could model the outcome as a function of group, but for simply testing whether the distributions differ between the two groups, the chi-square test of homogeneity gives a direct and standard assessment.