What test is most appropriate for measuring the association between gender and favorite color when both variables are categorical?

What test is most appropriate for measuring the association between gender and favorite color when both variables are categorical?

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

Answer: (A)

When you want to know if two categorical variables relate to each other, you test for association using a chi-square test of independence. Here, gender and favorite color are both categorical, and you’re asking whether the distribution of favorite colors differs by gender. You’d arrange the data in a contingency table with counts for each gender-color combination and compare the observed counts to the counts you’d expect if gender and color were independent. A significant result implies an association between gender and color. The other tests aren’t appropriate here. The chi-square test of homogeneity would be used to compare the distribution of a single categorical variable across two or more populations, not to assess the relationship between two categorical variables within one population. The 2-proportion z-test handles a binary outcome across two groups, not multiple color categories and not the broader question of whether two categorical variables are associated. ANOVA is for comparing means of a numeric variable across groups, which doesn’t apply to categorical data.

When you want to know if two categorical variables relate to each other, you test for association using a chi-square test of independence. Here, gender and favorite color are both categorical, and you’re asking whether the distribution of favorite colors differs by gender. You’d arrange the data in a contingency table with counts for each gender-color combination and compare the observed counts to the counts you’d expect if gender and color were independent. A significant result implies an association between gender and color.

The other tests aren’t appropriate here. The chi-square test of homogeneity would be used to compare the distribution of a single categorical variable across two or more populations, not to assess the relationship between two categorical variables within one population. The 2-proportion z-test handles a binary outcome across two groups, not multiple color categories and not the broader question of whether two categorical variables are associated. ANOVA is for comparing means of a numeric variable across groups, which doesn’t apply to categorical data.