For a 3x2 contingency table measuring two categorical variables across a single population, which test is appropriate to assess independence?

For a 3x2 contingency table measuring two categorical variables across a single population, which test is appropriate to assess independence?

• A. 1-proportion z-test
• B. 2-proportion z-test
• C. Chi-square test of independence
• D. Chi-square test of homogeneity

Answer: (C)

When you want to know if two categorical variables are related within a single population, you test independence using the chi-square test of independence. It compares the observed counts in each cell of the 3x2 table to the counts you would expect if the variables were independent, using the statistic that sums (O − E)² / E across all cells. For a 3x2 table, the degrees of freedom are (3 − 1) × (2 − 1) = 2. A small p-value suggests the variables are associated, while a large p-value suggests independence. This differs from the 1-proportion and 2-proportion z-tests, which compare proportions in one or two samples, not the joint distribution of two categorical variables. The chi-square test of homogeneity would be used to compare distributions across different populations, not to assess independence within a single population.

When you want to know if two categorical variables are related within a single population, you test independence using the chi-square test of independence. It compares the observed counts in each cell of the 3x2 table to the counts you would expect if the variables were independent, using the statistic that sums (O − E)² / E across all cells. For a 3x2 table, the degrees of freedom are (3 − 1) × (2 − 1) = 2. A small p-value suggests the variables are associated, while a large p-value suggests independence. This differs from the 1-proportion and 2-proportion z-tests, which compare proportions in one or two samples, not the joint distribution of two categorical variables. The chi-square test of homogeneity would be used to compare distributions across different populations, not to assess independence within a single population.