In a study of how the burden of poverty varies among U. S. regions, a random sample of 1000 individuals from each of four regions was collected. Which test is appropriate to assess whether poverty levels differ by region?

In a study of how the burden of poverty varies among U. S. regions, a random sample of 1000 individuals from each of four regions was collected. Which test is appropriate to assess whether poverty levels differ by region?

• A. 2-proportion z-test
• B. Chi-square test of homogeneity with 3 degrees of freedom
• C. Linear regression t-test
• D. ANOVA

Answer: (B)

Assessing differences in poverty across four regions involves a binary outcome (poverty: yes or no) observed in each region. When you want to see if the distribution of a categorical outcome is the same across multiple groups, the chi-square test of homogeneity is the appropriate tool. You set up a contingency table with regions as rows and poverty status (in poverty vs not) as columns, and you test whether the row distributions are identical. The degrees of freedom for this test are (number of regions − 1) × (number of poverty categories − 1) = (4 − 1) × (2 − 1) = 3, which matches the given option. Why not the others: a 2-proportion z-test compares only two groups, not four; using it would require multiple pairwise comparisons and can inflate error. Linear regression t-tests and ANOVA are meant for continuous outcomes like means, not a binary poverty status.

Assessing differences in poverty across four regions involves a binary outcome (poverty: yes or no) observed in each region. When you want to see if the distribution of a categorical outcome is the same across multiple groups, the chi-square test of homogeneity is the appropriate tool. You set up a contingency table with regions as rows and poverty status (in poverty vs not) as columns, and you test whether the row distributions are identical.

The degrees of freedom for this test are (number of regions − 1) × (number of poverty categories − 1) = (4 − 1) × (2 − 1) = 3, which matches the given option.

Why not the others: a 2-proportion z-test compares only two groups, not four; using it would require multiple pairwise comparisons and can inflate error. Linear regression t-tests and ANOVA are meant for continuous outcomes like means, not a binary poverty status.