In July 2011, Ma-Vib fired 15 of 18 women and none of the 12 men. Which test would be appropriate to assess whether layoff rates differ by gender?

In July 2011, Ma-Vib fired 15 of 18 women and none of the 12 men. Which test would be appropriate to assess whether layoff rates differ by gender?

• A. 2-proportion z-test
• B. Chi-square test of independence
• C. Fisher's exact test
• D. Chi-square test of homogeneity

Answer: (D)

The main idea is to compare how a binary outcome (fired vs not fired) is distributed across different groups (women vs men). A chi-square test of homogeneity is designed for exactly this situation: it asks whether the firing rate is the same in each gender group by analyzing a 2x2 table of group (gender) by outcome (fired/not fired). Here, the observed counts show a stark difference—many more women were fired and none of the men were—so the test would assess whether such a difference is likely under the assumption that layoff rates are the same across genders. The null would place equal firing proportions in both groups, and the chi-square statistic would reflect the large deviation from that expectation, typically yielding a very small p-value. This framework is preferred over a simple two-proportion comparison in this context because it treats the data as a comparison of distributions across groups and uses the contingency-table approach; Fisher’s exact test would be more conservative but unnecessary with these sample sizes, and a 2-proportion z-test would also compare the two proportions but is not the standard framing for examining differences across multiple groups in a contingency-table context.

The main idea is to compare how a binary outcome (fired vs not fired) is distributed across different groups (women vs men). A chi-square test of homogeneity is designed for exactly this situation: it asks whether the firing rate is the same in each gender group by analyzing a 2x2 table of group (gender) by outcome (fired/not fired). Here, the observed counts show a stark difference—many more women were fired and none of the men were—so the test would assess whether such a difference is likely under the assumption that layoff rates are the same across genders. The null would place equal firing proportions in both groups, and the chi-square statistic would reflect the large deviation from that expectation, typically yielding a very small p-value. This framework is preferred over a simple two-proportion comparison in this context because it treats the data as a comparison of distributions across groups and uses the contingency-table approach; Fisher’s exact test would be more conservative but unnecessary with these sample sizes, and a 2-proportion z-test would also compare the two proportions but is not the standard framing for examining differences across multiple groups in a contingency-table context.