Wilt et al. (2012) studied whether surgery improves men’s survival after localized prostate cancer. After about 10 years, 21 of 364 in the surgery group and 31 of 367 in the observation group died. Which test should be used to compare these two proportions?

Wilt et al. (2012) studied whether surgery improves men’s survival after localized prostate cancer. After about 10 years, 21 of 364 in the surgery group and 31 of 367 in the observation group died. Which test should be used to compare these two proportions?

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

Answer: (D)

When you want to know if the proportion of a binary outcome differs between two independent groups, you use a chi-square test of independence in a 2x2 table. Here, death (yes/no) is the binary outcome and the groups are surgery versus observation, which are independent. The chi-square test asks whether the observed pattern of deaths and survivals across the two groups is what you’d expect if there were no difference in survival between treatments. With about 360 people per group and death counts of 21 and 31, all four cell counts are well above 5, so the chi-square approximation is appropriate and will give a reliable p-value. This test effectively checks whether the two proportions differ beyond what random variation would produce. While the two-proportion z-test would also address the same question and, in large samples, yields the same conclusion, the chi-square test of independence is a standard, straightforward way to compare proportions in a 2x2 context. The other options involve paired data (McNemar) or are reserved for very small counts (Fisher’s exact), which aren’t necessary here.

When you want to know if the proportion of a binary outcome differs between two independent groups, you use a chi-square test of independence in a 2x2 table. Here, death (yes/no) is the binary outcome and the groups are surgery versus observation, which are independent. The chi-square test asks whether the observed pattern of deaths and survivals across the two groups is what you’d expect if there were no difference in survival between treatments.

With about 360 people per group and death counts of 21 and 31, all four cell counts are well above 5, so the chi-square approximation is appropriate and will give a reliable p-value. This test effectively checks whether the two proportions differ beyond what random variation would produce.

While the two-proportion z-test would also address the same question and, in large samples, yields the same conclusion, the chi-square test of independence is a standard, straightforward way to compare proportions in a 2x2 context. The other options involve paired data (McNemar) or are reserved for very small counts (Fisher’s exact), which aren’t necessary here.