Which test is used to compare the mortality proportions between the depressed and non-depressed groups in this data?

Which test is used to compare the mortality proportions between the depressed and non-depressed groups in this data?

• A. Chi-square test
• B. Z-test for two proportions
• C. Paired t-test
• D. ANOVA

Answer: (B)

Comparing two independent proportions for a binary outcome. When you want to know if the mortality rate differs between two groups, and the outcome is death or survival, the Z-test for two proportions is the standard approach if the sample sizes are large enough. It looks at the difference between the observed proportions in each group and tests whether that difference could plausibly occur if the true mortality rates were the same. You compute the observed proportions p1 and p2 from each group, and under the null you use a pooled proportion to estimate the variability: p_hat = (deaths in both groups) / (total in both groups). The test statistic is z = (p1 − p2) / sqrt[p_hat(1 − p_hat) * (1/n1 + 1/n2)]. A large absolute z (or a small p-value) suggests a real difference in mortality proportions between the groups. If the sample sizes are small or expected counts are very low, an exact test (like Fisher’s exact) or a chi-square test for a 2x2 table could be considered, but the Z-test for two proportions directly targets the question of two independent mortality proportions. This is why it’s the appropriate choice here.

Comparing two independent proportions for a binary outcome. When you want to know if the mortality rate differs between two groups, and the outcome is death or survival, the Z-test for two proportions is the standard approach if the sample sizes are large enough. It looks at the difference between the observed proportions in each group and tests whether that difference could plausibly occur if the true mortality rates were the same.

You compute the observed proportions p1 and p2 from each group, and under the null you use a pooled proportion to estimate the variability: p_hat = (deaths in both groups) / (total in both groups). The test statistic is z = (p1 − p2) / sqrt[p_hat(1 − p_hat) * (1/n1 + 1/n2)]. A large absolute z (or a small p-value) suggests a real difference in mortality proportions between the groups.

If the sample sizes are small or expected counts are very low, an exact test (like Fisher’s exact) or a chi-square test for a 2x2 table could be considered, but the Z-test for two proportions directly targets the question of two independent mortality proportions. This is why it’s the appropriate choice here.