Which statistic is appropriate to compare mortality proportions between the depressed and non-depressed groups?

Which statistic is appropriate to compare mortality proportions between the depressed and non-depressed groups?

• A. 2-sample t-test
• B. Chi-square test
• C. 2-proportion z-test
• D. Paired t-test

Answer: (C)

Comparing two independent groups on a binary outcome requires a method that tests whether two proportions differ. Here, mortality is a yes/no outcome and you want to know if the death rate in the depressed group differs from the death rate in the non-depressed group. The two-proportion z-test uses the normal approximation to the binomial distribution to determine if the difference between the observed proportions is statistically significant, assuming the sample sizes are large enough for the approximation to hold. This directly addresses whether p_depressed equals p_non-depressed. Other options are aimed at different data types or designs. A two-sample t-test compares means of a continuous variable, not proportions. A paired t-test is for matched or paired data, not independent groups. A chi-square test can compare proportions in a contingency table, but the two-proportion z-test is the standard, more direct choice for comparing two independent proportions when the sample size supports the normal approximation, with Fisher’s exact test as an alternative for small samples.

Comparing two independent groups on a binary outcome requires a method that tests whether two proportions differ. Here, mortality is a yes/no outcome and you want to know if the death rate in the depressed group differs from the death rate in the non-depressed group. The two-proportion z-test uses the normal approximation to the binomial distribution to determine if the difference between the observed proportions is statistically significant, assuming the sample sizes are large enough for the approximation to hold. This directly addresses whether p_depressed equals p_non-depressed.

Other options are aimed at different data types or designs. A two-sample t-test compares means of a continuous variable, not proportions. A paired t-test is for matched or paired data, not independent groups. A chi-square test can compare proportions in a contingency table, but the two-proportion z-test is the standard, more direct choice for comparing two independent proportions when the sample size supports the normal approximation, with Fisher’s exact test as an alternative for small samples.