Singer et al. (2000) investigated whether offering a monetary incentive with an advance letter would improve response rates to a telephone survey. Among those who received the incentive, 286 of 368 responded; among those who received only the advance letter, 245 of 367 responded. Which test would compare these two proportions?

Singer et al. (2000) investigated whether offering a monetary incentive with an advance letter would improve response rates to a telephone survey. Among those who received the incentive, 286 of 368 responded; among those who received only the advance letter, 245 of 367 responded. Which test would compare these two proportions?

• A. 2-proportion z-test
• B. Chi-square test of homogeneity
• C. Fisher's exact test
• D. Paired t-test

Answer: (A)

When you’re comparing two independent groups on a binary outcome (respond yes or no), you want to know if the two proportions differ. The standard method for this is the two-proportion z-test. It uses a normal approximation to the distribution of the difference between the observed proportions under the assumption that the true proportions are equal. Here you’d take p1 = 286/368 and p2 = 245/367, note the difference in response rates, and compute a z statistic based on a pooled estimate of the common proportion and the two sample sizes. The large sample sizes make the normal approximation reliable, so this test directly assesses whether the incentive changed response rates. A chi-square test of homogeneity could also be used with the same 2x2 data and would give similar conclusions in large samples, but the two-proportion z-test is the direct choice for comparing two proportions. Fisher’s exact test is reserved for very small counts, and a paired t-test is for matched or before-after data, not independent groups.

When you’re comparing two independent groups on a binary outcome (respond yes or no), you want to know if the two proportions differ. The standard method for this is the two-proportion z-test. It uses a normal approximation to the distribution of the difference between the observed proportions under the assumption that the true proportions are equal. Here you’d take p1 = 286/368 and p2 = 245/367, note the difference in response rates, and compute a z statistic based on a pooled estimate of the common proportion and the two sample sizes. The large sample sizes make the normal approximation reliable, so this test directly assesses whether the incentive changed response rates.

A chi-square test of homogeneity could also be used with the same 2x2 data and would give similar conclusions in large samples, but the two-proportion z-test is the direct choice for comparing two proportions. Fisher’s exact test is reserved for very small counts, and a paired t-test is for matched or before-after data, not independent groups.