Which statement best describes the independent samples t-test and its assumptions?

• A. It compares the means of two related groups and assumes normality.
• B. It compares the means of two independent groups and assumes independence, normality, and equal variances.
• C. It compares the variances of two independent groups and assumes non-normal distributions.
• D. It compares proportions in two samples and assumes large samples.

Answer: (B)

The independent samples t-test is used to compare the means of two separate groups. It relies on three key conditions. First, the observations must be independent within and between groups, meaning the selection or outcome of one participant does not affect another. Second, the populations underlying each group should be normally distributed, which is especially important when sample sizes are small; with larger samples, the test is fairly robust to mild departures from normality. Third, the two groups should have equal variances (homogeneity of variance); if this assumption is violated, a variation called Welch’s t-test is more appropriate. This test is not about comparing variances or proportions—that would involve other tests (such as tests for equality of variances or a chi-square test for proportions).