What assumptions underlie the independent two-sample t-test?

• A. Independence, normality of each group (or large samples), and equal variances if using pooled t-test.
• B. Independence within groups, non-normal distribution in both groups, and equal sample sizes.
• C. Paired observations are required.
• D. Data are ordinal.

Answer: (A)

The test compares mean differences between two groups and relies on three main ideas about the data: the observations are independent, the outcome is approximately normally distributed within each group (or the sample sizes are large enough for the normal approximation to hold), and the two groups have equal variances if you’re using the pooled variance version of the test. If the variances aren’t equal, you should use the version that does not assume equal variances (Welch’s t-test). The data should be on an interval or ratio scale.

This is why the option describing independence, normality (or large samples), and equal variances for the pooled version best fits the assumptions. The other statements are not accurate: non-normality is not a required condition and is mitigated by large samples; equal sample sizes aren’t required; paired data refer to a different test; and ordinal data aren’t appropriate for a standard independent two-sample t-test because it relies on means and variances rather than ordinal ranks.