What is the assumption of normality in t-tests?

• A. The distribution of all data must be perfectly normal.
• B. The sampling distribution of the mean is approximately normal; data do not need to be perfectly normal for large samples (Central Limit Theorem).
• C. Variances must be equal across groups.
• D. The sample size must be equal across groups.

Answer: (B)

In t-tests, the assumption of normality refers to the sampling distribution of the mean being approximately normal. This matters because the t statistic is based on the mean and its standard error, so we rely on the mean’s distribution to be normal to make accurate inferences. The Central Limit Theorem helps here: with a reasonably large sample, the distribution of the sample mean tends to normal even if the underlying data aren’t perfectly normal, so the test remains valid. For small samples, you do need more attention to how nonnormal the data are because departures from normality can affect results. If the data are highly skewed or contain outliers and sample sizes are small, nonparametric tests or bootstrap methods may be more appropriate. The other considerations involve whether variances are equal across groups or whether sample sizes are equal; these affect which version of the t-test you use and its power, but they are separate from the normality assumption itself.