Why is the assumption of normality important for parametric tests, and what are alternatives if violated?

• A. Parametric tests do not depend on distribution shape; always use them
• B. Parametric tests require equal variances only
• C. If data are not normally distributed, transform data to normal and continue
• D. Parametric tests assume normal distribution; if violated, use nonparametric tests (Mann-Whitney, Wilcoxon, Kruskal-Wallis)

Answer: (D)

Parametric tests rely on normal distribution assumptions for the sampling distribution of the test statistic, which underpins the accuracy of p-values and confidence intervals. When data are not normally distributed, especially with small samples, those calculations can be biased, making results unreliable. The best alternative in that case is to switch to nonparametric tests that don’t assume normality and instead use ranks or medians to compare groups or conditions. Examples include the Mann-Whitney U test for two independent groups, the Wilcoxon signed-rank test for paired data, and the Kruskal-Wallis test for more than two groups. While data transformations or bootstrapping can be useful in some situations, nonparametric tests provide a robust option when the normality assumption is violated.