In ANOVA, each group within the sample is normally distributed. Which statement best describes this assumption?

In ANOVA, each group within the sample is normally distributed. Which statement best describes this assumption?

• A. Each group within the sample is normally distributed
• B. The dependent variable is nominal
• C. There is no assumption about variances
• D. Groups must have equal sample sizes

Answer: (A)

In ANOVA, the normality of each group’s distribution means the dependent variable is roughly bell-shaped within every treatment level. This ensures the sampling distribution of the group means behaves as the theory assumes, which underpins the F statistic used to test whether those means differ. When group populations are normal (especially with smaller samples), the test has the intended Type I error rate and good power. With larger samples, the result is still reliable even if some normality is violated, thanks to the central limit theorem. It's helpful to keep in mind what else matters in ANOVA: the dependent variable should be measured on a continuous scale, and there should be roughly equal variances across groups (homogeneity of variance). Unequal sample sizes are possible, so requiring equal group sizes isn’t correct. The statement about normality describes the distribution of the data within each group, which is why it’s the best description of this assumption.

In ANOVA, the normality of each group’s distribution means the dependent variable is roughly bell-shaped within every treatment level. This ensures the sampling distribution of the group means behaves as the theory assumes, which underpins the F statistic used to test whether those means differ. When group populations are normal (especially with smaller samples), the test has the intended Type I error rate and good power. With larger samples, the result is still reliable even if some normality is violated, thanks to the central limit theorem.

It's helpful to keep in mind what else matters in ANOVA: the dependent variable should be measured on a continuous scale, and there should be roughly equal variances across groups (homogeneity of variance). Unequal sample sizes are possible, so requiring equal group sizes isn’t correct. The statement about normality describes the distribution of the data within each group, which is why it’s the best description of this assumption.