What are the assumptions underlying a one-way ANOVA?

What are the assumptions underlying a one-way ANOVA?

• A. It compares medians instead of means.
• B. It assumes independence of observations, normality of residuals, and homogeneity of variances.
• C. It requires equal sample sizes in all groups.
• D. It can only be used with two groups.

Answer: (B)

One-way ANOVA relies on a few essential conditions to make its F-test valid. The observations across all groups must be independent, so one individual's data don’t influence another’s. Within each group, the residuals should be approximately normally distributed, which helps the sampling distribution of the F statistic behave as expected under the null hypothesis. The variances across the groups should be roughly equal, known as homogeneity of variances, so no single group unduly sways the comparison. These assumptions matter because violating them can distort the test’s reliability and the accuracy of p-values. If variances are very different or if normality is severely broken, the inference about whether group means are equal becomes less trustworthy. It’s also worth noting that equal sample sizes aren’t required—ANOVA can handle unequal group sizes—though extreme imbalance can affect power and robustness. And while ANOVA compares means across multiple groups, it doesn’t limit you to two groups; it’s designed for any number of groups. Options that talk about comparing medians, requiring equal sample sizes, or restricting to two groups don’t describe the underlying assumptions of one-way ANOVA.

One-way ANOVA relies on a few essential conditions to make its F-test valid. The observations across all groups must be independent, so one individual's data don’t influence another’s. Within each group, the residuals should be approximately normally distributed, which helps the sampling distribution of the F statistic behave as expected under the null hypothesis. The variances across the groups should be roughly equal, known as homogeneity of variances, so no single group unduly sways the comparison.

These assumptions matter because violating them can distort the test’s reliability and the accuracy of p-values. If variances are very different or if normality is severely broken, the inference about whether group means are equal becomes less trustworthy. It’s also worth noting that equal sample sizes aren’t required—ANOVA can handle unequal group sizes—though extreme imbalance can affect power and robustness. And while ANOVA compares means across multiple groups, it doesn’t limit you to two groups; it’s designed for any number of groups.

Options that talk about comparing medians, requiring equal sample sizes, or restricting to two groups don’t describe the underlying assumptions of one-way ANOVA.