In a one-way ANOVA, the null hypothesis is that all group means are equal.

In a one-way ANOVA, the null hypothesis is that all group means are equal.

• A. All group means are equal
• B. At least one group mean differs
• C. The variances are equal across groups
• D. The medians are equal

Answer: (A)

The main idea here is how the one-way ANOVA frames the question about group differences. The null hypothesis says that all group means are equal, meaning there is no real difference in the population means across the groups and any differences you see in the sample are just due to random sampling error. The ANOVA tests this by comparing how much the group means vary from each other (between-group variance) to how much the observations vary within each group (within-group variance). If all means truly equal, the between-group variance should be small relative to the within-group variance, giving an F statistic around 1 and a non-significant result. If at least one group mean is different, the between-group variance increases, the F statistic grows, and you’re more likely to reject the null. It’s helpful to note why the other statements aren’t the null. Equal variances across groups is an assumption called homogeneity of variances and relates to the test’s validity, not the null being tested. The test focuses on means, not variances. Saying medians are equal would pertain to nonparametric tests (like Kruskal-Wallis), not the one-way ANOVA’s framework. And the alternative hypothesis is the opposite of the null: at least one group mean differs.

The main idea here is how the one-way ANOVA frames the question about group differences. The null hypothesis says that all group means are equal, meaning there is no real difference in the population means across the groups and any differences you see in the sample are just due to random sampling error. The ANOVA tests this by comparing how much the group means vary from each other (between-group variance) to how much the observations vary within each group (within-group variance). If all means truly equal, the between-group variance should be small relative to the within-group variance, giving an F statistic around 1 and a non-significant result. If at least one group mean is different, the between-group variance increases, the F statistic grows, and you’re more likely to reject the null.

It’s helpful to note why the other statements aren’t the null. Equal variances across groups is an assumption called homogeneity of variances and relates to the test’s validity, not the null being tested. The test focuses on means, not variances. Saying medians are equal would pertain to nonparametric tests (like Kruskal-Wallis), not the one-way ANOVA’s framework. And the alternative hypothesis is the opposite of the null: at least one group mean differs.