Which statement lists the three assumptions of one-way ANOVA?

Which statement lists the three assumptions of one-way ANOVA?

• A. Independence, normality of residuals within groups, and equal variances across groups.
• B. Independence only.
• C. Normality of the response variable across all data only.
• D. Equal variances across groups only.

Answer: (A)

The key idea being tested is the set of conditions that make the F-test in one-way ANOVA valid. One-way ANOVA assumes three things: observations are independent, the residuals within each group are approximately normal, and the variances across the groups are equal (homogeneity of variances). These ensure that the distribution of the F statistic under the null hypothesis is what we expect, so the p-values are trustworthy. If any of these are violated, the results can be unreliable. Independence is fundamental for accurate standard errors; without it, the test can misstate variability. Normality of residuals within groups helps the F distribution approximation be accurate, especially with smaller samples. Homogeneity of variances ensures the variability is comparable across groups, which is essential for comparing group means fairly. The other options miss at least one of these requirements: independence alone doesn’t address normality or equal variances; normality of the response variable across all data isn’t the precise condition—it's the normality of residuals within groups that matters; and equal variances alone ignore independence and normality.

The key idea being tested is the set of conditions that make the F-test in one-way ANOVA valid. One-way ANOVA assumes three things: observations are independent, the residuals within each group are approximately normal, and the variances across the groups are equal (homogeneity of variances). These ensure that the distribution of the F statistic under the null hypothesis is what we expect, so the p-values are trustworthy.

If any of these are violated, the results can be unreliable. Independence is fundamental for accurate standard errors; without it, the test can misstate variability. Normality of residuals within groups helps the F distribution approximation be accurate, especially with smaller samples. Homogeneity of variances ensures the variability is comparable across groups, which is essential for comparing group means fairly.

The other options miss at least one of these requirements: independence alone doesn’t address normality or equal variances; normality of the response variable across all data isn’t the precise condition—it's the normality of residuals within groups that matters; and equal variances alone ignore independence and normality.