Welch's F is used to accommodate what condition in comparing group means?

• A. Used when the assumption of equal variances across groups is violated.
• B. Used when sample sizes across groups are equal.
• C. Used when data are normal and variances are equal.
• D. Used to accommodate heterogeneity of variance, i.e., unequal variances across groups.

Answer: (D)

Welch's F is used when the spread of scores differs across groups—that is, when variances are not equal from group to group (heterogeneity of variance). In standard ANOVA we assume equal variances, and when that assumption is violated, the regular F test can mislead. Welch's approach adjusts the degrees of freedom (via the Satterthwaite approximation) to provide a more accurate test of whether the group means differ under unequal variances and often unequal sample sizes. This makes it the appropriate choice specifically for handling variance heterogeneity across groups. The other scenarios—equal variances, equal sample sizes, or data that are normal with equal variances—don’t require Welch’s correction.