Hartley's Fmax is a rule-of-thumb used to assess what?

• A. Normality
• B. Homogeneity of variances
• C. Sphericity
• D. Independence

Answer: (B)

Hartley’s Fmax is a quick check of the homogeneity of variances across groups in ANOVA. You look at the variances within each group, take the largest and the smallest, and form the ratio Fmax = largest variance divided by smallest variance. If this ratio is not too large (with a cutoff that depends on how many groups you have and their sample sizes), you can treat the variances as roughly equal. If the ratio is large, the assumption of equal variances is questionable and you might need to use a different approach, like a Welch ANOVA or a data transformation.

This topic isn’t about normality, which is about the shape of each group’s distribution; it isn’t about sphericity, which concerns variances of differences in repeated measures; and it isn’t about independence, which is about whether observations influence each other. Hartley’s Fmax specifically targets whether the spread (variability) is similar across groups.