Which F-statistic is designed to be accurate when the assumption of homogeneity of variance has been violated?

Which F-statistic is designed to be accurate when the assumption of homogeneity of variance has been violated?

• A. Levene F
• B. Brown-Forsythe F
• C. Welch F
• D. F-max

Answer: (B)

When comparing several group means, the standard F-test assumes equal variances across groups. If that variances assumption is violated, the usual F-test can be unreliable. The Brown-Forsythe F statistic is a robust alternative designed for this situation. It works by measuring deviations from the group median rather than the group mean, which reduces the influence of unequal spreads and non-normal shapes. Then it analyzes those deviations with an F-like test to assess whether the group means are equal under heterogeneity of variances. This makes the Brown-Forsythe F statistic more accurate when variances differ than the standard F test. Levene’s F is another variance-focused test, but Brown-Forsythe tends to be more robust to non-normal distributions. Welch F is also used for unequal variances, but in this question the Brown-Forsythe approach is the intended robust option. F-max isn’t designed to handle variance differences and can be unreliable under heteroscedasticity.

When comparing several group means, the standard F-test assumes equal variances across groups. If that variances assumption is violated, the usual F-test can be unreliable. The Brown-Forsythe F statistic is a robust alternative designed for this situation. It works by measuring deviations from the group median rather than the group mean, which reduces the influence of unequal spreads and non-normal shapes. Then it analyzes those deviations with an F-like test to assess whether the group means are equal under heterogeneity of variances. This makes the Brown-Forsythe F statistic more accurate when variances differ than the standard F test. Levene’s F is another variance-focused test, but Brown-Forsythe tends to be more robust to non-normal distributions. Welch F is also used for unequal variances, but in this question the Brown-Forsythe approach is the intended robust option. F-max isn’t designed to handle variance differences and can be unreliable under heteroscedasticity.