What is an important limitation of Tukey's HSD according to the material?

What is an important limitation of Tukey's HSD according to the material?

• A. Sample sizes have to be the same.
• B. It assumes equal variances.
• C. It requires a normal distribution of the underlying populations.
• D. It is unaffected by sample size.

Answer: (A)

Tukey's HSD is used after an ANOVA to compare all pairs of group means while keeping the overall error rate under control. Its standard form relies on the assumption that all groups have the same sample size because this gives a common standard error for every pairwise difference and makes the distribution used to determine significance exact. When sample sizes are equal, the studentized range approach works cleanly and the cutoff for declaring a difference is reliable. If group sizes are unequal, the standard HSD isn’t exact without adjustments, so you’d typically turn to the Tukey-Kramer approach to account for the differing n. So, the main limitation highlighted is that the standard Tukey's HSD assumes equal sample sizes. Variances and normality are also considerations in ANOVA, but they’re not the defining limitation of this procedure in the same way.

Tukey's HSD is used after an ANOVA to compare all pairs of group means while keeping the overall error rate under control. Its standard form relies on the assumption that all groups have the same sample size because this gives a common standard error for every pairwise difference and makes the distribution used to determine significance exact. When sample sizes are equal, the studentized range approach works cleanly and the cutoff for declaring a difference is reliable. If group sizes are unequal, the standard HSD isn’t exact without adjustments, so you’d typically turn to the Tukey-Kramer approach to account for the differing n. So, the main limitation highlighted is that the standard Tukey's HSD assumes equal sample sizes. Variances and normality are also considerations in ANOVA, but they’re not the defining limitation of this procedure in the same way.