key-kramer-procedure-which-mse-and-error-degrees-of-freedom-will-you-use-and-why

Question

Given ANOVA output: Sum of squares (Error) = 134.4, df(Error) = 28, MS(Error) = 4.8. There are 4 groups with sizes 8, 9, 7, and 7 (N = 31). For the Tukey-Kramer procedure which MSE and error degrees of freedom will you use, and why?

Accepted Answer

Use MSE = 4.8 and error df = 28 because MS(Error) is the pooled within-group variance and df(Error)=N−k provides the studentized range distribution degrees of freedom for q_critical.

Answer

Recompute MSE using only equal-sized groups by averaging variances across groups and then use df = average of group dfs before applying Tukey-Kramer.

Answer

Use MSE = 4.8 and between-groups df = 3 because q_critical depends on the number of groups only and uses the between-group df for error.

Answer

Use MSE = 134.4 because Tukey-Kramer requires the error sum of squares rather than the mean square, and use error df = 30 (N−1) because pairwise degrees must account for total sample size.