What are the degrees of freedom for Tukey's test statistic for a one-factor ANOVA with n₁ = 6, n₂ = 6, n₃ = 6? A)3, 6 B)6, 3 C)6, 15 D)3, 15

Question

Quizplus · Accepted Answer

Tukey's test statistic for a one-factor ANOVA involves two degrees of freedom: the first is the number of groups minus one (k - 1), and the second is the total sample size minus the number of groups (N - k). Here, with three groups of equal size (6 each), k = 3, and N = 18. Thus, the degrees of freedom are (3 - 1) = 2 for the numerator and (18 - 3) = 15 for the denominator. However, the correct answer should reflect the degrees of freedom for the groups and the error term, which are 3 - 1 = 2 for the groups (not provided in the options) and 18 - 3 = 15 for the error term, aligning closest with option D by interpreting the first value as the number of groups (k) rather than the degrees of freedom for the groups.

What Are the Degrees of Freedom for Tukey's Test Statistic