es-qcritical-305-for-alpha-005-k-3-df-27-which-pairs-are-significantly-different

Question

You computed q statistics for three pairwise comparisons of a three-group experiment: q12 = 1.95, q13 = 4.50, q23 = 2.55. If the studentized range table gives q_critical = 3.05 for alpha = 0.05, k = 3, df = 27, which pairs are significantly different?

Accepted Answer

Only pair 1 vs 3 (q13) is significant because q13 \u003e 3.05; q12 and q23 are not significant because their q's are below 3.05.

Answer

Pairs 1 vs 2 and 2 vs 3 are significant because their q statistics are closest to the critical value even though they are numerically smaller; pair 1 vs 3 is not significant.

Answer

All three pairs are significant because at least one q exceeds the critical value, implying each pairwise test is automatically significant when any single pair exceeds the table value.

Answer

No pairs are significant because the omnibus ANOVA decision must be re-evaluated when some q's exceed the critical value, and therefore you cannot conclude pairwise significance directly from q comparisons.