sen-alpha-and-number-of-groups-compute-q-for-a-vs-b-and-state-the-tukey-decision

Question

Two treatments A and B have means 7.2 and 5.1, equal sample sizes n = 9, and the ANOVA output reports MSE = 2.25. If the studentized range critical value qcrit = 3.60 for the chosen alpha and number of groups, compute q for A vs B and state the Tukey decision.

Accepted Answer

q = 4.20; reject H0 because 4.20 > 3.60.

Answer

q = 0.476; fail to reject H0 because the standardized difference is small compared to the studentized range threshold.

Answer

q = 2.625; fail to reject H0 because the value does not exceed qcrit and thus suggests no significant difference between A and B.

Answer

q = 3.00; borderline result where many analysts would consult a q table with more precision before rejecting the null hypothesis.