The primary purpose of conducting Tukey pairwise comparisons after a significant ANOVA is to:

In a manufacturing study two machine settings yield average defect rates 14 and 11 (units: percent). Each setting used n = 16 samples, and MSE from ANOVA is 4.0. If the q critical value is 4.30, compute q for these two settings and the Tukey decision.

In a pilot study with groups P, Q, R, S each with n = 6, the ANOVA indicates a significant overall F. MSE = 5.0, group means are P = 10, Q = 12, R = 16, S = 23. Degrees of freedom for error is 24, and the studentized range critical value for k = 4 and df = 24 at alpha = 0.05 is qcrit = 4.03. Calculate which pairwise comparisons are significant.