An experimenter ran a study that consisted of four groups, each with 16 participants. This research study was exploratory research, and the experimenter did not have any specific hypotheses or expectations about the results of the analyses. He found a significant \(F\)-ratio for the one-way ANOVA and now would like to compare each group to each of the other groups to locate the differences.

a. How many unplanned comparisons will he need to conduct?

b. What are the concerns about conducting so many comparisons?

c. What is the value of \(q_{\mathrm{T}}\) ?

d. Assuming familywise error is set at the traditional value of \(.05\left(\mathrm{a}_{\mathrm{FW}}=.05\right)\), what is the critical value for each of the unplanned comparisons \(\left(F_{\mathrm{T}}\right)\) ?