The "fourth" argument against the traditional implementation of an initial omnibus F-test stems from the fact that its well-intentioned but unnecessary protection contributes to a decrease in power. The first test in a pairwise MCP, such as that of the most disparate means in Tukey's test, is a form of omnibus test all by itself, controlling the family-wise error rate at the α-level in the weak sense. Requiring a preliminary omnibus F-test amount to forcing a researcher to negotiate two hurdles to proclaim the most disparate means significantly different, a task that the range test accomplished at an acceptable α -level all by itself. If these two tests were perfectly redundant, the results of both would be identical to the omnibus test; probabilistically speaking, the joint probability of rejecting both would be α when the complete null hypothesis was true. However, the two tests are not completely redundant; as a result the joint probability of their rejection is less than α. The F-protection therefore imposes unnecessary conservatism (see Bernhardson, 1975, for a simulation of this conservatism). For this reason, and those listed before, we agree with Games' (1971) statement regarding the traditional implementation of a preliminary omnibus F-test: There seems to be little point in applying the overall F test prior to running c contrasts by procedures that set family-wise error rate α ... If the c contrasts express the experimental interest directly, they are justified whether the overall F is significant or not and (family-wise error rate) is still controlled.