A "third" point, which Games (1971) demonstrated in his study, is that the F-test may not be completely consistent with the results of a pairwise comparison approach. Consider, for example, a researcher who is instructed to conduct Tukey's test only if an alpha-level F-test rejects the complete null. It is possible for the complete null to be rejected but for the widest ranging means not to differ significantly. This is an example of what has been referred to as non-consonance/dissonance (Gabriel, 1969) or incompatibility (Lehmann, 1957). On the other hand, the complete null may be retained while the null associated with the widest ranging means would have been rejected had the decision structure allowed it to be tested. This has been referred to by Gabriel (1969) as incoherence. One wonders if, in fact, a practitioner in this situation would simply conduct the MCP contrary to the omnibus test's recommendation.