William B. Ware (1997) claims that the omnibus test significance is required depending on the Post Hoc test is conducted or planned: "... Tukey's HSD and Scheffé's procedure are one-step procedures and can be done without the omnibus F having to be significant. They are "a posteriori" tests, but in this case, "a posteriori" means "without prior knowledge", as in "without specific hypotheses." On the other hand, Fisher's Least Significant Difference test is a two-step procedure. It should not be done without the omnibus F-statistic being significant."