sentences:  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.