Multiple Comparisons of Means

Textbook authors-at least in the area of psychological statistics-have not been particularly helpful. Authors such as Edwards (1960), Federer (1955), Hays (1963), McNemar (1962), and Winer (1962) either offer no evaluation as to which method is preferable, or preface their remarks with a cautionary statement to the effect that these methods are still under study and that mathematical statisticians are not entirely in agreement concerning the preferred method. Similarly, disagreement exists as to when these methods may be used. Some discussions state that a significant F ratio over all conditions must be obtained before multiple comparison methods can be used (Hays, 1963; McNemar, 1962); other discussions make no mention of such a requirement (Federer, 1955; Winer, 1962), or deny that it is necessary at all (Edwards, 1960; Ryan, 1959a).