A more practical scheffe-type multiple comparison procedure for commonly encountered numbers of comparisons

Abstract

Multiple comparison procedures are important tools used in the analysis and interpretation of linear combinations of means from several populations. These procedures are used for two different types of comparisons: 1) the comparisons of all possible pairs of means and 2) testing a set of “g” comparisons. The Scheffé procedure is one of several techniques available for multiple comparisons but is generally regarded as too conservative for most practical analyses. Some authors have suggested ad hoc adjustments to the significance level to overcome the conservative nature of the Scheffé method. A heuristic approach is proposed to achieve the same objective which is quite satisfactory for commonly encountered numbers of comparisons Simulations clearly indicate that the modification of the Scheffé test is always superior to the unmodi-fied Scheffé and has acceptable experimentwise error rates and more power than the Bonferroni test for the investigation of a moderate number of comparisons.