A Comparison of the Modified-Tukey and Scheffé Methods of Multiple Comparisons for Pairwise Contrasts

The Kramer (1956), Spjøtvoll and Stoline (1975), Hochberg (1976), and Games and Howell (1976) modified forms of the Tukey test are compared with the Scheffé (1959) test for (1) rates of Type I error and (2) sensitivity to varying degrees of sample-size imbalance and variance heterogeneity when sampling from normal and skewed distributions. Only the Hochberg (1976) and Games and Howell (1976) procedures control their rates of Type I error at or below the nominal five percent level for all conditions investigated; however, the Games and Howell (1976) procedure is more powerful and always results in Type I error values which are closer to the level of significance.