Current Status of Multiple Comparisons of Means in Designed Experiments

Procedures for differentiating means in designed contrasts and post-data comparisons are appraised on recent evidence on sensitivity (power) and degree of protection of type I error rate. Orthogonal f-tests, Bonferroni t-statistics, Scheff6's interval, Tukey's Honestly Significant Difference, Student-Newman-Keuls procedure, Duncan's multiple range test, Least Significant Difference, and Dunnett's ttest are discussed. Designed contrasts (especially orthogonal ones) permit use of tests more sensitive than those recommended for testing of comparisons selected post-data. If one must resol~ to all possible pair-wise comparisons, then Tukey's Honestly Significant Difference test (or possibly the Student-Newman-Keuls procedure) should be used to avoid the large inflation of t~e I error rate incurred by Least Significant Difference or Duncan's test. Examples of applications of recommended techniques are given.