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Current Status of Multiple Comparisons of Means in Designed Experiments¹

Department of Dairy Science, Michigan State University, East Lansing 48823

ABSTRACT

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, Scheffé's interval, Tukey's Honestly Significant Difference, Student-Newman-Keuls procedure, Duncan's Multiple range test, Least Significant Difference, and Dunnett's t-test 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 resort 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 type I error rate incurred by Least Significant Difference of Duncan's test. Examples of applications of recommended techniques are given.

¹ Michigan Agricultural Experiment Station Journal Article 6300.