Computer simulation techniques were used to study the properties of five procedures for pairwise multiple comparisons of treatment means. Procedures studied were: (1) the ordinary least significant difference, LSD, (2) use of a preliminary F test with the least significant difference, FLSD, (3) Tukey's Significant Difference, TSD, (4) Duncan's Multiple Range Test, DMRT, and (5) a relatively new Bayesian modification of the least significant difference, BLSD. Results presented are based on simulation of 60,000 experiments involving 3, 4, 6, or 8 replicates of either 10 or 20 treatments with various patterns of homogeneity among treatment means. Observed rates of correct decisions when real differences occur among treatments, and observed rates of three types of possible errors indicated that the FLSD, DMRT, and BLSD are more appropriate for use in research than the LSD or TSD. Based on the statistical properties observed in this study a choice among the FLSD, DMRT, and BLSD is difficult; however, the FLSD may be preferred due to its familiarity to researchers and its simplicity of application.
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Carmer et al. (1971) studied this question.