Bayes Least Significant Difference: A Review and Comparison1

The Bayesian approach to mean separation overcomes the objections to previous least significant difference (LSD) procedures by having a direct dependence upon the calculated F value. This procedure has the power of a comparisonwise approach when F is moderate to large in size and is conservative at F values less than about 3.0. The Bayes LSD has the same form as the Fisher LSD, i.e., LSD = sdt, where the Bayes t is not to be confused with Student's t. In the example cited, the Bayes LSD was found to be a more powerful test than the Fisher LSD, Tukey's honest significant difference (HSD), or the Duncan new multiple range (DMR) when F = 45.36, moderate in size and comparative to the Fisher LSD and the DMR when F = 4.43, and conservative and comparable to Tukey's HSD when F = 1.4. The use of BLSD rather than LSD to designate the Bayes Least Significant Difference procedure is suggested.