Baby Bear's Dilemma: A Statistical Tale 1

An allegorical and satirical, but also, we hope an accurate and humorous expository look at the problem researchers face in choosing a pairwise multiple comparisons procedure for detecting differences among treatment means. The primary objective is to present, from several points of view, some of the arguments and resulting confusion surrounding the use of the least significant difference vis-a-vis Tukey's w procedure or honest significant difference, Duncan's Multiple Range Test, and the Waller-Duncan Bayesian k-ratio t test. Particular emphasis is placed on demonstrating that the concept of comparisonwise error rate is considerably more logical, sound, and useful in pairwise multiple comparisons than the concept of experimentwise error rate. As a consequence, despite what researchers may have read in the statistical Literature or what they may have heard from statistical experts, the least significant difference is appropriate whenever a pairwise multiple comparisons procedure is in order.