Letters in Mean Comparisons: What They Do and Don't Mean

Letter displays are often used to report results of all pairwise comparisons among treatment means in comparative experiments. In captions to tables and charts using such letter displays, it is crucial to explain properly what the letters mean. In this paper I explain what the letters mean and how this meaning can be succinctly conveyed in a single sentence without ambiguity. This is contrasted to counter-examples commonly found in publications.