Compact letter display

Compact Letter Display (CLD) is a statistical method to clarify the output of multiple hypothesis testing when using the ANOVA and Tukey's range tests. CLD can also be applied following the Duncan's new multiple range test (which is similar to Tukey's range test). CLD facilitates the identification of variables, or factors, that have statistically different means (or averages) vs. the ones that do not have statistically different means (or averages).

The basic technique of compact letter display is to label variables by one or more letters, so that variables are statistically indistinguishable if and only if they share at least one letter. The problem of doing so, using as few distinct letters as possible can be represented combinatorially as the problem of computing an edge clique cover of a graph representing pairs of indistinguishable variables.

As well as marking distinguishability in this way, CLD also ranks variables, or factors, by their respective mean (or average) in descending order. The CLD methodology can be applied to tabular data (spreadsheet, data frame) or visual data (box plot and bar chart).