A SAS macro for generating letter displays of pairwise mean comparisons

Data from many experiments are routinely subjected to analysis of variance, followed by a multiple comparison of means. A popular way to present the result of mean comparisons is by attaching super-scripted letters to the means, with a common letter on two means indicating that they are not significantly different. When the standard error of a difference is not constant, the algorithm traditionally used for generating such displays may fail to represent all significant differences. This paper reports on a so-called insert-and-absorb algorithm that is guaranteed to always truthfully represent all significant differences. This algorithm was implemented in a SAS macro %MULT. Its usage is illustrated using three examples.