Algorithms for compact letter displays: Comparison and evaluation

Multiple pairwise comparisons are one of the most frequent tasks in applied statistics. In this context, letter displays may be used for a compact presentation of results of multiple comparisons. A heuristic previously proposed for this task is compared with two new algorithmic approaches. The latter rely on the equivalence of computing compact letter displays to computing clique covers in graphs, a problem that is well-studied in theoretical computer science. A thorough discussion of the three approaches aims to give a comparison of the algorithms’ advantages and disadvantages. The three algorithms are compared in a series of experiments on simulated and real data, e.g., using data from wheat and triticale yield trials.