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The paper by Faith and Cranston (1991) is but the latest manifestation ofa disturbing phenomenon in cladistics. In their paper, as well as in Archie (1989) and Faith (I99 1)~ randomizations of character data are used to specify a decision criterion. It is my purpose here to argue that such applications are ill-conceived. In Faith and Cranston (199 11 and Archie [1989), c aracter states from a given data h matrix are reassigned to taxa under an equiprobable random model, the number and frequency of states being maintained. Cladistic analysis is then performed on the contrived data set. The procedure is repeated a specified number of times (99 or 100, respectively). The frequency of cladograms having a length at least as short as that tbr the real data is treated as the critical value for determining whether the data arc phylogenetically informative, that is, as the level ofsignificance for a Type I error (in this case, incorrect rejection of random congruence). If the conclusion is no difference between lengths for real and contrived data, the cladogram for the real data is regarded as poorly supported. Faith (199 1) extended the matrix permutation approach to specific groups on the cladogram.