Summary When a number of tests are carried out simultaneously on a set of data some overall guarantee against making type I errors is required. Various solutions to this problem have been suggested with different approaches to this overall protection level. The joint operating characteristics of simultaneous tests are usually incompletely specified and simulation has to be employed to evaluate the power of the tests. A new simulation is reported, comparing seven methods of pairwise comparisons and four for constructing simultaneous sets of confidence limits. The general conclusions are that Duncan's multiple range test is the best method of those considered for the former and the Bonferroni t‐based limits for the latter. The findings are generally in agreement with all but one of the previous simulations which have been carried out on multiple comparisons.

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The problems inherent in making a number of simultaneous inferences about a set of sample means centre around the degree of protection against Type I errors afforded by the test in use. The various viewpoints and the better known techniques for solving the problems are discussed and other, less well‐known, methods are introduced, particularly that due to Duncan with its basis in the Bayesian approach. The use of the methods is exemplified by the results of a trial on a large number of treatments and the need for the multiple comparisons methods is clearly shown. Results of a new simulation shed light on the operating characteristics of many of the tests discussed and recommendations are made as to the best techniques to use in various circumstances.

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The Method of Paired Comparisons H. A. David London, Charles Griffin, 1988, 2nd edn vi+188 pp., £21·50 ISBN 0 85264 290 3