The Analysis of a 2N Experiment by Means of Ranks

Peter Macdonald

Journal of the Royal Statistical Society Series C, 1971, vol. 20, issue 3, 259-275

Abstract: A method is proposed for the analysis of variance of ranked data from a factorial experiment of size 2n which may be replicated or not. A test of the hypothesis that a given linear contrast of means is zero is based on the corresponding contrast of the ranks of the observations in each replicate. An approximate critical region for the test is based on the rank sum test, which is equivalent to the new test under certain null hypotheses. Two other forms of test are also suggested. Estimates of the population contrasts may be obtained by means of an ad hoc procedure for resolving the ambiguity in the mean of the test statistic, together with normalization.

Date: 1971
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