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In previous papers 3 4 a ranking method has been described for the rapid approximate determination of the significance of differences between two treatments, when the experimental data consists of unpaired replications, paired replications, or replications occurring in two or more groups. Brief tables were given which furnished the rank totals for the 0.05%o, 0.02% and 0.01% level of significance. These tables were prepared by making use of certain properties of the partitions of numbers, but the method becomes impractical with larger numbers of replicates. A recent paper by Mann and Whitney 1 describes a similar test and gives probability tables covering the range from 3 to 8 replicates per treatment, including the case of unequal numbers of unpaired replicates under the two treatments. These authors tabulated the probabilities against the serial number of possible rank totals, 0-1-2 .... U, instead of the rank total itself. Their tables give probabilities for one tail of the distribution only.
Frank Wilcoxon (1947) studied this question.