Dominance Statistics: Ordinal Analyses to Answer Ordinal Questions

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Much behavioral research involves comparing the central tendencies of different groups, or of the same subjects under different conditions, and the usual analysis is some form of mean comparison. This article suggests that an ordinal statistic, d, is often more appropriate. d compares the number of times a score from one group or condition is higher than one from the other, compared with the reverse. Compared to mean comparisons, d is more robust and equally or more powerful; it is invariant under transformation; and it often conforms more closely to the experimenter's research hypothesis. It is suggested that inferences from d be based on sample estimates of its variance rather than on the more traditional assumption of identical distributions. The statistic is extended to simple repeated measures designs, and ways of extending its use to more complex designs are suggested.

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