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A Note on Inferences About the Median of the Distribution of Difference Scores

University of Southern California

For two random variables, X and Y, let D = X - Y, and let _x, _y, and _d be the corresponding medians. It is known that the Wilcoxon-Mann-Whitney test and its modern extensions do not test H₀: _x = _y, but rather, they test H₀: _d = 0. The article deals with an extension of these methods to dependent groups, so the goal is not to make inferences about the median of the pairwise differences or even the median of the marginal distributions. Rather, if an individual is randomly sampled from the first group and another individual is randomly sampled from the second group, the goal is to make inferences about the median value of the typical difference. The goal is not to suggest that alternative methods be abandoned but rather to provide a perspective on how dependent groups compare that it is similar in spirit to the perspective provided by the Wilcoxon-Mann-Whitney test.

Key Words: comparing dependent groups • Wilcoxon-Mann-Whitney • bootstrap methods

Educational and Psychological Measurement, Vol. 66, No. 4, 624-630 (2006)
DOI: 10.1177/0013164405285547


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