ERIC Number: EJ739964
Record Type: Journal
Publication Date: 2006
A Note on Inferences about the Median of the Distribution of Difference Scores
Wilcox, Rand R.
Educational and Psychological Measurement, v66 n4 p624-630 2006
For two random variables, X and Y, let D = X - Y, and let theta[subscript x], theta[subscript y], and theta[subscript d] be the corresponding medians. It is known that the Wilcoxon-Mann-Whitney test and its modern extensions do not test H[subscript o] : theta[subscript x] = theta[subscript y], but rather, they test H[subscript o] : theta[subscript 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.
Descriptors: Scores, Inferences, Comparative Analysis, Statistical Analysis, Evaluation Methods, Measurement Techniques, Sampling, Simulation, Hypothesis Testing, Error Patterns
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Publication Type: Journal Articles; Reports - Evaluative
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