Review of Five Multilevel Analysis Programs: BMDP-5V,GENMOD, HLM,ML3, VARCL |
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| Authors: | Ita G G Kreft Jan de Leeuw Rien van der Leeden |
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| Institution: | 1. Division of Educational Foundations and Interdivisional Studies , California State University , Los Angeles , CA , 90032-8143 , USA;2. Departments of Psychology and Mathematics , University of California Los Angeles , Los Angeles , CA , 90024-1555 , USA;3. Department of Psychometrics and Research Methods , University of Leiden , 2300 RB , Leiden , The Netherlands |
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| Abstract: | A class of statistics is introduced for testing stochastic ordering between two independent distributions. This class includes as a special case the celebrated Mann—Whitney—Wilcoxon statistic. The new class is shown to be asymptotically normal both under the null and nonnull hypotheses. It is distribution-free. Using Pitman's asymptotic efficacy it is shown that for some alternatives the Mann—Whitney—Wilcoxon statistic is the member with the highest efficacy, although for others it is not, and the member with the highest efficacy is identified. |
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| Keywords: | Asymptotic normality Distribution-free Mann—Whitney—Wilcoxon statistic Pitman's asymptotic efficiency |
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