Nonparametric multiple comparison procedures for unbalanced two-way layouts

In this paper, we consider nonparametric multiple comparison procedures for unbalanced two-way factorial designs under a pure nonparametric framework. For multiple comparisons of treatments versus a control concerning the main effects or the simple factor effects, the limiting distribution of the as...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2008-12, Vol.138 (12), p.3674-3686
Main Authors: Gao, Xin, Alvo, Mayer
Format: Article
Language:English
Subjects:
Combinatorics
Combinatorics. Ordered structures
Designs and configurations
Exact sciences and technology
Experimental design
General topics
Linear inference, regression
Linear pseudo rank statistics
Logically related hypotheses
Mathematics
Multivariate totally positive of order two condition
Nonparametric relative effects
Probability and statistics
Sciences and techniques of general use
Simes inequality
Statistics
Stepwise procedures
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Summary:In this paper, we consider nonparametric multiple comparison procedures for unbalanced two-way factorial designs under a pure nonparametric framework. For multiple comparisons of treatments versus a control concerning the main effects or the simple factor effects, the limiting distribution of the associated rank statistics is proven to satisfy the multivariate totally positive of order two condition. Hence, asymptotically the proposed Hochberg procedure strongly controls the familywise type I error rate for the simultaneous testing of the individual hypotheses. In addition, we propose to employ Shaffer's modified version of Holm's stepdown procedure to perform simultaneous tests on all pairwise comparisons regarding the main or simple factor effects and to perform simultaneous tests on all interaction effects. The logical constraints in the corresponding hypothesis families are utilized to sharpen the rejective thresholds and improve the power of the tests.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2007.11.019