Nonparametric Hypotheses and Rank Statistics for Unbalanced Factorial Designs

Factorial designs are studied with independent observations, fixed number of levels, and possibly unequal number of observations per factor level combination. In this context, the nonparametric null hypotheses introduced by Akritas and Arnold are considered. New rank statistics are derived for testi...

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Bibliographic Details
Published in:Journal of the American Statistical Association 1997-03, Vol.92 (437), p.258-265
Main Authors: Akritas, Michael G., Arnold, Steven F., Brunner, Edgar
Format: Article
Language:English
Subjects:
Applied statistics
Approximation
Distribution functions
Exact sciences and technology
Experimental design
Factorial design
Factorial designs
Hypotheses
Linear models
Mathematics
Nonparametric hypotheses
Nonparametric inference
Null hypothesis
Ordinal data
P values
Probability and statistics
Rank test
Rank tests
Sample size
Sciences and techniques of general use
Statistical methods
Statistics
Theory and Methods
Ties
Unbalanced designs
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Summary:Factorial designs are studied with independent observations, fixed number of levels, and possibly unequal number of observations per factor level combination. In this context, the nonparametric null hypotheses introduced by Akritas and Arnold are considered. New rank statistics are derived for testing the nonparametric hypotheses of no main effects, no interaction, and no factor effects in unbalanced crossed classifications. The formulation of all results includes tied observations. Extensions of these procedures to higher-way layouts are given, and the efficacies of the test statistics against nonparametric alternatives are derived. A modification of the test statistics and approximations to their finite-sample distributions are also given. The small-sample performance of the procedures for two factors is examined in a simulation study. As an illustration, a real dataset with ordinal data is analyzed.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.1997.10473623