How to compare small multivariate samples using nonparametric tests

In the life sciences and other research fields, experiments are often conducted to determine responses of subjects to various treatments. Typically, such data are multivariate, where different variables may be measured on different scales that can be quantitative, ordinal, or mixed. To analyze these...

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Bibliographic Details
Published in:Computational statistics & data analysis Vol. 52; no. 11; pp. 4951 - 4965
Main Authors: Bathke, Arne C., Harrar, Solomon W., Madden, Laurence V.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 15.07.2008
Elsevier Science
Elsevier
Series:Computational Statistics & Data Analysis
Subjects:
Exact sciences and technology
General topics
Mathematics
Multivariate analysis
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Parametric inference
Probability and statistics
Sciences and techniques of general use
Statistics
Correlation
Large sample
Non parametric estimation
Multivariate analysis
Statistical test
Law of large numbers
Sample survey
Rank test
Hotelling test
Discriminant analysis
Data analysis
Non parametric test
Covariance analysis
Asymptotic behavior
Statistical association
Variance analysis
Statistical method
Statistical regression
Sampling theory
Statistical computation
Experimental unit
Correlation analysis
Experimental design
Small sample
Asymptotic approximation
Factorial design
Number theory
ISSN:0167-9473, 1872-7352
Online Access:Get full text
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Summary:In the life sciences and other research fields, experiments are often conducted to determine responses of subjects to various treatments. Typically, such data are multivariate, where different variables may be measured on different scales that can be quantitative, ordinal, or mixed. To analyze these data, we present different nonparametric (rank-based) tests for multivariate observations in balanced and unbalanced one-way layouts. Previous work has led to the development of tests based on asymptotic theory, either for large numbers of samples or groups; however, most experiments comprise only small or moderate numbers of experimental units in each individual group or sample. Here, we investigate several tests based on small-sample approximations, and compare their performance in terms of α levels and power for different simulated situations, with continuous and discrete observations. For positively correlated responses, an approximation based on [Brunner, E., Dette, H., Munk, A., 1997. Box-type approximations in nonparametric factorial designs. J. Amer. Statist. Assoc. 92, 1494–1502] ANOVA-Type statistic performed best; for responses with negative correlations, in general, an approximation based on the Lawley–Hotelling type test performed best. We demonstrate the use of the tests based on the approximations for a plant pathology experiment.
ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2008.04.006