Tests for aggregated dispersion: Van Valen’s test and a new competitor

Van Valen’s test is usually applied as a two sample test for equality of dispersion for multivariate data. Motivated by a comment of Manly (Van Valen’s test. Encyclopedia of Statistical Sciences, 2006) that “Little is known about the properties of Van Valen’s test” we develop an alternative test and...

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Bibliographic Details
Published in:Environmental and ecological statistics 2022-06, Vol.29 (2), p.223-239
Main Authors: Livingston, Glen, Allingham, David, Rayner, J. C. W.
Format: Article
Language:English
Subjects:
Biomedical and Life Sciences
Chemistry and Earth Sciences
Computer Science
Dispersion
Ecology
Encyclopaedias
Encyclopedias
Health Sciences
Hypotheses
Life Sciences
Math. Appl. in Environmental Science
Medicine
Multivariate analysis
Null hypothesis
Permutations
Physics
Robustness
Statistics for Engineering
Statistics for Life Sciences
Theoretical Ecology/Statistics
Citations: Items that this one cites
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Summary:Van Valen’s test is usually applied as a two sample test for equality of dispersion for multivariate data. Motivated by a comment of Manly (Van Valen’s test. Encyclopedia of Statistical Sciences, 2006) that “Little is known about the properties of Van Valen’s test” we develop an alternative test and compare the Van Valen test with our alternative robust test in an extensive simulation study. We find that Van Valen’s test does not actually test for equality of variance sums; however, for that null hypothesis it still performs well in terms of closeness to the nominal significance level. Due to testing the correct null hypothesis and the excellent adherence to the nominal significance level, we recommend the use of the robust test as a permutation test.
ISSN:1352-8505
1573-3009
DOI:10.1007/s10651-021-00517-0