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Adjustments for Kurtosis and Continuity on the Prentice Test
Math Department, Occidental College, Los Angeles, USA
Department of Statistics, University of New Jersey, Piscataway, USA
- 1 Math Department, Occidental College, Los Angeles, USA
- 2 Department of Statistics, University of New Jersey, Piscataway, USA
Advances in Pure Mathematics·Volume 14 (2024)·Pages 101–117·Published 29 February 2024·DOI10.4236/apm.2024.142005
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Abstract
The test of Prentice [1] is a non-parametric statistical test for the two-way analysis of variance using ranks. The null distribution of this test typically is approximated using the Chi-square distribution. However, the exact null distribution deviates from the Chi-square approximation in certain cases commonly found in applications of the test, motivating adjustments to the distribution. This manuscript presents adjustments to this null distribution correcting for continuity, multivariate skewness, and multivariate kurtosis. The effects of alternative scoring methods as non-polynomial functions of rank sums are also presented as a broader application of the approximation.
KeywordsFriedman TestPrentice TestEdgeworth Approximation
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