It is well known that a best permutation test for all population distributions P does not generally exist, because the most powerful unbiased permutation test is a function of the population distribution P which is assumed to be unknown (Pesarin and Salmaso, 2010). In this work, we focus our attention on the randomized complete block design in case of an ordered categorical response variable, which is the typical reference setting in many psychometric studies. We compared via a Monte Carlo simulation study several combination-based permutation test statistics and we found out that the Multi-focus statistic (Finos and Salmaso, 2004) using the Fisher’s combining function appears to be the more powerful solution which we proved also to be better under non normal errors than traditional parametric and rank-based nonparametric counterparts.
A Comparison among Combination-Based Permutation Statistics for Randomized Complete Block Design
ARBORETTI GIANCRISTOFARO, ROSA;CORAIN, LIVIO;
2012
Abstract
It is well known that a best permutation test for all population distributions P does not generally exist, because the most powerful unbiased permutation test is a function of the population distribution P which is assumed to be unknown (Pesarin and Salmaso, 2010). In this work, we focus our attention on the randomized complete block design in case of an ordered categorical response variable, which is the typical reference setting in many psychometric studies. We compared via a Monte Carlo simulation study several combination-based permutation test statistics and we found out that the Multi-focus statistic (Finos and Salmaso, 2004) using the Fisher’s combining function appears to be the more powerful solution which we proved also to be better under non normal errors than traditional parametric and rank-based nonparametric counterparts.Pubblicazioni consigliate
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