Empirical Validation of DIMTEST on Nonnormal Ability Distributions

Abstract

DIMTEST is a nonparametric statistical test procedure for assessing unidimensionality of binary item response data. The development of Stout's statistic, T, used in the DIMTEST procedure, does not require the assumption of a particular parametric form for the ability distributions or the item response functions. The purpose of the present study was to empirically investigate the performance of the statistic T with respect to different shapes of ability distributions. Several nonnormal distributions, both symmetric and nonsymmetric, were considered for this purpose. Other factors varied in the study were test length, sample size, and the level of correlation between abilities. The results of Type I error and power studies showed that the test statistic T exhibited consistently similar performance for all different shapes of ability distributions investigated in the study, which confirmed the nonparametric nature of the statistic T.