Rasch-transformed raw scores and Two-way ANOVA: a simulation analysis

This article demonstrates, through the exposition of underestimated variable effects or spurious interaction effects, the inherent inadequacy of untransformed 0-1 raw scores for analysis via Two-Way analysis of variance (ANOVA). The pioneering work in this field, conducted in the 1990's by Dr. Susan Embretson of the University of Kansas, USA, is highlighted, and the eminent suitability of Rasch transformations of 0-1 raw scores for analysis via Two-Way ANOVA is also demonstrated. In this study Monte Carlo techniques or simulations are utilized to determine the precise psychometric conditions under which differences between raw scores and Rasch transformations of those raw scores are detectable via Two-Way ANOVA. This study partially replicates Dr. Embretson's studies, and also defines the extent of underestimation and spuriousness which ensue when uniform or skewed distributions of item difficulties are used instead of normal distributions, and misfitting raw data are utilized instead of fitting data.