Calculating theoretical base rates of score differences

AbstractObjective: In this study, we developed new methods to calculate theoretical base rates of score differences when more than two test scores are involved in score comparisons. The study compares the results of theoretical and observed base rates, and then explores whether these methods can be used in practice. Methods: We proposed the formulas and the Monte Carlo methods calculating theoretical base rates of score differences between a single test score and a mean of several test scores by overall sample and subsamples. We also compared observed and theoretical base rates of score differences in the Wechsler Intelligence Scale for Children (5th ed.). using the normative sample data. Results: The theoretical base rates obtained from the new methods were close to the observed base rates. Conclusions: The new methods can derive reasonable theoretical base rates and are usable practically.