Determination of Type I Error and Power Rate in Differential Item Functioning by Several Methods

Abstract

In this study, the methods based on Classical Test Theory and Item Response Theory were used comparatively to determine Type I error and power rates in Differential Item Functioning. Logistic regression, Mantel-Haenszel, Lord's 𝜒 2 , Breslow-Day and Raju's area index methods were used for the analyses, which were conducted using the R programming language. Determination of Type I error and power rates of these methods under certain conditions was carried out by simulation study. For data generation, analyzes were made under eight conditions in total by examining different sample sizes and DIF rates created with the WinGen 3 program. The results of the study indicate that, in general when the ratio of items containing DIF increased, Type I error increased and the power ratio decreased. Among the methods based on Item Response Theory, Lord's 𝜒 2 and Raju's area index methods gave better results than other methods with low error and high power.