Testing for Differential Item Functioning Under the D-Scoring Method.

This study offers an approach to testing for differential item functioning (DIF) in a recently developed measurement framework, referred to as D-scoring method (DSM). Under the proposed approach, called P-Z method of testing for DIF, the item response functions of two groups (reference and focal) are compared by transforming their probabilities of correct item response, estimated under the DSM, into Z-scale normal deviates. Using the liner relationship between such Z-deviates, the testing for DIF is reduced to testing two basic statistical hypotheses about equal variances and equal means of the Z-deviates for the reference and focal groups. The results from a simulation study support the efficiency (low Type error and high power) of the proposed P-Z method. Furthermore, it is shown that the P-Z method is directly applicable in testing for differential test functioning. Recommendations for practical use and future research, including possible applications of the P-Z method in IRT context, are also provided.

Latent D-Scoring Modeling: Estimation of Item and Person Parameters.

This study presents a latent (item response theory-like) framework of a recently developed classical approach to test scoring, equating, and item analysis, referred to as D-scoring method. Specifically, (a) person and item parameters are estimated under an item response function model on the D-scale (from 0 to 1) using marginal maximum-likelihood estimation and (b) analytic expressions are provided for item information function, test information function, and standard error of estimation for D-scores obtained under the proposed latent treatment of the D-scoring method. The results from a simulation study reveal very good recovery of item and person parameters via the marginal maximum-likelihood estimation method. Discussion and recommendations for practice are provided.