Simulations were conducted to examine the effect of differential item functioning (DIF) on measurement consequences such as total scores, item response theory (IRT) ability estimates, and test reliability in terms of the ratio of true-score variance to observed-score variance and the standard error of estimation for the IRT ability parameter. The…

The Mantel-Haenszel (MH) procedure is commonly used to detect items that function differentially for groups of examinees from various demographic and linguistic backgrounds--for example, in international assessments. As in some other DIF methods, the total score is used to match examinees on ability. In thin matching, each of the total score…

The importance of sample size, although widely discussed in the literature on structural equation modeling (SEM), has not been widely recognized among applied SEM researchers. To narrow this gap, we focus on second language testing and learning studies and examine the following: (a) Is the sample size sufficient in terms of precision and power of…