Three counterexamples demonstrate that the Dutch Identity conjecture of P. Holland about examinee ability (1990) does not hold in general. The counterexamples suggest that only under strong assumptions can it be true that the limits of log-manifest probabilities are quadratic. Three propositions giving such strong conditions are given. (Author/SLD)

A hypothesis testing and estimation procedure, Crossing SIBTEST, is presented for detecting crossing differential item functioning (DIF), which exists when the difference in probabilities of a correct answer for two examinee groups changes signs as ability level is varied. The procedure estimates the matching subtest score at which crossing…

The empirical Bayes modeling approach--latent ability random sampling in the item response theory (IRT) context--to the IRT modeling of psychological tests is described. Under the usual empirical Bayes unidimensional IRT modeling approach, the posterior distribution of examinee ability given test response is approximately normal for a long test.…

A statistical procedure is presented that is designed to test for unidirectional test bias existing simultaneously in several items of an ability test, based on the assumption that test bias is incipient within the two groups' ability differences. The proposed procedure--Simultaneous Item Bias (SIB)--is based on a multidimensional item response…

The asymptotic posterior normality of latent variable distributions is established under very general and appropriate hypotheses, providing a probabilistic basis for assessing ability estimation/prediction accuracy in the long test case, as well as a first step in making the Dutch Identity conjecture rigorous. (SLD)

This paper presents a conceptualization of test bias for standardized ability tests which is based on multidimensional, non-parametric, item response theory. An explanation of how individually-biased items can combine through a test score to produce test bias is provided. It is contended that bias, although expressed at the item level, should be…

A model-based modification of the standardization index based on a multidimensional item response theory bias modeling approach is presented that detects and estimates differential item functioning (DIF) (item bias) simultaneously for several items as well as differential test functioning (DTF). This SIBTEST procedure is tested through a computer…