Uses principles of latent trait theory to derive conditions under which mean differences between groups on an observed variable are in fact indicative of mean differences on an underlying construct. Pays particular attention to the logistic curve as a model for describing the relation between the observed variable and the construct. (Author/CB)

Two strategies for assessing item bias are discussed: methods comparing item difficulties unconditional on ability and methods comparing probabilities of response conditional on ability. Results suggest that the iterative logit method is an improvement on the noniterative one and is efficient in detecting biased and unbiased items. (Author/DWH)

The stability of selected indices for detecting differential item performance (item bias), from one randomly equivalent sample to another, is addressed. Some recent research has criticized these indices as too unreliable for utility in measuring bias in achievement test items. Using data from a national testing of the ACT Assessment, however, this…

Two order theoretic techniques were presented and compared. Ordering theory of Krus and Bart (1974) and an extended Takeya's item relational structure analysis (IRS) by Tatsuoka and Tatsuoka (1981) were used to extract the hierarchical item structure from three datasets. Directed graphs were constructed and both methods were assessed as to how…

The purpose of this paper is to further the cause of clarifying construct interpretations of tests, by proposing that non-metric multidimensional scaling may be more useful than factor analysis or other latent structure models for investigating the internal structure of tests. It also suggests that typical problems associated with scaling…

Item analysis procedures appropriate for domain-referenced classroom testing are described. A conceptual framework within which item statistics can be considered and promising statistics in light of this framework are presented. The sampling fluctuations of the more promising item statistics for sample sizes comparable to the typical classroom…

Significant to a latent trait or item response theory analysis of a mental test is the determination of exactly what is being quantified. The following are practical problems to be considered in the formulation of a good theory: (1) deciding whether two tests measure the same trait or traits; (2) analyzing the relative contributions of a pair of…

The Mantel-Haenszel procedure (MH) is a practical, inexpensive, and powerful way to detect test items that function differently in two groups of examinees. MH is a natural outgrowth of previously suggested chi square methods, and it is also related to methods based on item response theory. The study of items that function differently for two…

In latent trait theory the latent space, or space of the hypothetical construct, is usually represented by some unidimensional or multi-dimensional continuum of real numbers. Like the latent space, the item response can either be treated as a discrete variable or as a continuous variable. Latent trait theory relates the item response to the latent…

Differential item performance (DIP) is discussed as a concept that does not necessarily imply item bias or unfairness to subgroups of examinees. With curriculum-based achievement tests, DIP is presented as a valid reflection of group differences in requisite skills and instruction. Using data from a national testing of the ACT Assessment, this…

The effects of varying degrees of correlation between abilities and of various correlation configurations between item parameters on ability and item parameter estimation using the three parameter logistic model were examined. Ten two-trait configurations and one unidimensional test configuration for 30 item tests were simulated. Each…

To assess the effects of correlated abilities on test characteristics, and to explore the effects of correlated abilities on the use of a multidimensional item response theory model which does not explicitly account for such a correlation, two tests were constructed. One had two relatively unidimensional subsets of items, the other had all…

The purpose of this research study was to assess item response model-test data fit using residuals. First, a comparison of raw and standardized residuals for describing model-test data fit was carried out. Second, hypotheses concerning the relationship between residual sizes and several item characteristics were studied. The analyses with…

A procedure for assessing content-area and total-test dimensionality which uses response function discrepancies (RFD) was studied. Three different versions of the RFD procedure were compared to Bejar's principal axis content-area procedure and Indow and Samejima's exploratory factor analytic technique. The procedures were compared in terms of the…

Three item response models were evaluated for estimating item parameters and equating test scores. The models, which approximated the traditional three-parameter model, included: (1) the Rasch one-parameter model, operationalized in the BICAL computer program; (2) an approximate three-parameter logistic model based on coarse group data divided…