Measurement invariance is crucial for an effective and valid measure of a construct. Invariance holds when the latent trait varies consistently across subgroups; in other words, the mean differences among subgroups are only due to true latent ability differences. Differential item functioning (DIF) occurs when measurement invariance is violated.…

This article provides information for Extension professionals on the correct analysis of Likert data. The analyses of Likert-type and Likert scale data require unique data analysis procedures, and as a result, misuses and/or mistakes often occur. This article discusses the differences between Likert-type and Likert scale data and provides…

Recent studies of visual statistical learning (VSL) have demonstrated that statistical regularities in sequences of visual stimuli can be automatically extracted, even without intent or awareness. Despite much work on this topic, however, several fundamental questions remain about the nature of VSL. In particular, previous experiments have not…

The (univariate) isotonic psychometric (ISOP) model (Scheiblechner, 1995) is a nonparametric IRT model for dichotomous and polytomous (rating scale) psychological test data. A weak subject independence axiom W1 postulates that the subjects are ordered in the same way except for ties (i.e., similarly or isotonically) by all items of a psychological…

The comparability of examinations in different subjects has been a controversial topic for many years and a number of criticisms have been made of statistical approaches to estimating the "difficulties" of achieving particular grades in different subjects. This paper argues that if comparability is understood in terms of a linking…

A model of test item dependency is presented and used to illustrate the effect that violations of local independence have on the behavior of item characteristic curves. The dependency model is flexible enough to simulate the interaction of a number of factors including item difficulty and item discrimination, varying degrees of item dependence,…

The applicability of a new multiple-group factor analysis of dichotomous variables is shown and contrasted with the item response theory approach to item bias analysis. Situations are considered where the same set of test items has been administered to more than one group of examinees. (Author/BS).

Rasch model total-fit statistics and between-item fit statistics were compared for their ability to detect measurement disturbances through the use of simulated data. Results indicate that the between-fit statistic appears more sensitive to systematic measurement disturbances and the total-fit statistic is more sensitive to random measurement…

The effect of reducing the number of score groups in the matching criterion of the Mantel-Haenszel procedure when screening for differential item functioning was investigated with a simulated data set. Results suggest that more than modest reductions cannot be recommended when ability distributions of reference and focal groups differ. (SLD)

Given a Masters partial credit item with n known step difficulties, conditions are stated for the existence of a set of (locally) independent Rasch binary items such that their raw score and the partial credit raw score have identical probability density functions. (Author/SLD)

Conjunctive item response models are introduced such that: (1) sufficient statistics for latent traits are not necessarily additive in item scores; (2) items are not necessarily locally independent; and (3) existing compensatory (additive) item response models including the binomial, Rasch, logistic, and general locally independent model are…

For the purpose of obtaining data to use in test development, multiple matrix sampling plans were compared to examinee sampling plans. Data were simulated for examinees, sampled from a population with a normal distribution of ability, responding to items selected from an item universe. (Author/LMO)

Drawing on recently developed methodology for structural equation modeling with categorical data, this article proposes a new approach for investigating the behavior of dichotomously scored test items in relation to other relevant (observed) variables. A linear structural model relates the latent ability variable to a set of observed scores.…

Five sets of paired comparison judgments were made concerning test item difficulty, in order to identify the most probable source of intrasensitivity in the data. The paired comparisons method was useful in providing information about sensitivity to stimulus differences, but less useful for assessing dimensionality of judgment criteria.…

Three measures of differential item functioning for the dichotomous response model are extended to include Samejima's graded response model. Two are based on area differences between item true score functions, and one is a chi-square statistic for comparing differences in item parameters. (SLD)