Methods are presented for comparing grades obtained in a situation where students can choose between different subjects. It must be expected that the comparison between the grades is complicated by the interaction between the students' pattern and level of proficiency on one hand, and the choice of the subjects on the other hand. Three methods…

Two types of answer-copying statistics for detecting copiers in small-scale examinations are proposed. One statistic identifies the "copier-source" pair, and the other in addition suggests who is copier and who is source. Both types of statistics can be used when the examination has alternate test forms. A simulation study shows that the…

The standardized log-likelihood of a response vector (l[subscript z]) is a popular IRT-based person-fit test statistic for identifying model-misfitting response patterns. Traditional use of l[subscript z] is overly conservative in detecting aberrance due to its incorrect assumption regarding its theoretical null distribution. This study proposes a…

No Child Left Behind (NCLB) performance mandates, embedded within state accountability systems, focus school AYP (adequate yearly progress) compliance squarely on the percentage of students at or above proficient. The singular importance of this quantity for decision-making purposes has initiated extensive research into percent proficient as a…

A potential undesirable effect of multistage testing is differential speededness, which happens if some of the test takers run out of time because they receive subtests with items that are more time intensive than others. This article shows how a probabilistic response-time model can be used for estimating differences in time intensities and speed…

Data from a large-scale performance assessment (N = 105,731) were analyzed with five differential item functioning (DIF) detection methods for polytomous items to examine the congruence among the DIF detection methods. Two different versions of the item response theory (IRT) model-based likelihood ratio test, the logistic regression likelihood…

An approach called generalizability in item response modeling (GIRM) is introduced in this article. The GIRM approach essentially incorporates the sampling model of generalizability theory (GT) into the scaling model of item response theory (IRT) by making distributional assumptions about the relevant measurement facets. By specifying a random…

This study explored the use of kernel equating for integrating and extending two procedures proposed for assessing item order effects in test forms that have been administered to randomly equivalent groups. When these procedures are used together, they can provide complementary information about the extent to which item order effects impact test…

This article reports two studies to illustrate methodologies for conducting a conditional covariance-based nonparametric dimensionality assessment using data from two forms of the Test of English as a Foreign Language (TOEFL). Study 1 illustrates how to assess overall dimensionality of the TOEFL including all three subtests. Study 2 is aimed at…

The central idea of differential item functioning (DIF) is to examine differences between two groups at the item level while controlling for overall proficiency. This approach is useful for examining hypotheses at a finer-grain level than are permitted by a total test score. The methodology proposed in this paper is also aimed at estimating…

In studies of the SAT, correlations of SAT scores, high school grades, and socioeconomic factors (SES) are usually obtained using a university as the unit of analysis. This approach obscures an important structural aspect of the data: The high school grades received by a given institution come from a large number of high schools, all of which have…

Using longitudinal data from a cohort of middle school students from a large school district, we estimate separate "value-added" teacher effects for two subscales of a mathematics assessment under a variety of statistical models varying in form and degree of control for student background characteristics. We find that the variation in estimated…

A Monte Carlo simulation technique for generating dichotomous item scores is presented that implements (a) a psychometric model with different explicit assumptions than traditional parametric item response theory (IRT) models, and (b) item characteristic curves without restrictive assumptions concerning mathematical form. The four-parameter beta…

It is a widely held belief that anchor tests should be miniature versions (i.e., "minitests"), with respect to content and statistical characteristics, of the tests being equated. This article examines the foundations for this belief regarding statistical characteristics. It examines the requirement of statistical representativeness of anchor…

Hypotheses about aberrant test-response behavior and hence invalid person-measurement have hitherto included factors like ability, gender, language, test-anxiety, and motivation, but these have not previously been collectively investigated with real data, or with multilevel models. This study analyzes the effect of these factors on person…