Designing a theory-based assessment with sound psychometric qualities to measure a higher-order cognitive construct is a highly desired yet challenging task for many practitioners. This paper proposes a framework for designing a theory-based assessment to measure a higher-order cognitive construct. This framework results in a modularized yet…

For trinary partial credit items, the shape of the item information and item discrimination functions is examined in relation to the item parameters. Conditions under which these functions are unimodal and bimodal are discussed, and the locations and values of maxima are derived. Practical relevance of the results is discussed. (SLD)

This handbook explains how to do Rasch measurement. The emphasis is on practice, but theoretical explanations are also provided. The Forward contains an introduction to the topic of Rasch measurement. Chapters 2, 4, 5, and 7 use a small problem to illustrate the application of Rasch measurement in detail, and methodological issues are considered…

A class of multidimensional latent trait models is described. The properties of the model parameters, and initial results on the accuracy of a maximum likelihood procedure for estimating the model parameters are discussed. The model presented is a special case of the general model described by Rasch (1961), with close similarities to the models…

Binary or graded disagree-agree responses to attitude items are often collected for the purpose of attitude measurement. Although such data are sometimes analyzed with cumulative measurement models, recent investigations suggest that unfolding models are more appropriate (J. S. Roberts, 1995; W. H. Van Schuur and H. A. L. Kiers, 1994). Advances in…

One means of learning about the processes operating in a multiple choice test is to include some test items, called nonsense items, which have no correct answer. This paper compares two versions of a mathematical model of test performance to interpret test data that includes both genuine and nonsense items. One formula is based on the usual…

In three lectures, Benjamin D. Wright of the University of Chicago introduces the Rasch model and its basic concepts. The first lecture, March 30, 1994 discusses the model created by Georg Rasch, a Danish mathematician, which Dr. Wright initially saw as merely a way to make raw scores into measures. Eventually, the model developed into a…

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…

This paper reviews the existing multidimensional item response theory (IRT) models and demonstrates how one of the models can be applied to estimation of abilities from a test measuring more than one dimension. The purposes of this paper were threefold. First, the fundamental concepts required when considering multidimensional models for the…

Several special cases of the general Rasch model, varying in complexity, were investigated to determine whether they could successfully model realistic multidimensional item response data. Whether the parameters of the model could be readily interpreted was also investigated. The models investigated included: (1) the vector model; (2) the product…

Research related to the multiple choice test item is reported, as it is conducted by educational technologists in Japan. Sato's number of hypothetical equivalent alternatives is introduced. The based idea behind this index is that the expected uncertainty of the m events, or alternatives, be large and the number of hypothetical, equivalent…

The feasibility of using item response theory (IRT) as a psychometric model for the Graduate Record Examination (GRE) Aptitude Test was addressed by assessing the reasonableness of the assumptions of item response theory for GRE item types and examinee populations. Items from four forms and four administrations of the GRE Aptitude Test were…

A formal analysis is presented of the effects of item deletion on equating/scaling functions and reported score distributions. The phrase "item deletion" refers to the process of changing the original key of a flawed item to either all options correct, including omits, or to no options correct, i.e., not scoring the flawed item. There…

When learning is taking place, students test their hypotheses and evaluate them, and modify their current theories on the basis of new information. This phenomenon is known as "hypothesis testing view" or "theory changes." Many students change their rules to another while they are taking a test. This study introduced a new…

In the answer-until-correct mode of multiple-choice testing, respondents are directed to continue choosing among the alternatives to each item until they find the correct response. There is no consensus as to how to convert the resulting pattern of responses into a measure because of two conflicting models of item response behavior. The first…