Wilcox has described three probability models which characterize a single test item in terms of a population of examinees (ED 156 718). This note indicates indicates that similar models can be derived which characterize a single examinee in terms of an item domain. A numerical illustration is given. (Author/JKS)

The purpose of this paper is to derive explicit estimates of the parameters of a latent structure model when the skills represented by the test items are hierarchically related. Two special cases are described, which may be used as an approximation to the Dayton and Macready model and also provide initial estimates in an iterative estimation…

Two fundamental problems in mental test theory are to estimate true score and to estimate the amount of error when testing an examinee. In this report, three probability models which characterize a single test item in terms of a population of examinees are described. How these models may be modified to characterize a single examinee in terms of an…

Procedures are presented for equating simultaneously several tests which have been calibrated by the Rasch Model. Three multiple test equating designs are described. A Full Matrix Design equates each test to all others. A Chain Design links tests sequentially. A Vector Design equates one test to each of the other tests. For each design, the Rasch…

The reliability and validity of a tailored testing procedure based on the simple logistic model was determined for an achievement test in statistics and measurement. The test was administered on a CRT terminal to students from graduate and undergraduate measurement courses. Equivalent form reliability over a one-week interval was found to be 0.595…

The psychometric research done by G. Rasch between 1951 and 1959, which is explained and illustrated in this book, takes psychometrics from being purely descriptive to being a science of objective measurement. Individual centered statistics require models in which each individual is characterized separately and from which, given adequate data,…

This book shows the advantages of Rasch measurement (G. Rasch) for school district testing programs. The results of Rasch methods are contrasted with conventional statistics for assessing student responses to basic skills testing. Chapter 1 shows how the Rasch probability-based method produces measures that are more useful for students, parents,…

An elementary survey of item characteristic curve theory, centered around the problems of individualized (tailored) testing, is presented. Following the introduction, discussions are provided of the following: Test Theory for Itemized Tests; The Guttman Scale; Item Characteristic Curve Theory; An Alternative Model; Specialization, Application, and…