The growing use of scales in survey questionnaires warrants the need to address how does polytomous differential item functioning (DIF) affect observed scale score comparisons. The aim of this study is to investigate the impact of DIF on the type I error and effect size of the independent samples t-test on the observed total scale scores. A…

In this paper, a new item analysis index, e, is derived as a function of difficulty and discrimination to represent item efficiency. Item discrimination in this paper is not independent of item difficulty, and it is demonstrated algebraically that the maximum discriminating power of an item may be determined from its difficulty. Item efficiency is…

Mathematical and statistical relationships between factor analysis and smallest space analysis are discussed. As spatial analysis of correlation matrices, factor analysis is a special case of smallest space analysis. The two differ in six ways: Shepard diagram, dimensionality, correction for communality, similarity coefficients, regions versus…

The interaction of subjects with test items is investigated. It is suggested that psychometricians rely too heavily on inferences about the nature of the interaction. An approach to data analysis is proposed which is more directly related to this interaction. (JKS)

It has been argued that item variance and test variance are not necessary characteristics for criterion-referenced tests, although they are necessary for norm-referenced tests. This position is in error because it considers sample statistics as the criteria for evaluating items and tests. Within a particular sample, an item or test may have no…

Confirmatory multidimensional item response theory (CMIRT) was used to assess the structure of the Graduate Record Examination General Test, about which much information about factorial structure exists, using a sample of 1,001 psychology majors taking the test in 1984 or 1985. Results supported previous findings that, for this population, there…

It is shown that empirical mental test P - P plots are approximately equal to theoretical item-item curves, at least for long tests administered to many people. This result is important because it leads to (1) a distribution free method for estimating points on item-item curves; (2) a general method for defining estimates of item parameters; and…

This study examines a common set of equating items for their appropriateness to both American and Canadian populations and, to determine the equations for converting scores from the verbal and mathematical scales of the 1971 form of the Canadian Scholastic Aptitude Test (the future standard continuing scales of the CSAT) to the corresponding…

The Minnesota-Briggs History Record (M-B) is a self-administered history inventory. This monograph summarizes studies of the M-B and describes the development of seven scales based upon M-B items. (Authors)

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…

The literature on criterion referenced testing is full of discussions concerning whether classical measurement techniques are appropriate, whether variance is necessary, whether new indices of reliability are needed, and the like. What appears to be lacking, however, is a clear and simple discussion of why the problems occur. This paper suggests…

When classes are the units of analyses, estimates of the reliability of class means are needed. Using classical test theory it is difficult to treat this problem adequately. Generalizability theory, however, provides a natural framework for dealing with the problem. Each of four possible formulas for the generalizability of class means is derived…

Since all commonly used latent trait models assume a unidimensional test, the applicability of the procedure to obviously multidimensional tests is questionable. This paper presents the results of the application of latent trait, traditional, and factor analyses to a series of actual and hypothetical tests that vary in factoral complexity.…

This text was written to help the reader acquire a base of knowledge about classical psychometrics and to integrate new ideas into that framework of knowledge. The material is organized into five units: (1) introduction to measurement theory; (2) reliability; (3) validity; (4) item analysis in test development; and (5) test scoring and…