The frequently neglected and often misunderstood relationship between classical test theory and item response theory is discussed for the unidimensional case with binary measures and no guessing. It is pointed out that popular item response models can be directly obtained from classical test theory-based models by accounting for the discrete…

The majority of large-scale assessments develop various score scales that are either linear or nonlinear transformations of raw scores for better interpretations and uses of assessment results. The current formula for coefficient alpha (a; the commonly used reliability coefficient) only provides internal consistency reliability estimates of raw…

This article studies the ordinal reliability of (total) test scores. This study is based on a classical-type linear model of observed score (X), true score (T), and random error (E). Based on the idea of Kendall's tau-a coefficient, a measure of ordinal reliability for small-examinee populations is developed. This measure is extended to large…

Because test scores are ordinal not cordinal attributes, the average test score often is a misleading way to summarize the scores of a group of individuals. Similarly, correlation coefficients may be misleading summary measures of association between test scores. Proper, readily interpretable, summary statistics are developed from a theory of…

The reliability of a gain is determined by the reliabilities of the components, the correlation between them, and their standard deviations. Reliability is not inherently low, but the components of gains in many investigations make low reliability likely and require caution in the use of gain scores. (SLD)

The critiques by L. Collins and L. Humphreys in this issue illustrate problems with the use of gain scores. Collins' examples show that familiar formulas for the reliability of differences do not reflect the precision of measures of change. Additional examples demonstrate flaws in the conventional approach to reliability. (SLD)

The present paper reviews the techniques commonly used to correct an observed correlation coefficient for the simultaneous influence of attenuation and range restriction effects. It is noted that the procedure which is currently in use may be somewhat biased because it treats range restriction and attenuation as independent restrictive influences.…

This paper discusses cognitive and noncognitive variables, and their relationship with each other, in learning and in educational evaluation. The nature of noncognitive learning environment variables is examined. The following instruments that have been widely used in assessing classroom environment are described: (1) the Learning Environment…

Value-added models in education research allow researchers to explore how a wide variety of policies and measured school inputs affect the academic performance of students. Researchers typically quantify the impacts of such interventions in terms of "effect sizes", i.e., the estimated effect of a one standard deviation change in the…

A method of estimating the operating characteristics of a new test item added to an established test without assuming a prior model has been proposed by the author. In this paper, the author extends this logic by proposing a different hypothesized distribution of the resulting estimate. The former method used a normal approximation; the present…

The purpose of this paper is to compare the precision of direct and indirect measures of writing assessment using the test information functions from a graded response Item Response Theory (IRT) model. Subjects were 192 sophomore English students from a parochial high school in Wisconsin. Both direct and indirect measures of writing ability were…

The idea that validity should be considered a property of inferences, rather than of assessments, has developed slowly over the past century. In early writings about the validity of educational assessments, validity was defined as a property of an assessment. The most common definition was that an assessment was valid to the extent that it…

Although perfectly scalable items rarely occur in practice, Guttman's concept of a scale has proved to be valuable to the development of measurement theory. If the score distribution is uniform and there is an equal number of items at each difficulty level, both the elements and the eigenvalues of the Pearson correlation matrix of dichotomous…

Levels of learning can probably be measured by questions containing various conceptual dimensions which relate to the amount of thinking or creativity required to complete the questions. A method for measuring concept levels in child development course material was evaluated. Student proctors (N=41) and instructors (N=6) rated 73 short-answer…

Correlational analysis, classical test theory, confirmatory factor analysis, and multilevel Rasch modeling were used to refine a measure of adolescents' exposure to violence (ETV). Interpersonal violence could be distinguished from other potentially traumatic events; it was also possible to distinguish three routes of exposure (victimization,…