To resolve a recent controversy between Klein and Cleary and Levy, a model for dichotomous congeneric items is presented which has mean errors of zero, dichotomous true scores that are uncorrelated with errors, and errors that are mutually uncorrelated. (Author)

Aggregation, or grouping, is a statistical procedure through which all members of a study within a specified range of scores (usually observed scores) are assigned a common or "group" score (for example, the group mean). The various social science methodology literatures agree on the costs of grouping: not only does one always lose…

Ordinal measurement is the rank ordering of individuals in a population. For ordinal measurement, the concept of an individual propensity distribution is his or her true score. Estimation of, as well as other aspects of the distribution, are discussed. (Author/JKS)

The usual formulas for the reliability of differences between two test scores are based on the assumption that the error scores are uncorrelated. Formulas are presented for the general case where this assumption is unnecessary. (Author/JKS)

Finding and interpreting lower bounds for reliability coefficients for tests with nonhomogenous items has been a problem for psychometricians. This paper presents a mathematical formula for finding the greatest lower bound for such a coefficient. (Author/JKS)

This discussion illustrates the application of generalizability theory to a design commonly employed in the collection of evaluation data and provides a detailed analysis of the dependability of student evaluations of college teaching. (RC)

This paper provides analytic evaluations of expected (marginal) true-score measures for binary items given their item response theory (IRT) calibration. Under the assumption of normal trait distributions, marginalized true scores, error variance, true score variance, and reliability for norm-referenced and criterion-references interpretations are…

This paper reviews various procedures for constructing an interval for an individual's true score given the assumption that errors of measurement are distributed as binomial. This paper also presents two general interval estimation procedures (i.e., normal approximation and endpoints conversion methods) for an individual's true scale score;…

Exact formulas for classical error variance are provided for Rasch measurement with logistic distributions. An approximation formula with the normal ability distribution is also provided. With the proposed formulas, the additive contribution of individual items to the population error variance can be determined without knowledge of the other test…

Classical test theory is based on the concept of a true score for each examinee, defined as the expected or average score across an infinite number of repeated parallel tests. In most cases, there is only a score from a single administration of the test in question. The difference between this single observed score and the underlying true score is…

Article commented on a study by Harris, who presented formulas for the variance of errors of estimation (of a true score from an observed score) and the variance of errors of prediction (of an observed score from an observed score on a parallel test). (Author/RK)

This reply refers to PS 502 345 which in turn is a criticism of EJ 045 083. (CB)

The problem of whether a precise connection exists between the stochastic processes considered in mathematical learning theory and the Guttman simplex is investigated. The approach used is to derive a set of conditions which a probabilistic model must satisfy in order to generate inter-trial correlations with the perfect simplex property.…

Compares four closed-formula estimators (Burkett, Claudy, Rozeboom, Browne) and the omit-one method for estimating TRS, the true shrunken correlation (not to be confused with TR, the true multiple correlation). Recommendations are based on artificial populations with known TRS. (Author/SV)