Chalmers recently published a critique of the use of ordinal a[alpha] proposed in Zumbo et al. as a measure of test reliability in certain research settings. In this response, we take up the task of refuting Chalmers' critique. We identify three broad misconceptions that characterize Chalmers' criticisms: (1) confusing assumptions with…

A model is proposed for the description of ordinal test scores based on the definition of true score as expected rank; its deviations are compared with results from classical test theory. An unbiased estimator of population true score from sample data is calculated. Score variance and population reliability are examined. (Author/BJG)

Both the binomial and beta-binomial models are applied to various problems occurring in mental test theory. The paper reviews and critiques these models. The emphasis is on the extensions of the models that have been proposed in recent years, and that might not be familiar to many educators. (Author)

Unreliable profiles impose the difficulty that ordinal and interval relations among the individual's scores become uncertain or unstable. A profile reliability coefficient is derived to estimate the relative expected extent of this ordinal and interval "inversion" for any profile of K measures. (Author/DWH)

A mathematical link between test reliability and test validity is derived, taking into account the correlation between error scores on a test and error scores on a criterion measure. When this correlation is positive, the "paradoxical" nonmonotonic relation between test reliability and test validity occurs universally. (Author/BW)

Limitations and extensions of Feldt's approach to testing the equality of Cronbach's alpha coefficients in independent and matched samples are discussed. In particular, this approach is used to test equality of intraclass correlation coefficients. (Author)

A Bayesian alternative to interpretations based on classical reliability theory is presented. Procedures are detailed for calculation of a posterior score and credible interval with joint consideration of item sample and occasion error. (Author/SLD)

Reliability coefficients of linear combinations of observed scores have anomalous properties which have led to difficulties in the investigation of difference scores and gain scores in test theory. Discrepancies between classical results and correct results obtained from more general formulas, which allow for correlated errors, are examined…

Using the concepts of conditional probability, conditional expectation, and conditional independence, the main results of the classical test theory model can be derived in a very few steps with minimal assumptions. The present effort explores the possibility that present classical test theories can be further condensed. (Author/RC)

The use of confirmatory factor analysis by the LISREL program is demonstrated as an assumption-testing method when computing reliability coefficients under different model assumptions. Results indicate that reliability estimates are robust against departure from the assumption of parallelism of test items. (SLD)

Describes four measures of test unreliability that quantify effects of question selection and guessing, both separately and together--three chosen for immediacy and one for greater mathematical elegance. Quantifies their dependence on test length and number of answer options per question. Concludes that many multiple choice tests are unreliable…

An alternative to the uniform probability distribution model for ordinal data is considered. Implications for statistics and for test theory are discussed. (JKS)

An important determinant of equating process efficiency is the correlation between the anchor test and components of each form. Use of some monotonic function of this correlation as a measure of equating efficiency is suggested. A model relating anchor test length and test reliability to this measure of efficiency is presented. (Author/DWH)

The binomial error model includes form-to-form difficulty differences as error variance and leads to Ruder-Richardson formula 21 as an estimate of reliability. If the form-to-form component is removed from the estimate of error variance, the binomial model leads to KR 20 as the reliability estimate. (Author/BW)

The reliability of a criterion referenced test was defined as a measure of the degree to which the test discriminates between an individual's level of performance and a predetermined criterion level. The variances of observed and true scores were defined as the squared deviation of the score from the criterion. Based on these definitions and the…