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 focus of this paper is assessing the impact of measurement errors on the prediction error of an observed-score regression. Measures are presented and described for decomposing the linear regression's prediction error variance into parts attributable to the true score variance and the error variances of the dependent variable and the predictor…

Background: A recent article published in "Educational Research" on the reliability of results in National Curriculum testing in England (Newton, "The reliability of results from national curriculum testing in England," "Educational Research" 51, no. 2: 181-212, 2009) suggested that: (1) classification accuracy can be…

In this report, an alternative item response theory (IRT) observed score equating method was newly developed. The proposed equating method was illustrated with two real data sets and the equating results were compared to those of traditional IRT true score and IRT observed score equating methods. Using three loss indices, the new method appeared…

Objective: The authors conducted a meta-analysis of empirical studies investigating associations between indices of posttraumatic stress disorder (PTSD) and intimate relationship problems to empirically synthesize this literature. Method: A literature search using PsycINFO, Medline, Published International Literature on Traumatic Stress (PILOTS),…

It is shown that the Angoff and bookmarking cut scores are examples of true score equating that in the real world must be applied to observed scores. In the context of defining minimal competency, the percentage "failed" by such methods is a function of the length of the measuring instrument. It is argued that this length is largely…

The authors propose a concise formula to evaluate the standard error of the estimated latent variable score when the true values of the structural parameters are not known and must be estimated. The formula can be applied to factor scores in factor analysis or ability parameters in item response theory, without bootstrap or Markov chain Monte…

The paradox that a Student t-test based on pretest-posttest differences can attain its greatest power when the difference score reliability is zero was explained by demonstrating that power is not a mathematical function of reliability unless either true score variance or error score variance is constant. (SLD)

It is demonstrated that, in the presence of population information, a linear combination of true scores can be estimated more efficiently than by the same linear combination of the observed scores. Three criteria for optimality are discussed, but they yield the same solution, described as a multivariate shrinkage estimator. (Author/SLD)

A decision-theoretic approach to the question of reliability in categorically scored examinations is explored. The concepts of true scores and errors are discussed as they deviate from conventional psychometric definitions and measurement error in categorical scores is cast in terms of misclassifications. A reliability measure based on…

Numerous studies have shown increasing item reliabilities as an effect of the item position in personality scales. Traditionally, these context effects are analyzed based on item-total correlations. This approach neglects that trends in item reliabilities can be caused either by an increase in true score variance or by a decrease in error…

Assuming errors of measurement are distributed binomially, this article reviews various procedures for constructing an interval for an individual's true number-correct score; presents two general interval estimation procedures for an individual's true scale score (i.e., normal approximation and endpoints conversion methods); compares various…

In a variable-length adaptive test with a stopping rule that relied on the asymptotic standard error of measurement of the examinee's estimated true score, M. S. Stocking (1987) discovered that it was sufficient to know the examinee's true score and the number of items administered to predict with some accuracy whether an examinee's true score was…

The distinction between two models of reliability is clarified. Reliability may be conceived of and estimated from a true score model or from the perspective of sampling precision. Basic models are developed and illustrated for each approach using data from the author's work on measuring organizational climate. (SLD)

A person's obtained score on a test provides an estimate of the individual's "true" score on that test. The obtained score is considered to have two parts, the true component and the error component. Classical test theory assumes that obtained scores for an individual over multiple administrations of the same test will lie symmetrically…