Simulations concerning the distributional assumptions of coefficient alpha are contradictory. To provide a more principled theoretical framework, this article relies on the Fréchet-Hoeffding bounds, in order to showcase that the distribution of the items play a role on the estimation of correlations and covariances. More specifically, these bounds…

The purpose of this study was to investigate a new way of evaluating interrater reliability that can allow one to determine if two raters differ with respect to their rating on a polytomous rating scale or constructed response item. Specifically, differential item functioning (DIF) analyses were used to assess interrater reliability and compared…

We examined the performance of coefficient alpha and its potential competitors (ordinal alpha, omega total, Revelle's omega total [omega RT], omega hierarchical [omega h], greatest lower bound [GLB], and coefficient "H") with continuous and discrete data having different types of non-normality. Results showed the estimation bias was…

This note confronts the common use of a single coefficient alpha as an index informing about reliability of a multicomponent measurement instrument in a heterogeneous population. Two or more alpha coefficients could instead be meaningfully associated with a given instrument in finite mixture settings, and this may be increasingly more likely the…

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 readily applicable procedure is discussed that allows evaluation of the discrepancy between the popular coefficient alpha and the reliability coefficient of a scale with second-order factorial structure that is frequently of relevance in empirical educational and psychological research. The approach is developed within the framework of the…

Cronbach's coefficient alpha is a widely used reliability measure in social, behavioral, and education sciences. It is reported in nearly every study that involves measuring a construct through multiple items. With non-tau-equivalent items, McDonald's omega has been used as a popular alternative to alpha in the literature. Traditional estimation…

In applications of item response theory (IRT), an estimate of the reliability of the ability estimates or sum scores is often reported. However, analytical expressions for the standard errors of the estimators of the reliability coefficients are not available in the literature and therefore the variability associated with the estimated reliability…

This article examines the possible dependency of composite reliability on presentation format of the elements of a multi-item measuring instrument. Using empirical data and a recent method for interval estimation of group differences in reliability, we demonstrate that the reliability of an instrument need not be the same when polarity of the…

The effect of guessing on the point estimate of coefficient alpha has been studied in the literature, but the impact of guessing and its interactions with other test characteristics on the interval estimators for coefficient alpha has not been fully investigated. This study examined the impact of guessing and its interactions with other test…

In the social sciences, latent traits often have a hierarchical structure, and data can be sampled from multiple levels. Both hierarchical latent traits and multilevel data can occur simultaneously. In this study, we developed a general class of item response theory models to accommodate both hierarchical latent traits and multilevel data. The…

Handheld calculators have been used on the job for more than 30 years, yet the degree to which these devices can affect performance on employment tests of mathematical ability has not been thoroughly examined. This study used a within-subjects research design (N = 167) to investigate the effects of calculator use on test score reliability, test…

The Spearman-Brown (S-B) formula for correction of the split-half coefficient of reliability is discussed as a conceptual precursor of modern formulations of internal-consistency reliability. Derived from the principal components of the product moment coefficient, an alternative S-B formulation facilitates an understanding of internal…

The general use of the Spearman-Brown formula for calculating the reliability of parallel tests with different lengths is reviewed. The importance of the assumption that the component tests be parallel is noted and the property that parallel tests must be non-negatively correlated is derived. (Author)

Bounds are obtained for a coefficient proposed by Kaiser as a measure of average correlation and the coefficient is given an interpretation in the context of reliability theory. It is suggested that the root-mean-square intercorrelation may be a more appropriate measure of degree of relationships among a group of variables. (Author)