This article presents some equivalent forms of the common Kuder-Richardson Formula 21 and 20 estimators for nondichotomous data belonging to certain other exponential families, such as Poisson count data, exponential data, or geometric counts of trials until failure. Using the generalized framework of Foster (2020), an equation for the reliability…

KR-21 reliability and its extension (coefficient [alpha]) gives the reliability estimate of test scores under the assumption of tau-equivalent forms. KR-21 reliability gives the reliability estimate for summed scores for dichotomous items when items are randomly sampled from an infinite pool of similar items (randomly parallel forms). The article…

One argument against the G index is that, unlike phi, it is not a correlation coefficient; yet, G conforms to the Kendall and E-coefficient definitions. The G index is also equal to the Pearson product moment correlation coefficient obtained from double scoring. (Author/CP)

A more general method for calculating the Kappa measure of nominal rating agreement among multiple raters is presented. It can be used across a broad range of rating designs, including those in which raters vary with respect to their base rates and how many subjects they rate in common. (Author/BW)

The proposed coefficient is derived by assuming that the average Goodman-Kruskal gamma between items of identical difficulty would be the same for items of different difficulty. An estimate of covariance between items of identical difficulty leads to an estimate of the correlation between two tests with identical distributions of difficulty.…

Use of the same term "split-half" for division of an n-item test into two subtests containing equal (Cronbach), and possibly unequal (Guttman), numbers of items sometimes leads to a misunderstanding about the relation between Guttman's maximum split-half bound and Cronbach's coefficient alpha. This distinction is clarified. (Author/JKS)

A necessary and sufficient condition for a perfectly homogeneous test in the sense of Loevinger is stated and proved. Using this result, a formula for computing the maximum possible KR-20 when the test variance is assumed fixed is presented. A new index of test homogeneity is also presented and discussed. (Author/BW)

Two lower bounds to reliability in classical test theory, Guttman's lamda and Cronbach's alpha, are shown to be terms of an infinite series of lower bounds. All terms of this series are equal to reliability if and only if the test contains items which are tau-equivalent. (Author/JKS)

An alternative derivation was given of Gaylord's formulas showing the relationships among the average item intercorrelation, the average item-test correlation, and test reliability. Certain parallels were also noted in analysis of variance and principal component analysis. (Author)

Reliability maximizing weights are related to theoretically specified true score scaling weights to show a constant relationship that is invariant under separate linear tranformations on each variable in the system. Test theoretic relations should be derived for the most general model available and not for unnecessarily constrained models.…

The purpose of this study was to present an empirical correction of the KR21 (Kuder Richardson test reliability) formula that not only yields a closer approximation to the numerical value of the KR20 without overestimation, but also simplifies computation. This correction was accomplished by introducing several correction factors to the numerator…

An important relationship is given for two generalizations of coefficient alpha: (1) Rajaratnam, Cronbach, and Gleser's generalizability formula for stratified-parallel tests, and (2) Raju's coefficient beta. (Author/CTM)

An approximation formula for the standard error of measurement was recently proposed by Garvin. The properties of this approximation to the standard error of measurement are described in this paper and illustrated with hypothetical data. It is concluded that the approximation is a systematic overestimate of the standard error of measurement…

Eight asymptotically robust tests of population correlation coefficient equality are proposed and are studied along with two parametric tests. Monte Carlo simulation is used to compare the small sample performance of these ten procedures. The sampled distributions consist of the normal distribution, two mixed normal distributions and four…

Some procedures for estimating internal consistency reliability may be superior mathematically to the more commonly used methods such as Coefficient Alpha. One problem is computational difficulty; the other is the possibility of overestimation due to capitalization on chance. (Author/CTM)