The primary purpose of this study is to investigate the mathematical characteristics of the test reliability coefficient rho[subscript XX'] as a function of item response theory (IRT) parameters and present the lower and upper bounds of the coefficient. Another purpose is to examine relative performances of the IRT reliability statistics and two…

Two new reliability coefficients have been derived for situations in which a test must be divided into parts of unequal length. This report summarizes a study of the statistical bias and the standard errors of these coefficients and compares them to Guttman's lambda coefficients and Cronbach's alpha coefficient. (Author/JKS)

Evaluating a test's reliability often requires dividing it into 3 or more unequal parts, which causes violation of the tau equivalence assumption of Cronbach's alpha. This article presents a criterion for abandoning alpha and an approach for computing a more appropriate estimate of reliability, the Gilmer-Feldt coefficient. (Author)

In some situations where reliability must be estimated it is impossible to divide the measuring instrument into more than two separately scoreable parts. In such a case, neither Cronbach's coefficient alpha nor Kristof's three-part approach are satisfactory. A technique is developed for estimating reliability in such situations. (Author/BJG)

Rigorous comparison of the reliability coefficients of several tests or measurement procedures requires a sampling theory for the coefficients. This paper summarizes the important aspects of the sampling theory for Cronbach's (1951) coefficient alpha--a widely used internal consistency coefficient. This theory enables researchers to test a…

Estimating the reliability of measures derived from separate questions on essay tests or individual judges on a rater panel is considered. Cronbach's alpha is shown to underestimate reliability in these cases. Some alternative coefficients are presented. (JKS)

Procedures are developed for testing the hypothesis that Cronbach's alpha reliability coefficient is equal for two tests given to the same subjects. (Author/JKS)

Presented is a detailed description of two true score confidence interval approaches, their use, interpretation, and a philosophical conflict that arises in many applied instances. (Contains 27 references.) (Author)

To meet the requirements of the No Child Left Behind Act, school districts and states must compile summary reports of the levels of student achievement in reading and mathematics. The levels are to be described in broad categories: "basic and below," "proficient," or "advanced." Educational units are given considerable latitude in defining the…

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 recommendation that the reliability of multiple-choice tests will be enhanced if the distribution of item difficulties is concentrated at approximately 0.50 is reinforced and extended in this article by viewing the 0/1 item scoring as a dichotomization of an underlying normally distributed ability score. (SLD)

The Feldt-Gilmer congeneric reliability coefficients make it possible to estimate the reliability of a test composed of parts of unequal, unknown length. The approximate standard errors of the Feldt-Gilmer coefficients are derived via a method using the multivariate Taylor's expansion. Monte Carlo simulation is employed to corroborate the…

This paper considers, from a theoretical point of view, two measurement approaches used in measuring success and failure in skills tests in physical education. The first, "fixed length" (FL) testing, entails counting the number of successful performances in a fixed number of trials. The second, "trials-to-criterion" (TTC)…

The reliabilities of two types of measurement plans were compared across six hypothetical distributions of true scores or abilities. The measurement plans were: (1) fixed-length, where the number of trials for all examinees is set in advance; and (2) trials-to-criterion, where examinees must keep trying until they complete a given number of trials…

This paper presents 11 statistical procedures which test the equality of m coefficient alphas when the sample alpha coefficients are dependent. Several of the procedures are derived in detail, and numerical examples are given for two. (Author/LMO)