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…

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)

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 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…

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)