Reliability analysis is one of the most conducted analyses in applied psychometrics. It entails the assessment of reliability of both item scores and scale scores using coefficients that estimate the reliability (e.g., Cronbach’s alpha), measurement precision (e.g., estimated standard error of measurement), or the contribution of individual items to the reliability (e.g., corrected item-total correlations). Most statistical software packages used in social and behavioral sciences offer these reliability coefficients, whereas standard errors are generally unavailable, which is a bit ironic for coefficients about measurement precision. This article provides analytic nonparametric standard errors for coefficients used in reliability analysis. As most scores used in behavioral sciences are discrete, standard errors are derived under the relatively unrestrictive multinomial sampling scheme. Tedious derivations are presented in appendices, and R functions for computing standard errors are available from the Open Science Framework. Bias and variance of standard errors, and coverage of the corresponding Wald-based confidence intervals are studied using simulated item scores. Bias and variance, and coverage are generally satisfactory for larger sample sizes, and parameter values are not close to the boundary of the parameter space.

This research note proposes two reliability coefficients for tests with components of unknown functional lengths. The derived coefficients are extensions of the techniques devised by Kristof and Feldt and do not require a reduction of test components into parts. Simulation study indicates that the new coefficients yield reasonably stable reliability estimates when the number of test components is small.

In measurement studies the researcher may wish to test the hypothesis that Cronbach’s alpha reliability coefficient is the same for two measurement procedures. A statistical test exists for independent samples of subjects. In this paper three procedures are developed for the situation in which the coefficients are determined from the same sample. All three procedures are computationally simple and give tight control of Type I error when the sample size is 50 or greater.

The separate questions on an essay test or the individual judges on a rater panel may constitute congeneric parts rather than tau-equivalent parts. Also, it may be necessary to infer the lengths of the congeneric parts from their variances and covariances, rather than from some obvious feature of each part, such as the range of possible scores. Cronbach's alpha coefficient applied to such part-tests data will underestimate total score reliability. Several reliability coefficients are developed for such instruments. They may be regarded as extensions of the coefficient developed by Kristof for a three-part test.