Standard Errors for Reliability Coefficients
L. Andries van der Ark
TL;DR
This paper introduces analytic standard errors for reliability coefficients used in psychometrics, addressing a gap in measurement precision assessment.
Contribution
The paper provides nonparametric standard errors for reliability coefficients under a multinomial sampling scheme.
Findings
Standard errors are derived for coefficients like Cronbach’s alpha and item-total correlations.
R functions for computing these standard errors are available on the Open Science Framework.
Simulation studies show satisfactory performance for larger sample sizes and typical parameter values.
Abstract
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.…
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Taxonomy
TopicsReliability and Maintenance Optimization · Software Reliability and Analysis Research · Risk and Safety Analysis