Exact distributions of intraclass correlation and Cronbach's alpha with Gaussian data and general covariance

DOI10.1007/BF02295646zbMath1306.62451OpenAlexW2019620073WikidataQ30844558 ScholiaQ30844558MaRDI QIDQ2260001

Keith E. Muller, Emily O. Kistner

Publication date: 5 March 2015

Published in: Psychometrika (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02295646

zbMATH Keywords

quadratic formsconfidence intervalcompound symmetryinterrater reliability

Mathematics Subject Classification ID

Applications of statistics to psychology (62P15)

Related Items (7)

The Mellin Transform to Manage Quadratic Forms in Normal Random Variables ⋮ Sample size considerations for stepped wedge designs with subclusters ⋮ Asymptotic standard errors of intraclass correlation coefficients for two-way model ⋮ The density of the sample correlations under elliptical symmetry with or without the truncated variance-ratio ⋮ Functional response models for intraclass correlation coefficients ⋮ On the Bayesian estimation for Cronbach's alpha ⋮ On the use, the misuse, and the very limited usefulness of Cronbach's alpha

Uses Software

• SAS/IML
• SAS
• AS 155

Cites Work

• On the distribution of the maximum likelihood estimator of Cronbach's alpha
• Coefficient alpha and the internal structure of tests
• The statistical theory of stepped-up reliability coefficients when a test has been divided into several equivalent parts
• Algorithm AS 155: The Distribution of a Linear Combination of χ 2 Random Variables
• On the trace of a wishart
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