Testing hypotheses involving Cronbach's alpha using marginal models

R.E. Kuijpers, L.A. van der Ark, M.A. Croon

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We discuss the statistical testing of three relevant hypotheses involving Cronbach's alpha: one where alpha equals a particular criterion; a second testing the equality of two alpha coefficients for independent samples; and a third testing the equality of two alpha coefficients for dependent samples. For each of these hypotheses, various statistical tests have been proposed. Over the years, these tests have depended on progressively fewer assumptions. We propose a new approach to testing the three hypotheses that relies on even fewer assumptions, is especially suited for discrete item scores, and can be applied easily to tests containing large numbers of items. The new approach uses marginal modelling. We compared the Type I error rate and the power of the marginal modelling approach to several of the available tests in a simulation study using realistic conditions. We found that the marginal modelling approach had the most accurate Type I error rates, whereas the power was similar across the statistical tests.
Original languageEnglish
Pages (from-to)503-520
JournalBritish Journal of Mathematical and Statistical Psychology
Volume66
Issue number3
DOIs
Publication statusPublished - 2013

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Marginal Model
Testing Hypotheses
Testing
Type I Error Rate
Statistical test
Equality
Modeling
Hypothesis Test
Coefficient
Simulation Study
Hypothesis Testing
Dependent
Statistical Tests

Cite this

Kuijpers, R.E. ; van der Ark, L.A. ; Croon, M.A. / Testing hypotheses involving Cronbach's alpha using marginal models. In: British Journal of Mathematical and Statistical Psychology. 2013 ; Vol. 66, No. 3. pp. 503-520.
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Testing hypotheses involving Cronbach's alpha using marginal models. / Kuijpers, R.E.; van der Ark, L.A.; Croon, M.A.

In: British Journal of Mathematical and Statistical Psychology, Vol. 66, No. 3, 2013, p. 503-520.

Research output: Contribution to journalArticleScientificpeer-review

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