Premium
Testing hypotheses involving Cronbach's alpha using marginal models
Author(s) -
Kuijpers Renske E.,
Ark L. Andries,
Croon Marcel A.
Publication year - 2013
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/bmsp.12010
Subject(s) - cronbach's alpha , type i and type ii errors , alpha (finance) , statistical hypothesis testing , marginal model , statistics , mathematics , statistical power , econometrics , type (biology) , computer science , psychometrics , regression analysis , ecology , biology
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.