Re: [R] Significance test, Cronbach's Alpha

From: Jonathan Baron <>
Date: Mon 05 Jun 2006 - 21:05:54 EST

On 06/05/06 19:19, Jim Lemon wrote:
> Tom Backer Johnsen wrote:
> > Hello:
> >
> > I am reviewing a paper at the moment where the author reports a
> > Cronbach's Alpha and adds a significance test of the value. I was not
> > aware that such a test exists. Does it? If so, how is it done in R?
> >
> Hi Tom,
> This may be due to the fact that some interpret Cronbach's alpha as a
> correlation between items, thus encouraging the unwary to assume that
> the probability of a numerically equivalent correlation can be used as a
> test of significance.

SPSS has a test for alpha. I don't know what it does.

It also seems to me that, if the assumptions of alpha are met, then the assumptions of analysis of variance are also met. In particular, alpha equals the reliability if the measurements (items) are "parallel" (Lord and Novick, "Statistical theories of mental test scores," 1968, pp. 47 and 90 in particular). That means (among other things) that they have equal true variances. If this can be assumed, then you can do an ANOVA using items and subjects, and look for a significant effect of subjects.

If the measures are not parallel, then alpha is a lower bound on the reliability of the test, so an ANOVA might be conservative, but I have not thought this through.

It is rare to see anyone report a test for alpha because it is usually used descriptively. If it isn't .7 or higher, people get upset, yet even .5 would be wildly significant in most cases.


Jonathan Baron, Professor of Psychology, University of Pennsylvania
Home page:
Editor: Judgment and Decision Making (

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