[R] Significance test, Cronbach's Alpha

Jonathan Baron baron at psych.upenn.edu
Mon Jun 5 13:05:54 CEST 2006

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: http://www.sas.upenn.edu/~baron
Editor: Judgment and Decision Making (http://journal.sjdm.org)

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