Date:         Thu, 17 Apr 1997 22:06:22 GMT
Reply-To:     David Nichols <nichols@SPSS.COM>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@UGA.CC.UGA.EDU>
From:         David Nichols <nichols@SPSS.COM>
Organization: SPSS, Inc.
Subject:      Re: Cronbach's alpha

In article <5ih0kn$48i@usenet.srv.cis.pitt.edu>,
Richard F Ulrich <wpilib+@pitt.edu> wrote:
>If you score one variable the wrong way, each of its correlations
>are negative.  But what is harder for a program to notice is what
>happens when you score half your correlations in the wrong direction.
>Then, assuming all the correlations were about equal, your "average
>correlation", off the diagonal of your correlation matrix, actually
>becomes negative -  if you have two sets of your variables, nxn,
>where each set is consistent but scored opposite, then there will be
>n*n NEGATIVE correlations, and  (n*(n-1))  positive correlations:
>more negative than positive.  It works out with more negatives, also,
>if the two sets differ in size only by one variable.
>
>I think that I do agree that some warnings should be offered - what
>Dick Campbell suggests is really quite simple, and would give some
>protection.  It is hard to recommend any step that goes beyond
>warnings, since there IS some justification, at times, to stick in
>a variable that has negative correlations (conceptually, some "correction
>factor").
>
>
>Rich Ulrich, biostatistician                wpilib+@pitt.edu
>http://www.pitt.edu/~wpilib/index.html   Univ. of Pittsburgh
>
>===============> concerning note:
>Dick Campbell (DCAMP@UIC.EDU) wrote:
>:          .... Thus a negative alpha says not that the software is
>: incorrect but rather that you have a serious problem, probably resulting
>: from a directional coding error in one or more of the items. I apologize for
>: the lack of clarity. Since users frequently calculate alpha without asking
for
>: the item correlation matrix, it might be useful to put in a flag warning the
>: user if there are negative covariances present.
 
Implementing such a suggestion is actually not such a simple issue. RELIABILITY
has two modes of computation. The default mode doesn't calculate correlations
or covariances; these aren't necessary for alpha or for some other output. The
second method computes a covariance matrix and in this case it would indeed be
trivial to include a message when negative covariances are found.
 
Method 2 (covariance matrix) is the more general method, offering all output
options and reading of matrix files. Method 1 is faster and requires fewer
computational resources. It also allows items with no variance to remain in
the scale. These are removed when using Method 2, since an inverse of the
covariance matrix is computed. Computational resources aren't such a big deal
these days, at least for what RELIABILITY does, but the other issue is not
something I want to ignore.
 
Before I suggest to our developers that they add a message like this (and
if I do this I'll do it with some trepidation, since it will undoubtedly
increase the number of calls I get asking what that means and why people
should care), I'd like to make sure that I'm not missing something when I
assume that we could get by reasonably well using only the second method.
I don't think speed or memory would be a big issue these days, but I'd like
to see if anyone out there thinks it's important to be able to keep items
with 0 variance in the scale, and if so why, before I conclude anything.
 
--
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David Nichols             Senior Support Statistician              SPSS, Inc.
Phone: (312) 329-3684     Internet:  nichols@spss.com     Fax: (312) 329-3668
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