# Re: [R] Cronbach's alpha

From: Lucke, Joseph F <Joseph.F.Lucke_at_uth.tmc.edu>
Date: Wed 24 Jan 2007 - 22:25:50 GMT

Continuing off topic:

1. The range of alpha -infinity < alpha < 1.
2. Alpha is NOT reliability
3. There are trivial examples of alpha < 1 with reliability approaching 1.
4. There are trivial examples of alpha = 0 with reliability approaching 1.
5. Alpha cannot assess dimensionality.

Lucke, Joseph F. The $\alpha$ and the $\omega$ of congeneric test theory: An extension of reliability and internal consistency to heterogeneous tests. Applied Psychological Measurement, 2005} 29(1),65--81}.

-----Original Message-----
From: r-help-bounces@stat.math.ethz.ch
[mailto:r-help-bounces@stat.math.ethz.ch] On Behalf Of Weiwei Shi Sent: Wednesday, January 24, 2007 3:45 PM To: Doran, Harold
Cc: R-help@stat.math.ethz.ch; Dave Atkins Subject: Re: [R] Cronbach's alpha

I read that article (thanks Chucks, etc to point that out). Now I understand how those negatives are generated since my research subject "should" have negative convariance but they "are" measuring the same thing. So, I am confused about this "same" thing and about if it is proper to go ahead to use this measurement.

To clear my point , I describe my idea here a little bit. My idea is to look for a way to assign a "statistic" or measurement to a set of variables to see if they "act" cohesively or coherently for an event. Instead of using simple correlation, which describes var/var correlation; I wanted to get a "total correlation" so that I can compare between setS of variables. Initially I "made" that word but google helps me find that statistic exists! So I read into it and post my original post on "total correlation". (Ben, you can find total correlation from wiki).

I was suggested to use this alpha since it measures a "one latent construct", in which matches my idea about one event. I have a feeling it is like factor analysis; however, the grouping of variables has been fixed by domain knowledge.

Sorry if it is off-list topic but I feel it is very interesting to go ahead.

Thanks,

Weiwei

On 1/24/07, Doran, Harold <HDoran@air.org> wrote:
> Hi Dave
>
> We had a bit of an off list discussion on this. You're correct, it can

> be negative IF the covariance among individual items is negative AND
> if that covariance term is larger than the sum of the individual item
> variances. Both of these conditions would be needed to make alpha go
> negative.
>
> Psychometrically speaking, this introduces some question as to whether

> the items are measuring the same latent trait. That is, if there is a
> negative covariance among items, but those items are thought to
> measure a common trait, then (I'm scratching my head) I think we have
> a dimensionality issue.
>
>
>
> > -----Original Message-----
> > From: r-help-bounces@stat.math.ethz.ch
> > [mailto:r-help-bounces@stat.math.ethz.ch] On Behalf Of Dave Atkins
> > Sent: Wednesday, January 24, 2007 4:08 PM
> > To: R-help@stat.math.ethz.ch
> > Subject: Re: [R] Cronbach's alpha
> >
> >
> > Harold & Weiwei--
> >
> > Actually, alpha *can* go negative, which means that items are
> > reliably different as opposed to reliably similar. This happens
> > when the sum of the covariances among items is negative. See the
> > ATS site below for a more thorough explanation:
> >
> > http://www.ats.ucla.edu/STAT/SPSS/library/negalpha.htm
> >
> > Hope that helps.
> >
> > cheers, Dave
> > --
> > Dave Atkins, PhD
> > Assistant Professor in Clinical Psychology Fuller Graduate School of

> > Psychology
> > Email: datkins@fuller.edu
> > Phone: 626.584.5554
> >
> >
> > Weiwei
> >
> > Something is wrong. Coefficient alpha is bounded between 0 and 1, so

> > negative values are outside the parameter space for a reliability
> > statistic. Recall that reliability is the ratio of "true score"
> > variance to "total score variance". That is
> >
> > var(t)/ var(t) + var(e)
> >
> > If all variance is true score variance, then var(e)=0 and the
> > reliability is var(t)/var(t)=1. On the other hand, if all variance
> > is measurement error, then var(t) = 0 and reliability is 0.
> >
> > Here is a function I wrote to compute alpha along with an example.
> > Maybe try recomputing your statistic using this function and see if
> > you get the same result.
> >
> > alpha <- function(columns){
> > k <- ncol(columns)
> > colVars <- apply(columns, 2, var)
> > total <- var(apply(columns, 1, sum))
> > a <- (total - sum(colVars)) / total * (k/(k-1))
> > a
> > }
> >
> > data(LSAT, package='ltm')
> > > alpha(LSAT)
> > [1] 0.2949972
> >
> >
> > Harold
> >
> > > -----Original Message-----
> > > From: r-help-bounces at stat.math.ethz.ch >
> > [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Weiwei Shi

> > > Sent: Wednesday, January 24, 2007 1:17 PM > To: R R > Subject:
> > [R] Cronbach's alpha > > Dear Listers:
> > >
> > > I used cronbach{psy} to evaluate the internal consistency and >
> > some set of variables gave me alpha=-1.1003, while other, >
> > alpha=-0.2; alpha=0.89; and so on. I am interested in knowing > how

> > to interpret 1. negative value 2. negative value less than -1.
> > >
> > > I also want to re-mention my previous question about how to >
> > evaluate the consistency of a set of variables and about the >
> > total correlation (my 2 cent to answer the question). Is > there
> > any function in R to do that?
> > >
> > > Thank you very much!
> > >
> > >
> > >
> > > --
> > > Weiwei Shi, Ph.D
> > > Research Scientist
> > > GeneGO, Inc.
> > >
> > > "Did you always know?"
> > > "No, I did not. But I believed..."
> > > ---Matrix III
> > >
> > > ______________________________________________
> > > R-help at stat.math.ethz.ch mailing list >
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > > http://www.R-project.org/posting-guide.html
> > > and provide commented, minimal, self-contained, reproducible
code.
> > >
> > --
> > Dave Atkins, PhD
> > Assistant Professor in Clinical Psychology Fuller Graduate School of

> > Psychology
> > Email: datkins@fuller.edu
> > Phone: 626.584.5554
> >
> > ______________________________________________
> > R-help@stat.math.ethz.ch mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
> >
>
> ______________________________________________
> R-help@stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

--
Weiwei Shi, Ph.D
Research Scientist
GeneGO, Inc.

"Did you always know?"
"No, I did not. But I believed..."
---Matrix III

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