From: Lucke, Joseph F <Joseph.F.Lucke_at_uth.tmc.edu>

Date: Wed 24 Jan 2007 - 22:25:50 GMT

Date: Wed 24 Jan 2007 - 22:25:50 GMT

Continuing off topic:

- The range of alpha -infinity < alpha < 1.
- Alpha is NOT reliability
- There are trivial examples of alpha < 1 with reliability approaching 1.
- There are trivial examples of alpha = 0 with reliability approaching 1.
- 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

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

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
**> > > PLEASE do read the posting guide
**> > > 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
**> > PLEASE do read the posting guide
**> > 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
**> PLEASE do read the posting guide
**> 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 ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide 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 PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.Received on Thu Jan 25 15:21:04 2007

Archive maintained by Robert King, hosted by
the discipline of
statistics at the
University of Newcastle,
Australia.

Archive generated by hypermail 2.1.8, at Thu 25 Jan 2007 - 04:30:35 GMT.

*
Mailing list information is available at https://stat.ethz.ch/mailman/listinfo/r-help.
Please read the posting
guide before posting to the list.
*