From: Weiwei Shi <helprhelp_at_gmail.com>

Date: Wed 24 Jan 2007 - 21:44:37 GMT

Date: Wed 24 Jan 2007 - 21:44:37 GMT

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.Received on Thu Jan 25 16:18:14 2007

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