From: Rense Nieuwenhuis <r.nieuwenhuis_at_student.ru.nl>

Date: Mon 29 Jan 2007 - 17:59:50 GMT

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 Tue Jan 30 06:17:33 2007

Date: Mon 29 Jan 2007 - 17:59:50 GMT

Dear all,

on a practical level an alpha < 0 can be found, when a scale is constructed / evaluated consisting only a few items (say 5) and one of the items is coded in the wrong direction (values that should represent a high score wrongfully represent a low score).

Rense

On Jan 24, 2007, at 22:44 , Weiwei Shi wrote:

> Hi, there:

*>
**> 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
**>>>> 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.
**>
*

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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 Tue Jan 30 06:17:33 2007

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