[R] Cronbach's alpha

Lucke, Joseph F Joseph.F.Lucke at uth.tmc.edu
Wed Jan 24 23:25:50 CET 2007 

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

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 at 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 at stat.math.ethz.ch 
> > [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Dave Atkins
> > Sent: Wednesday, January 24, 2007 4:08 PM
> > To: R-help at 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 at 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 at fuller.edu
> > Phone: 626.584.5554
> >
> > ______________________________________________
> > 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.
> >
>
> ______________________________________________
> 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.
>


--
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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