[R] Cronbach's alpha

[Dave Atkins]

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
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 > 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