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 <[EMAIL PROTECTED]> 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: [EMAIL PROTECTED] >>> [mailto:[EMAIL PROTECTED] 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: [EMAIL PROTECTED] >>> 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: [EMAIL PROTECTED] >>> 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.
