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: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Weiwei Shi Sent: Wednesday, January 24, 2007 3:45 PM To: Doran, Harold Cc: [email protected]; 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 <[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: [email protected] > > 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 > > > > ______________________________________________ > > [email protected] 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. > > > > ______________________________________________ > [email protected] 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 ______________________________________________ [email protected] 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. ______________________________________________ [email protected] 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.
