# [R] Cronbach's alpha

Rense Nieuwenhuis r.nieuwenhuis at student.ru.nl
Mon Jan 29 18:59:50 CET 2007

```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
> 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
>
> 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
>>>> 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
>>> 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
>> 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 at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help