[R] Bartlett's Test of Sphericity

[Daniel Malter]

I do not understand why that would be the case as the only input involving
the relationship of the data is the determinant of the correlation matrix.
For what you suggest to be true, the non-normality of the data  would have
to introduce correlation.

If what you are saying is true, we would expect the p.value in uncorrelated
samples to be significant more or less often than 5 percent of the times
(dependent on what exactly you mean by sensitivity) when we use a random
sample of highly skewed gamma and Poisson distributions as data. At least
for two data columns the example below does not suggest that this is the
case.

Daniel


set.seed(4785)

cor.data<-NULL
chi.square<-NULL
p.value<-NULL

for(i in 1:1000){
y<-rgamma(100,1,2)
x<-rpois(100,2)

data=data.frame(x,y)

cor.data[i]=cor(data,use='pairwise.complete.obs')[1,2]
chi.square[i]=-( (dim(data)[1]-1) - (2*dim(data)[2]-5)/6 )*
log(det(cor(data,use='pairwise.complete.obs')))
p.value[i] = 1-pchisq(chi.square[i],(dim(data)[2]^2-dim(data)[2])/2)
}

hist(p.value)
quantile(p.value,prob=0.95)


ted.harding-3 wrote:
> 
> To add to Jeremy's comment below: The Bartlett test is very
> sensitive to non-normality in the data, so can readily give
> "significant" results even for non-correlated data.
> 
> Ted.
> 
> On 18-Jun-11 06:47:52, Jeremy Miles wrote:
>> cortest.bartlett() in the psych package.
>> 
>> I've never seen a non-significant Bartlett's test.
>> 
>> Jeremy
>> 
>> 
>> 
>> On 17 June 2011 12:43, thibault grava <thibault.grava at gmail.com>
>> wrote:
>>> Hello Dear R user,
>>>
>>> I want to conduct a Principal components analysis and I need to
>>> run two tests to check whether I can do it or not. I found how
>>> to run the KMO test, however i cannot find an R fonction for the
>>> Bartlett's test of sphericity. Does somebody know if it exists?
>>>
>>> Thanks for your help!
>>>
>>> Thibault
> 
> --------------------------------------------------------------------
> E-Mail: (Ted Harding) <ted.harding at wlandres.net>
> Fax-to-email: +44 (0)870 094 0861
> Date: 18-Jun-11                                       Time: 09:48:13
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