[R] sphericity calculation (more formulas?)

[John Christie]

I believe that the following function is a good function for eyeballing 
sphericity.  But, I can't find functions for tests anywhere (g-g or 
h-f).  Anyone who wants to can feel free to use it.

It is bad that R does not provide any tests for sphericity AND cannot 
do a MANOVA on repeated measures (although lme is an alternative add on 
package).  One of these solutions must be provided in the base 
configuration.  My understanding is that the R community is opposed to 
F corrections and I can see the argument.  But, not providing any way 
of looking at sphericity at all in order to see if you need to go 
through the extra steps of adding a separate package and learning a 
somewhat more complicated command set is just wrong.

Also, Loftus & Masson have long been arguing that one use the MSE error 
term from repeated measures in order to generate confidence intervals 
for the means.  But, without a test of sphericity one cannot check to 
see if this is OK to do.  It is not entirely unreasonable to want to 
provide some variance for graphical presentation even if your analyses 
use the "correct" lme.  You can explain in the text.  But, the lme 
cannot provide a variance measure since it just uses likelihood ratios.

Oh, and if this little sphericity function is wrong please correct.

# this returns an array with the variances between each condition.  This
# can be calculated using a covariance matrix and that might technically
# be faster.  But this method is more transparent with respect to 
defining
# sphericity.
jcsphericity <- function(x){
	# x is a matrix that consists of columns containing each condition and
	# rows for each s. e.g. matrix(s$x,ncol=3) where s$x is a long 
formatted
	# dv with 3 cond and with cond moving faster than s if all the values 
returned
	# are roughly equal sphericity is OK (never happens :))
	n<- length(x[1,])
	t<-array()
	l<-array()
	k<-0
	for (i in 1:(n-1)){
		for (j in (i+1):n){
			k<-k+1
			t[k]<- var(x[,i] - x[,j])
			l[k]<- paste(i,j, sep=",")
		 }
	}
	names(t)<-l
	t
}