I posted some R code that could be an h-f sphericity test. Is there anyone out there with SPSS, Systat, or some other package that has a built in test who can verify whether it is accurate or not? John (here is the code again) # This returns the Huynh-Feldt or "Box Correction" for degrees of freedom hf <- function(m){ # m is a matrix with subjects as rows and conditions as columns # note that checking for worst case scenarios F correction first might # be a good idea using J/(J-1) as the df correction factor n<- length(m[,1]) J<-length(m[1,]) X<-cov(m)*(n-1) r<- length(X[,1]) D<-0 for (i in 1: r) D<- D+ X[i,i] D<-D/r SPm<- mean(X) SPm2<- sum(X^2) SSrm<-0 for (i in 1: r) SSrm<- SSrm + mean(X[i,])^2 epsilon<- (J^2*(D-SPm)^2) / ((J-1) * (SPm2 - 2*J*SSrm + J^2*SPm^2)) epsilon }