(My previous reply got held up for moderator approval because somehow it was too big - too much extra text at the bottom. This is the shortened version) Hi Gordon, Thank you!! Now I can either use > solve(crossprod(design),t(design)) as the contrast matrix to turn the main effects & interaction into the group means, and then do a second contrast matrix to get the pairwise comparisons I want, or I could first do the cell means model, then use > t(solve(crossprod(design),t(design))) as the contrast matrix to get the main effects & interactions. I never quite understood matrix algebra, but at least now I can go back and forth either way that's convenient. I assume this also extends to n-way ANOVAs? > Pop <- gl(2,4,labels=c("BMA","BVO")) > Trt <- gl(2,2,8,labels=c("c","e")) > Time <- gl(2,1,8,labels=c("0","1")) > contrasts(Pop) <- contr.sum(2) > contrasts(Trt) <- contr.sum(2) > contrasts(Time) <- contr.sum(2) > design <- model.matrix(~Pop*Trt*Time) > rownames(design) <- paste(Pop,Trt,Time,sep=".") > solve(crossprod(design),t(design)) BMA.c.0 BMA.c.1 BMA.e.0 BMA.e.1 BVO.c.0 BVO.c.1 BVO.e.0 BVO.e.1 (Intercept) 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 Pop1 0.125 0.125 0.125 0.125 -0.125 -0.125 -0.125 -0.125 Trt1 0.125 0.125 -0.125 -0.125 0.125 0.125 -0.125 -0.125 Time1 0.125 -0.125 0.125 -0.125 0.125 -0.125 0.125 -0.125 Pop1:Trt1 0.125 0.125 -0.125 -0.125 -0.125 -0.125 0.125 0.125 Pop1:Time1 0.125 -0.125 0.125 -0.125 -0.125 0.125 -0.125 0.125 Trt1:Time1 0.125 -0.125 -0.125 0.125 0.125 -0.125 -0.125 0.125 Pop1:Trt1:Time1 0.125 -0.125 -0.125 0.125 -0.125 0.125 0.125 -0.125 Thanks again, Jenny At 02:35 AM 1/13/2011, Gordon K Smyth wrote: >Hi Jenny, > >Here is a way to get the equivalent coefficients to put into your >contrast matrix for a 4x2 >factorial: > > > Pop <- gl(4,2,labels=c("BMA","BVO","BWF","CAR")) > > Trt <- gl(2,1,8,labels=c("c","e")) > > contrasts(Pop) <- contr.sum(4) > > contrasts(Trt) <- contr.sum(2) > > design <- model.matrix(~Pop*Trt) > > rownames(design) <- paste(Pop,Trt,sep=".") > > solve(crossprod(design),t(design)) > BMA.c BMA.e BVO.c BVO.e BWF.c BWF.e CAR.c CAR.e >(Intercept) 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 >Pop1 0.375 0.375 >-0.125 -0.125 -0.125 -0.125 -0.125 -0.125 Pop2 -0.125 >-0.125 0.375 0.375 -0.125 -0.125 >-0.125 -0.125 Pop3 -0.125 -0.125 -0.125 -0.125 0.375 0.375 >-0.125 -0.125 Trt1 >0.125 -0.125 0.125 -0.125 0.125 -0.125 0.125 -0.125 >Pop1:Trt1 0.375 -0.375 -0.125 0.125 >-0.125 0.125 -0.125 0.125 Pop2:Trt1 -0.125 0.125 0.375 -0.375 >-0.125 0.125 -0.125 0.125 >Pop3:Trt1 -0.125 0.125 -0.125 0.125 0.375 -0.375 -0.125 0.125 > >Best wishes >Gordon > >PS. Sending again, because the email didn't seem to get to BioC the >first time.