Hello all, I had an aha experience last night because of trying to count what would be in Venn diagrams. When calculating the expected overlaps of all pairwise combinations of 3 gene lists, I found out the the 3-way overlap is the combinatorial extension of the 2-way overlap formula. #Let Array Size = AS #Let List 1 Size = L1S #Let List 2 Size = L2S #Let List 3 Size = L3S #Expected overlap of list 1 with list 2 = EO12 = (L1S.L2S)/AS #Expected overlap of list 1 with list 3 = EO13 = (L1S.L3S)/AS #Expected overlap of list 2 with list 3 = EO23 = (L2S.L3S)/AS #The expected 3-way overlap is similar to the expected 2-way overlaps; just add another dimension. #Expected 3-way overlap = EO123 = (L1S.L2S.L3S)/AS^2 #An example is the predicted overlaps for List 1 Size = 100, L2S=150, L3S=200 and Array Size = 1000. c.table <- c(3,27, 17,153, 12,108, 68,612) dim(c.table) <- c(2,2,2) dimnames(c.table) <- list(List1=c("in1","not1"), List2=c("in2","not2"), List3=c("in3","not3")) c.table sum(c.table) mantelhaen.test(c.table) #p=1 exactly, as expected. #The shortcut to getting the expected values of your observed contingency table is the independence_table() of package vcd. library(vcd) ec.table <- independence_table(c.table, frequency="absolute") To some this might seem trivial, but to the non-statistician/mathematician/programmer this was an exciting discovery. This can be extended to hyperdimensional contingency tables, but I shall wait for another sleepless night to test it. Regards, -- Dr. Edwin Groot, postdoctoral associate AG Laux Institut fuer Biologie III Schaenzlestr. 1 79104 Freiburg, Deutschland +49 761-2032948