x <- c(30.6, 31.5, 32.4, 31.5, 32.8, 32.1, 32.4, 31.8, 32.4, 32.4, 32.1, 35.3, 31.5, 32.7, 33.4, 32.9, 32.6, 31.9, 33.3, 33.0, 32.0, 33.1, 32.9, 35.0, 30.7, 31.7, 32.2, 31.8, 32.0, 33.1, 32.2, 32.3) bl <- rep(1:4, each=8) ttttt <- expand.grid(A=0:1, B=0:1, C=0:1, D=0:1, E=0:1) id <- c(1,7,11,13,20,22,26,32, 2,8,12,14,19,21,25,31, 3,5,9,15,18,24,28,30, 17,23,27,29,4,6,10,16) df5 <- data.frame(ttttt[id,], x, bl) summary(aov(x~A*B+A*C+A*D+ B*C+B*D+B*E+C*D+C*E+D*E + bl, df5))