Hi I am trying to use ANOVA for mixture experiment. The data can be seen below Run Blend X1 X2 X3 Response 1 Pure 0.0 0.0 1.0 43.6 2 Pure 0.0 0.0 1.0 42.0 3 Pure 0.0 0.0 1.0 43.0 4 Binary 0.0 0.5 0.5 30.0 5 Binary 0.0 0.5 0.5 29.4 6 Binary 0.0 0.5 0.5 33.6 7 Pure 0.0 1.0 0.0 17.6 8 Pure 0.0 1.0 0.0 30.0 9 Pure 0.0 1.0 0.0 28.0 10 Binary 0.5 0.0 0.5 45.4 11 Binary 0.5 0.0 0.5 42.8 12 Binary 0.5 0.0 0.5 43.2 13 Binary 0.5 0.5 0.0 40.0 14 Binary 0.5 0.5 0.0 39.6 15 Binary 0.5 0.5 0.0 42.2 16 Pure 1.0 0.0 0.0 32.0 17 Pure 1.0 0.0 0.0 34.8 18 Pure 1.0 0.0 0.0 34.0 It was successful to get the prediction equation using mout = lm (Response~-1+x1*x2*x3) to get R=33.6 X1 + 25.2 X2 + 42.9X3 + 44.8X1X2 + 22.3X1X3. But the ANOVA results is incorrect when I use aov.out = aov(Response~-1+x1*x2*x3). The original paper shows the results should be Source DF SS MS F Pr > F X1 1 3386.88 3386.88 362.02 0.0001 X2 1 1905.12 1905.12 203.64 0.0001 X3 1 5512.65 5512.65 589.24 0.0001 X1*X2 1 250.88 250.88 26.82 0.0002 X1*X3 1 61.98 61.98 6.62 0.0244 X2*X3 1 18.40 18.40 1.97 0.1861 Model 5 829.08 165.82 17.72 0.0001 Error 12 112.27 9.36 Total 17 941.35 17 941.35 I appreciate your help and instruction. Best regards Zhiqiang [[alternative HTML version deleted]]
> But the ANOVA results is incorrect when I use > > aov.out = aov(Response~-1+x1*x2*x3).First, this doesn't work at all. Your variables are in upper case and your data environment is not specified, so you must have done something else. I can get an answer using something like anova(lm(Response~-1+X1*X2*X3-I(X1*X2*X3), data=d)) (I dropped the indetyerminable 3-way product explicitly) Second, your answer differs from that listed by 'the original paper' at least partly because you have done something different from what has been done in the paper. You have asked for anova using Type I sums of squares. The paper has apparently calculated something other than a Type I sums of squares ANOVA. Try calculating using Type 3 sums of squares using Anova from the car package. I did that using Anova(lm(Response~-1+X1+X2+X3+I(X1*X2)+I(X1*X3)+I(X2*X3), data=d), type=3) Then read the help page - especially the "Warning" section - for ?Anova very carefully ... S Ellison ******************************************************************* This email and any attachments are confidential. Any use...{{dropped:8}}