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

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