Statistical Design of Experiments
Statistical Design of Experiments
Statistical Design of Experiments
Statistical Design of Experiments
Two
Two
-Way ANOVA Example
-Way ANOVA Example
Use This ANOVA Table
Use This ANOVA Table
Use This ANOVA Table:
Use This ANOVA Table:
Source
d.f.
SS
MS ~ Variance
Error
TOTAL
F
F
Interactions (AB)
Materials (B)
Laboratories (A)
1
1
2
2
12
12
2
2
17
17
7.9294
7.9294
0.6000
0.6000
0.1344
0.1344
2.1811
2.1811
5.0139
5.0139
0.500
0.500
0.0672
0.0672
1.0906
1.0906
5.0139
5.0139
Test This Hypothesis:
Test This Hypothesis:
Null Hypothesis:
Null Hypothesis:
NO Interaction
NO Interaction
FFF
F
CalcCalc
Calc
===
=
= 1.34100.28
= 1.34
MSEMSE
MSEMSE
MS(AB)
MS(AB)
.0500.0500
.0500
0.06725.01391.0906
0.0672
===
=
F
F
Table
Table
= F
= F
0.05, 2, 12
0.05, 2, 12
=
=
3.89
3.89
1.34
1.34
Null Hypothesis:
Null Hypothesis:
NO Difference Among Laboratories
NO Difference Among Laboratories
FF
Calc
CalcCalc
==
= 100.28
= 100.28
MSE
MSEMSE
MS(A)MS(B)
MS(A)
.0500
.0500.0500
5.0139
==
F
F
Table
Table
= F
= F
0.05, 1, 12
0.05, 1, 12
=
=
4.75
4.75
100.28
100.28
Null Hypothesis:
Null Hypothesis:
NO Difference Among Materials
NO Difference Among Materials
= 21.81
= 21.81
MS(B)
1.0906
F
F
Table
Table
= F
= F
0.05, 2, 12
0.05, 2, 12
=
=
3.89
3.89
21.81
21.81
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