Experimental Design Answer

All data analysis performed on SPSS, a joint venture partner with Luftig & Warren International.

This is what you would get if you analyzed the production data properly using a full factorial regression model. It says that there is a statistically significant interaction between the two factors which accounts for an important amount of the variability seen in the data. This will give you the right answer, although there is not as much discrimination as in a designed experiment. A designed experiment  attempts to determine causality, unlike an after the fact analysis like the correlation shown which can only find correlations. 

Tests of Between-Subjects Effects

Dependent Variable: O1

Source Type III Sum of Squares df Mean Square F Sig. Eta Squared
Corrected Model 34.327a 3 11.442 4.351 .010 .266
Intercept 26.044 1 26.044 9.904 .003 .216
A1 23.604 1 23.604 8.976 .005 .200
B1 29.642 1 29.642 11.272 .002 .238
A1 * B1 31.639 1 31.639 12.031 .001 .250
Error 94.670 36 2.630      
Total 9072.767 40        
Corrected Total 128.997 39        

a R Squared = .266 (Adjusted R Squared = .205)

 

Experimental Design

Let’s say you have a suspicion about Setting A and Setting B, so you design an experiment (a full factorial). In this case, you plan to have a low (represented by “1”, a setting of “10” in the process) and high (“2”, a setting of “20” in the process) setting for both variables and run replicates of each possible setting in a random order. Here is what the data might look like:

Setting A Setting B Output

2

2

2

1

1

1

2

1

1

1

2

1

2

2

1

1

1

1

2

2

2

2

2

2

2

1

1

1

1

1

2

1

1

2

1

2

1

2

2

2

1

1

2

1

2

1

2

2

2

2

1

2

1

2

2

1

2

2

1

2

2

1

1

2

2

2

1

1

1

1

1

1

2

1

1

2

1

2

2

1

16.06

15.78

13.41

15.9

20.66

16.64

11.41

18.21

18.32

19.65

15.27

17.25

16.54

15.41

16.48

17.65

18.59

15.69

14.07

16.41

12.37

16.97

13.68

10.27

13.59

14.98

17.64

11.27

12.98

16.34

17.15

17.69

16.13

14.46

14.56

12.36

13.77

12.12

13.35

19.29

What is the answer now?