Page 471 - Design for Six Sigma a Roadmap for Product Development

430 Chapter Twelve

contrast contrast
Effect (12.7)
2 k 1
n N
n 2

where N is the total number of runs. The definition for any main effect,
for example, main effect of A, is

A y A y A (12.8)
which is the average response for A at high level minus the average of
response for A at low level.
By Eq. (12.7)

133.1
contrast A
A 16.63
2 k 1
n 2 2 1
4
Similarly

60.3
contrast B
B 7.54
2 k 1
n 2
4
69.7
contrast AB
AB 8.71
2 k 1
n 2 2 1
4

Step 3: Compute sum of squares. Sum of squares (SS) is the basis for
the analysis of variance computation; the formula for the sum of
squares is

contrast 2 contrast 2
SS (12.9)
k
2
n N
n
Therefore
2 133.1 2
contrast A
SS A 1107.22
2
2
n 4
4
2 60.3 2
contrast B
SS B 227.25
2
2
n 4
4
2 69.7 2
contrast AB
SS AB 303.6
2
2
n 4
4
To complete ANOVA, we also need SS T and SS E . In two-level factorial
design