Applied Statistics and Probability for Engineers

14-7 2kFACTORIAL DESIGNS 531

subtracting from this quantity the average of the four treatment combinations on the left-hand

side of the cube where Ais at the low level. This gives

This equation can be rearranged as



aabacabc

4 n



112 bcbc

4 n

AyAyA

A (14-15)

1

4 n

3 aabacabc 112 bcbc 4

 (14-16)

1

4 n

3 babbcabc 112 acac 4

ByByB

In a similar manner, the effect of Bis the difference in averages between the four treatment

combinations in the back face of the cube (Fig. 14-19a), and the four in the front. This yields

The effect of Cis the difference in average response between the four treatment combinations

in the top face of the cube in Figure 14-19(a) and the four in the bottom, that is,

The two-factor interaction effects may be computed easily. A measure of the ABinteraction

is the difference between the average Aeffects at the two levels of B. By convention, one-half

of this difference is called the ABinteraction. Symbolically,

B Ave r a g e AEffect

High ()

Low ()

Difference 3 abcbcabbacca 1124

2 n

51 acc 2  3 a 11246

2 n

31 abcbc 2  1 abb 24

2 n

 (14-17)

1

4 n

3 cacbcabc 112 abab 4

CyCyC

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