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TABLE 17.9 An Example Sign Table

I A B C AB AC BC ABC y

1 –1 –1 –1 1 1 1 –1 14
1 1 –1 –1 –1 –1 1 1 22
1 –1 1 –1 –1 1 –1 1 10
1 1 1 –1 1 –1 –1 –1 34
1 –1 –1 1 1 –1 –1 1 46
1 1 –1 1 –1 1 –1 –1 58
1 –1 1 1 –1 –1 1 –1 50
1 1 1 1 1 1 1 1 86
320 80 40 160 40 16 24 9 Total
40 10 5 20 5 2 3 1 Total/8

be computed from the effects as follows:

SST = 23(qA2 + qB2 + qC2 + qAB2 + qAC2 + qBC2 + qABC2

= 8(102 + 52 + 202 + 52 + 22 + 32 + 12)

= 800 + 200 + 3200 + 200 + 32 + 72 + 8 = 4512

The portion of variation explained by the seven effects are 800/4512 (18%), 200/4512 (4%), 3200/4512 (71%), 200/4512 (4%), 32/4512 (1%), 72/4512 (2%), and 8/4512 (0%), respectively.

EXERCISE

17.1  Analyze the 23 design shown in Table 17.10
a.  Quantify main effects and all interactions.
b.  Quantify percentages of variation explained.
c.  Sort the variables in the order of decreasing importance.
TABLE 17.10 A 23 Design

A1
A2
C1 C2 C1 C2

B1 100 15 120 10
B2 40 30 20 50


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