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Fundamentals of Experimental Design 461

TABLE 12.22 Example 12.10 with Missing Data

A B C AB AC BC ABC Y
1 1 1 1 1 1 1 60

1 1 1 1 1 1 1 72
1 1 1 1 1 1 1 y1
1 1 1 1 1 1 1 68
1 1 1 1 1 1 1 52

1 1 1 1 1 1 1 83
1 1 1 1 1 1 1 45
1 1 1 1 1 1 1 y2

abc
bc
X

c ac
+

X ab
C +
b
B
–
a
(1) A –
– +
Figure 12.22 Missing data points in Example 12.10.

Since the experimental runs b and abc are missing, we cannot calculate
the elementary effects ab b and abc bc, but we still have data to calcu-
late the elementary effects a 1 and ac c, so we will use the following par-
tial average of a 1 and ac c to estimate A, that is,

c) ⎡
⎤
A 1 ⎡ ( a 1) ( ac ⎤ ⎦ 2 ⎣ ( 72 60) ( 83 52) 2115
.
⎦
1
2 ⎣