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Introduction to
Factorial Designs
Centerpoints
© Diane Schaub, University of Florida
Lecture4B.ppt
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View Full Document Centerpoints
When we are not certain of linearity in the
factor effects, we may want to consider the
addition of centerpoints to the design
Our interaction terms do provide some degree
of curvature induced by the
Β
ij
x
i
x
j
terms in the
model
∑ ∑∑
= <
+
+
+
=
k
j j
i
j
i
ij
j
j
x
x
B
x
B
B
y
1
0
ε
Eqn 626
Model Inadequacy
In some cases the response function won’t be
adequately modeled by Eqn 626, so we must
add a pure secondorder term
Β
jj
x
j
2
We then create a secondorder response
surface model
∑ ∑∑ ∑
= < =
+
+
+
+
=
k
j j
i
k
j
j
jj
j
i
ij
j
j
x
B
x
x
B
x
B
B
y
1 1
2
0
ε
Eqn 627
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View Full Document Addition of Centerpoints
If we replicate certain points in a 2k design,
we:
1.
have protection against curvature from second
order effects, i.e., check for nonlinearity
2.
allow an independent estimate of error to be
obtained
3.
provide additional degrees of freedom
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This note was uploaded on 08/27/2011 for the course EIN 4905 taught by Professor Staff during the Spring '08 term at University of Florida.
 Spring '08
 Staff

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