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Design Matrix and Notation


 
Design Matrix for a 23 factorial design.  See Montgomery section 6-3 page 228.

 

 

FACTORS

 

 

 RUN

A

B

C

 1

 -

-

-

 2

 +

-

-

 3

 -

 +

-

 4

 +

 +

-

 5

 -

 -

+

 6

 +

 -

+

 7

 -

 +

+

 8

 +

 +

+



NOTATION
 
There are three basic types of notation.
  • The + and - notation (for high, low).  This is sometimes referred to as geometric notation.
  • The notation based on lowercase labels.
  • The 1 and 0 notation (for high, low).
 

 RUN

 A

B

C

Labels

Labels

A

B

C

 1

-

-

-

a0b0c0

(1)

0

0

0

 2

+

-

-

a1b0c0

a

1

0

0

 3

-

+

-

a0b1c0

b

0

1

0

 4

+

+

-

a1b1c0

ab

1

1

0

 5

-

-

+

a0b0c1

c

0

0

1

 6

+

-

+

a1b0c1

ac

1

0

1

 7

-

+

+

a0b1c1

bc

0

1

1

 8

+

+

+

a1b1c1

abc

1

1

1

 
The treatment combinations, along with the Label notation, are shown in standard order (1) a b ab c ac bc abc.
 
This notation can be very useful when planning a three level (3k) design for separating linear and quadratic terms and interactions.


For an example of the 2k factorial design matrix, see link.

For an example of the 3k factorial design matrix, see link.

 
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