Three Level Factorial Design Matrix


 
See link for 2k factorial design matrix.
 
See also Montgomery section 6.3 for the 2k design, and Hicks section 10.2 for the 3k design.
 


Explanation of the subscripts:
  • The "L" subscript indicates the "Linear" component of the term or interaction.
  • The "Q" subscript indicates the "Quadratic" component of the term or interaction.


 

 

 AL

 AQ

 BL

BQ

 ALBL

 ALBQ

 AQBL

AQBQ 

a0b0

(1)

 -1

+1 

-1

+1

+1

-1

-1

+1

a1b0

a

 0

 -2

-1

+1

0

0

+2

-2

a2b0

a2

 +1

 +1

-1

+1

-1

+1

-1

+1

a0b1

b

 -1

 +1

0

-2

0

+2

0

-2

a1b1

ab

 0

 -2

0

-2

0

0

0

+4

a2b1

a2b

 +1

 +1

0

-2

0

-2

0

-2

a0b2

b2

 -1

 +1

+1

+1

-1

-1

+1

+1

a1b2

ab2

 0

 -2

+1

+1

0

0

-2

-2

a2b2

a2b2

 +1

 +1

+1

+1

1

+1

+1

+1


 
The rows in bold blue text are those that are also in a 2-level 2-factor study that incorporates centerpoints.

The rows in red text are those that make a 3-level study different from a 2-level study with centerpoints.  They allow the experimenter to quantitatively explore the impact (size and the specific associated term or interaction) of quadratic terms in the model.






 
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