Statistics for Environmental Engineers

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The defining relation of the design allows us to determine all the confounding relationships in the fractional design. In this 24 1 design, the defining relation is I = 1234. I indicates a vector of +1’s.


Design Matrix for a 24 1 Fractional Factorial Design


TABLE 28.3


Factor (Independent Variable)


Run


1


2


3


4


1


2


+




+


3



+



+


4


+


+




5




+


+


6


+



+



7



+


+



8


+


+


+


+

TABLE 28.4


Model Matrix for the 24 1 Fractional Factorial Design


1


2


3


4 = 123


12 = 34


13 = 24


23 = 14


Run


Avg.


S


D


L


F (SDL)


SD (LF)


SL (DF)


DL (SF)


1


+






+


+


+


2


+


+




+




+


3


+



+



+



+


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