Statistics for Environmental Engineers

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Method: A Full 2k Factorial Design


The к independent variables whose possible influence on a response variable is to be assessed are referred to as factors. An experiment with к factors, each set at two levels, is called a two-level factorial design. A full factorial design involves making runs at 2k different experimental conditions which represent all combinations of the к factors at high and low levels. This is also called a saturated design. The high and low levels are conveniently denoted by + and -, or by +1 and -1. The factors can be continuous (pressure, temperature, concentration, etc.) or discrete (additive present, source of raw material, stirring used, etc.) The response variable (dependent variable) is y.


There are two-level designs that use less than 2к runs to investigate к factors. These fractional factorial designs are discussed in Chapter 28. An experiment in which each factor is set at three levels would be a three-level factorial design (Box and Draper, 1987; Davies, 1960). Only two-level designs will be considered here.


Design Matrices for 23 and 24 Full Factorial Designs


Run


Factor


Run


Factor


Number


1


2


3


Number


1


2


3


4


1


2


+




1


2


+





3



+



3



+




4


+

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