Experimental design application and interpretation in pharmaceutical technology - Computer-Aided Applications in Pharmaceutical Technology - page 35

infl uence of one factor on the response is different at different levels of
another factor(s). Interactions are calculated from the columns of contrast
coeffi cients (Table 3.2).
Fractional factorial designs are denoted as 2 f-v , where 2 − v (1/2 v ) represents
the fraction of experiments from the full factorial designs that are omitted
( v = 1, 2, 3 . . .). An example of fractional factorial design for 4 factors,
2 4-1 design, is represented in Table 3.3. By fractioning the combinations of
factors levels, some of the information is lost.

Table 3.2 Determination of factor interactions

Contrast coeffi cients

Experiment

AB AC BC ABC

1 1 1 1 −1

2 −1 −1 1 1

3 −1 1 −1 1

4 1 −1 −1 −1

5 1 −1 −1 1

6 −1 1 −1 −1

7 −1 −1 1 −1

8 1 1 1 1

Table 3.3 2 4-1 fractional factorial design

￿

￿ ￿

Factors

Experiment

A B C D

1 −1 −1 −1 −1

2 1 −1 −1 1

3 −1 1 −1 1

4 1 1 −1 −1

5 −1 −1 1 1

6 1 −1 1 −1

7 −1 1 1 −1

8 1 1 1 1