Design of Experiments and Statistical Process Control - Fundamentals of Industrial Chemistry: Pharmaceuticals, Polymers, and Business - page 230

The previous two examples are plausible and should serve to convince you
of the value of comparing averages versus single data points. The number of
individual runs that should be averaged depends upon the reproducibility of
experiments. The greater the precision, the fewer runs need to be averaged. It
also depends upon the magnitude of change that is of interest. The smaller the
magnitude of change that is of interest, the greater the number of experiments
that should be averaged. Commonly 4 to 16 experiments are averaged.
Let us consider a situation where we were not interested in minor effects
and had fairly good experimental precision. We might be able to compare the
effect of a variable by comparing the average of four experimental results for
each setting. So to look at agitation we might run four experiments with high
agitation and four with low and compare the averages.
If we wanted to look at another variable, for example, the effect of temper-
ature, we would need another eight experiments. To look at both variables, we
have now run 16 experiments. Often an experiment can be long and tedious.
To run 16 experiments might require more than a month of laboratory time.
If we combine the experiments and vary both the agitation and temperature,
we can “double dip”, essentially learning about two variables in eight exper-
iments. This is called a two-factor design. The experimental design would
look like this (Figure 13.7):
It is important that the experiments be run in a random order. The eight
experiments can be used to see the effect of either variable. We have saved our-
selves eight experiments by having these experiments perform double duty. If
agitation and temperature interact with each other we would not see the effect
if we studied each variable independently, but we would see the effect with

Experiment number Agitation Temperature

1 High High

2 High High

3 High Low

4 High Low

5 Low High

6 Low High

7 Low Low

8 Low Low

Figure 13.7 Two Factor Experimental Design