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Experimental Design

KEY WORDS blocking, Box-Behnken, composite design, direct comparison, empirical models, emul-
sion breaking, experimental design, factorial design, field studies, interaction, iterative design, mechanistic
models, one-factor-at-a-time experiment, OFAT, oil removal, precision, Plakett-Burman, randomization,
repeats, replication, response surface, screening experiments, standard error, t-test.

“It is widely held by nonstatisticians that if you do good experiments statistics are not
necessary. They are quite right.…The snag, of course, is that doing good experiments is
difficult. Most people need all the help they can get to prevent them making fools of
themselves by claiming that their favorite theory is substantiated by observations that do
nothing of the sort.…” (Coloquhon, 1971).

We can all cite a few definitive experiments in which the results were intuitively clear without statistical
analysis. This can only happen when there is an excellent experimental design, usually one that involves
direct comparisons and replication. Direct comparison means that nuisance factors have been removed.
Replication means that credibility has been increased by showing that the favorable result was not just
luck. (If you do not believe me, I will do it again.) On the other hand, we have seen experiments where
the results were unclear even after laborious statistical analysis was applied to the data. Some of these
are the result of an inefficient experimental design.
Statistical experimental design refers to the work plan for manipulating the settings of the independent
variables that are to be studied. Another kind of experimental design deals with building and operating
the experimental apparatus. The more difficult and expensive the operational manipulations, the more
statistical design offers gains in efficiency.
This chapter is a descriptive introduction to experimental design. There are many kinds of experimental
designs. Some of these are one-factor-at-a-time, paired comparison, two-level factorials, fractional
factorials, Latin squares, Graeco-Latin squares, Box-Behnken, Plackett-Burman, and Taguchi designs.
An efficient design gives a lot of information for a little work. A “botched” design gives very little
information for a lot of work. This chapter has the goal of convincing you that one-factor-at-a-time
designs are poor (so poor they often may be considered botched designs) and that it is possible to get
a lot of information with very few experimental runs. Of special interest are two-level factorial and
fractional factorial experimental designs. Data interpretation follows in Chapters 23 through 48.

What Needs to be Learned?
Start your experimental design with a clear statement of the question to be investigated and what you
know about it. Here are three pairs of questions that lead to different experimental designs:
1.a. If I observe the system without interference, what function best predicts the output y?
b. What happens to y when I change the inputs to the process?
θ
2.a. What is the value of θ in the mechanistic model y = x ?
b. What smooth polynomial will describe the process over the range [x 1 , x 2 ]?

© 2002 By CRC Press LLC