Introduction
Passive data collection leads to a number of problems in statistical
modeling. Observed changes in a response variable may be correlated
with, but not caused by, observed changes in individual factors (process
variables). Simultaneous changes in multiple factors may produce interactions
that are difficult to separate into individual effects. Observations
may be dependent, while a model of the data considers them to be independent.
Designed experiments address these problems. In a designed experiment,
the data-producing process is actively manipulated to improve the
quality of information and to eliminate redundant data. A common goal
of all experimental designs is to collect data as parsimoniously as
possible while providing sufficient information to accurately estimate
model parameters.
For example, a simple model of a response y in
an experiment with two controlled factors x1 and x2 might
look like this:
Here ε includes both experimental error
and the effects of any uncontrolled factors in the experiment. The
terms β1x1 and β2x2 are main effects and
the term β3x1x2 is
a two-way interaction effect.
A designed experiment would systematically manipulate x1 and x2 while
measuring y, with the objective of accurately estimating β0, β1, β2,
and β3.
 | Design of Experiments | | Full Factorial Designs |  |
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