Blocking in Experimental
Designs
In some experiments, observations are organized in natural
"chunks" or blocks.
You want to make sure that these blocks
do not bias your estimates of main effects or interactions. For example,
consider an experiment to improve the quality of special ceramics, produced
in a kiln. The size of the kiln is limited so that you cannot produce
all runs (observations) of your experiment at once. In that case you need
to break up the experiment into blocks.
However, you do not want to run positive factor settings (for all factors
in your experiment) in one block,
and all negative settings in the other. Otherwise, any incidental differences
between blocks would systematically
affect all estimates of the main effects and interactions of the factors
of interest. Rather, you want to distribute the runs over the blocks
so that any differences between blocks
(i.e., the blocking factor) do not bias your results
for the factor effects of interest. This is accomplished by treating the
blocking factor as another factor
in the design. Blocked designs
often also have the advantage of being statistically more powerful, because
they allow you to estimate and control the variability in the production
process that is due to differences between blocks.
For a detailed discussion of various blocked
designs, and for examples of how to analyze such designs, see the Experimental Design and General
Linear Models methods of analysis.