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.