Confounding in Blocks

Thus far, all of the designs we have looked at have been complete in that every treatment has appeared in every block. This is the best situation and gives us the best information for treatment comparisons. However, there are many situations where we cannot put every treatment in every block (often due to time, money, or physical constraints of the experiment). For example, a microarray experiment using a two-dye chip is restricted to two treatments per block (microarray). In these cases the design becomes incomplete in that not every treatment is in every block.

If the design is incomplete, then we immediately are faced with the fact that treatment comparisons are confounded with block effects which, of course, will cause problems. There is the obvious problem that the block difference may affect treatment comparisons, and we also have the problem that block variances could creep into the variance of a treatment comparison. The point of this chapter is to see how to deal with incomplete designs so that we can mitigate these problems.