Randomization and blocking in the design of experiments

It is suggested that, whenever possible, an experiment be run in a completely randomized fashion. One reason for randomizing Is to protect against violations in the usual linear model assump¬tions. The protection has always been argued on qualitative grounds. This paper quantitatively demonstrates the protection by hypothesizing models in violation of the usual assumptions, mathe¬matically representing the physical act of randomization, and algebraically deriving expected mean squares, EMS, and F tests. It is shown that randomization offers considerable but not com¬plete protection against model violations.

The same methodology is also applied to blocked experiments, i.e. to experiments performed under a specific type of incomplete randomization commonly referred to as blocking. It is shown that blocking offers little protection against certain model viola¬tions. The common practice of representing blocks as a treatment factor applied to the experimental units approximates the form of the EMS derived under the violated assumptions model.