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Suppose that an experimenter has collected a sample as well as baseline information about the units in the sample. How should she allocate treatments to the units in this sample? We argue that the answer does not involve randomization if we think of experimental design as a statistical decision problem. If, for instance, the experimenter is interested in estimating the average treatment effect and evaluates an estimate in terms of the squared error, then she should minimize the expected mean squared error (MSE) through choice of a treatment assignment. We provide explicit expressions for the expected MSE that lead to easily implementable procedures for experimental design.

Why Experimenters Might Not Always Want to Randomize, and What They Could Do Instead