14Sample size
In this chapter we discuss one of the most common decisions in statistical practice: the choice of the sample size for a study. We initially focus on the case in which the decision maker selects a fixed sample size n, collects a sample x1, ..., xn, and makes a terminal decision based on the observed sample. Decision-theoretic approaches to sample size determination formally model the view that the value of an experiment depends on the use that is planned for the results, and in particular on the decision that the results must help address. This approach, outlined in greater generality in Chapter 13, provides conceptual and practical guidance for determining an optimal sample size in a very broad variety of experimental situations. Here we begin with an overview of decision-theoretic concepts in sample size. We next move to a general simulation-based algorithm to solve optimal sample size problems in complex practical applications. Finally, we illustrate both theoretical and computational concepts with examples.
The main reading for this chapter is Raiffa and Schlaifer (1961, chapter 5), who are generally credited for providing the first complete formalization of Bayesian decision-theoretic approaches to sample size determination. The general ideas are implicit in earlier decision-theoretic approaches. For example Blackwell and Girshick (1954, page 170) briefly defined the framework for Bayesian optimal fixed sample size determination.
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