Bayesian subset selection approach to ranking normal means

In this, article we consider a Bayesian approach to the problem of ranking the means of normal distributed populations, which is a common problem in the biological sciences. We use a decision-theoretic approach with a straightforward loss function to determine a set of candidate rankings. This loss function allows the researcher to balance the risk of not including the correct ranking with the risk of increasing the number of rankings selected. We apply our new procedure to an example regarding the effect of zinc on the diversity of diatom species.