Ecological studies have often been incorrectly formulated so that the statistical error rate controlled is not the rate at which an error in decision is made. For example, water pollution monitoring under the U.S. Clean Water Act is currently formulated as a test-of-equalities problem, with proposals to reformulate it as a bioequivalence problem. Neither is correct; effluent toxicity trials are in fact non-inferiority trials. As another example, comparisons of biodiversity at the mesocosm level, based on indices such as Shannon's or Simpson's, currently treated most frequently as ANOVA problems, again often should be formulated as non-inferiority studies.

Using such non-exploratory studies with well defined errors in decision-making as examples, an outline of how a confidence set approach leads to statistical methods which control the error rate of decision-making will be indicated. These methods include average bioequivalence tests, intersection-union tests, stepdown methods with confidence sets, and multiple comparison with the best as special cases. Also indicated will be, in joint research with James Rogers, how second-order accurate, deterministic inference on Simpson's index can be achieved.