On Probability as a Basis for Action

Abstract The aim of the author is improvement of statistical practice. The author distinguishes between enumerative studies and analytic studies. An enumerative study has for its aim an estimate of the number of units of a frame that belong to a specified class. An analytic study has for its aim a basis for action on the cause-system or the process, in order to improve product of the future. A fair price to pay for an inventory is an example of an enumerative study. Tests of varieties of wheat, insecticides, drugs, manufacturing processes, are examples of analytic studies: the choice of variety or treatment will affect the future out-turn of wheat, future patients, future product. Techniques and methods of inference that are applicable to enumerative studies lead to faulty design and faulty inference for analytic problems. It is possible, in an enumerative problem, to reduce errors of sampling to any specified level. In contrast, in an analytic problem, it is impossible to compute the risk of making a wrong decision. The author provides a number of examples, and pleads for greater care in the writing and teaching of statistical theory and inference.