When is one experiment ‘always better than’ another?

Summary. Considering the choice between two experiments E and F, an experimenter may choose one or the other depending on the optimality criteria. However, sometimes by using the observations from E, he or she can do at least as well as by using the observations from F for every decision problem, and therefore for every inference problem as well. When that happens, it is said that experiment E is ‘always better than’F or equivalently that E is ‘sufficient for’F. The paper provides a simple explanation of what is meant by this phrase and presents a variety of situations in which one experiment E is known to be always better than an alternative F. In addition, simplifying connections between various results are also revealed. Even though these issues are important to the design of statistical experiments and to the concept of statistical information, the literature reviewed here has largely failed in communicating its results across to many researchers in these areas. One of the objectives is to fill that gap, by stressing the implications of the results, while omitting most of the technicalities that are required in their proofs.