This mini-review illustrates that testing the traditional null hypothesis is not always the appropriate strategy. Half in jest, we discuss Aristotle's scientific investigations into the shape of the earth in the context of evaluating the traditional null hypothesis. We conclude that Aristotle was actually interested in evaluating informative hypotheses. In contemporary science the situation is not much different. That is, many researchers have no particular interest in the traditional null hypothesis. More can be learned from data by evaluating specific expectations, or so-called informative hypotheses, than by testing the traditional null hypothesis. These informative hypotheses will be introduced while providing an overview of the literature on evaluating informative hypothesis.
Keywords: Bayesian analysis; inequality constraints; informative hypothesis; null hypothesis testing.