Composite hypothesis

A hypothesis with one or more free parameters. As an example, the hypothesis that the decay of a given particle is purely exponential with unknown lifetime, is a composite hypothesis. The testing of a composite hypothesis involves first estimating the unknown parameter(s). In the actual test, it is then necessary to compensate for the fact that the parameter(s) has (have) been fitted using the same data. Since one typically knows how to do this correctly only in the asymptotic limit of a large amount of data, such tests are never as safe as tests of simple (completely defined) hypotheses (see Eadie71).