Imprecise Tests and Imprecise Hypotheses

This paper argues that theoretical predictions can only ever be expected to hold inexactly empirically, and constructs a method of inexact tests of exact hypotheses. Using a two‐parameter cost structure of ‘acceptance’ and ‘rejection’ of a simple null hypothesis, recognising a distinction between ‘statistical’ and ‘material’ significance, hypotheses are ‘accepted’ if they are only ‘slightly’ false. This may be contrasted with the exact testing of inexact hypotheses and the circumstances in which the two methods are equivalent are identified. The proposal facilitates informed decisions regarding the size and power of tests of simple hypotheses, and provides a transparent method of testing.