Tests of Independence in Contingency Tables as Unconditional Tests

Abstract

Since the ordinary tests for independence in contingency tables use test criteria whose distributions depend on unknown parameters, the justification for the tests is usually made either by an appeal to asymptotic theory or by interpreting the tests as conditional tests. The latter approach employs the conditional distribution of the cell frequencies given the marginal totals, and was first described by Fisher [1]. The purpose of the present note is to show how these tests may be regarded as unconditional tests even though the parameters are unknown by augmenting the test criterion to include estimates of the unknown parameters. We present no new tests, merely a new setting for the old tests which seems to put them in a little better light.