Tests of Goodness of Fitt

SUMMARY An explicit account is given of a procedure for assessing goodness of fit of some observations with a hypothesis, generally known as a "test of significance"; the description is close in spirit to R. A. Fisher's original conception. The relation of this test procedure with Bayesian procedures and with the Neyman-Pearson theory of tests is discussed. Some very tentative suggestions are made regarding the choice of a test criterion and the use to which the result of the test can be put. The role of conditional sampling distributions is studied. Various examples are discussed. In particular, a brief exploration is made in the apparently virgin territory of testing goodness of fit when the observations have been taken according to a sequential rule.