In this paper slippage tests for variates following various specified distributions, viz the normal, the Poisson, the binomial and the negative binomial, as well as a slippage test for the method of m rankings and a distributionfree k-sample slippage test, are discussed. These tests are all of the general type discussed in section 2. The choice of a test criterion for this type is a plausible one, but in some cases the tests can be proved to be optimal in a sense as described by a theorem of W ALD. For discrete variates the tests are derived as special cases of a slippage test for a general class of distribution functions. The class of distribution functions consists of all distribution functions, for which a close approximation to the true significanee levels using a specified method is possible. In the case of a test for Poisson variates it is possible to give the powerfunctions of the test in very good approximation, using the same method. The same techniques were used previously for obtaining slippage tests for gamma variates by W. G. COCHRAN (1941), R. DOORNBOS (1956), and R. DOORNBOS and H. J. PRINS (1956) and for normal variates by E. PAULSON (1952). The slippage test for normal variates given here is a generalization of the one given by PAULSON. H. A. DAVID (1956) applied the same principle, without proof however, in two other cases.
|Journal||Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen: Series A: Mathematical Sciences|
|Publication status||Published - 1958|