Empirically relevant critical values for hypothesis tests: A bootstrap approach

Tests of statistical hypotheses can be based on either of two critical valu es: the Type I critical value or the size-corrected critical value. The for mer usually depends on unknown population parameters and cannot be evaluate d exactly in applications, but it can often be estimated very accurately by using the bootstrap. The latter does not depend on unknown population para meters but is likely to yield a lest with low power. The critical values us ed in most Monte Carlo studies of the powers of tests are neither Type I no r size-corrected. They are irrelevant to empirical research. (C) 2000 Elsev ier Science S.A. All rights reserved.