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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARYFor the past 40 years, there has been confusion on the differences between tests of significance and tests of hypotheses to the point where data interpretation is presented as an accept-reject process. This paper discusses the case of inference for a simple experiment, the paired design. It gives a rationale of the significance tester, and proceeds to a comparison of three tests of significance which can be viewed as competitors in the case of this design. These are the sign test, S, the Wilcoxon test, W, and the Fisher randomization test, R. The conclusion is that there is indeed an ordering of the tests, which is R preferred to W preferred to S. The S test should never be used if the others are possible. An Appendix gives a proof of monotonicity of the R test with respect to a shift alternative. I5

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