The behaviour of some significance tests under experimental randomization

For 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.