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Abstract

Standard approaches to hypothesis testing presuppose a partition of mutually exclusive and jointly exhaustive hypotheses. It is implicit in these approaches that one can assess an hypothesis only relative to a specified set of alternatives. R. A. Fisher was perhaps the one notable exception to this rule among influential statisticians. He regarded the likelihood function as the appropriate vehicle for comparing hypotheses, but developed significance tests as the appropriate measure of evidence when no alternatives are in question.¹ Significance tests, though variously interpreted, have played a major role in research. That is unsurprising, for in the preliminary stages of an investigation — the exploratory phase — no theories of the phenomena are at hand. The researcher wishes merely to get a feel for whether a hunch or proto-theory represents a promising line of attack on a problem. Unfortunately, Fisher’s conception is shot full of difficulties,² so much so, that many have doubted whether significance tests are more helpful than misleading.³