Statistical Dogma and the Logic of Significance Testing

Abstract

In a recent note ([3]) Roger Carlson presented a rather negative appraisal of my treatment of the logic of Fisherian significance testing in [10]. The main issue between us involves Carlson's thesis that, within the limits set by Fisher, standard significance tests are valuable tools of data analysis as they stand, i.e., without modification of the structure of the reasoning they employ. Call this the adequacy thesis. In my paper I argued that (i) the pattern of reasoning employed by tests of significance needs to be justified in spite of its unquestioned acceptance by most researchers, (ii) The best justification offered to date—by R. A. Fisher—is seriously defective. Therefore (iii) the adequacy thesis is not justified. I proposed some alterations of the pattern of reasoning employed by tests of significance and argued that they guarantee that tests are adequate epistemological tools.

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