Statistical Priesthood II: Sir Ronald on Scientific Inference*

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Summary: Partly as a critical review of Sir Ronald Fisher's latest book, partly as an essay, Fisher's theory of likelihood and fiducial inference is carefully considered. As to the latter, it is found that in the form presented it contains errors, but that an interpretation is possible which seems to be in agreement with Fisher's views and which admits of a mathematically correct treatment. This necessitates a clear distinction, also formally, between random variables and numbers. The definition given here of random variables possessing Fisher's fiducial distributions might perhaps provide a common platform on which adherents and opponents of Fisher's view could meet and maybe understand each other. Part of the method and its results can also be justified, and in this light fiducial inference appears as an elimination method for unknown parameters. As such it has indubitable merits, but a rather limited domain of applicability. In these cases the same results can also be obtained by other methods, in particular the theory of confidence domains. In other applications, however, not covered by the Neyman ‐ Pearson theory, in particular in the Behrens‐Fisher test, the confusion between random and constant quantities has caused irreparable errors. Notwithstanding a strenuous and prolonged effort to interpret Fisher's often obscure statements in agreement with his philosophical ideas, no justification for these applications could be found. Since the criticism by previous authors remains valid, or comes back in other places, there can no longer be any doubt that these applications are erroneous1).

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