R. A. Fisher's Exact Test Revisited

TL;DR

This paper revisits Fisher's exact test, clarifying its conceptual foundations and highlighting implicit assumptions in its calibration process, especially in the context of the Lady Testing Tea experiment.

Contribution

It provides a critical analysis of Fisher's original test, revealing implicit assumptions and questioning the rationale behind its rejection region without explicit alternative hypotheses.

Findings

Identifies implicit assumptions in Fisher's calibration

Clarifies the conceptual basis of Fisher's exact test

Questions the rationale behind the rejection region

Abstract

This note provides a conceptual clarification of Ronald Aylmer Fisher's (1935) pioneering exact test in the context of the Lady Testing Tea experiment. It unveils a critical implicit assumption in Fisher's calibration: the taster minimizes expected misclassification given fixed probabilistic information. Without similar assumptions or an explicit alternative hypothesis, the rationale behind Fisher's specification of the rejection region remains unclear.