The use of Fisher’s exact test in contingency table analysis in palaeopathology

OBJECTIVE: The controversial nature of Fisher's exact test (FET) in contingency table analysis is well-known in most disciplines. Our purpose is to outline the major difficulties with the test that underlie debates over its use as an alternative to chi-square for sparsely populated contingency tables; to assess their implications for the use of FET in palaeopathology; and to suggest possible alternatives. METHODS: Review of FET in the statistical and applied statistical literature, together with consideration of the circumstances under which FET is customarily used in palaeopathology. RESULTS: Palaeopathology data likely violate the fixed marginals assumption of FET. The extent to which this militates against its use is a matter of debate, but we note that analytical approaches more congruent with the nature of palaeopathology research designs have been developed in the 90 years since Fisher proposed his test. CONCLUSIONS: Chi-square is more robust to contingency table sparseness than is commonly realised. When it is countermanded, approaches such as Monte Carlo simulation may be more appropriate than FET. SIGNIFICANCE: FET is widely used in palaeopathology. Alternative approaches, for which we provide R scripts, may be preferable, and may help to provide increased rigour in statistical analysis in palaeopathology. LIMITATIONS: The extent to which violation of the fixed marginals assumption of FET militates against its use has long been debated, and we do not provide a definitive solution to this for palaeopathology, but instead limit ourselves to describing the problem and suggesting alternatives. SUGGESTIONS FOR FURTHER WORK: We hope our paper serves as a stimulus for wider discussion of statistical methods within palaeopathology, a field that currently lacks an extensive applied statistical literature.