Conditionality principle

There have been a number of conditionality principles proposed in statistics, beginning with Fisher (always condition on an ancillary statistic when one exists). The most well-known conditionality principle is the principle of statistical inference that Allan Birnbaum formally defined and studied in an article in the Journal of the American Statistical Association, Birnbaum (1962).

Informally, his conditionality principle can be taken as the claim that

Experiments which were not actually performed are not relevant to any statistical analysis

and the implicit admonition that unrealized experiments should be ignored: Not included as part of any calculation or discussion of results.

Together with the sufficiency principle, Birnbaum's version of the principle implies the famous likelihood principle. However, by 1970 Birnbaum had rejected both his own conditionality principle and the likelihood principle because they were both incompatible with what he called the “confidence concept of statistical evidence”. Note also that the likelihood principle was not adopted by frequentists. Nevertheless, even though the relevance of the principle and its proof to data analysis remains controversial among statisticians, many Bayesians and likelihoodists consider the likelihood principle foundational for statistical inference.