The conditionality principle is a Fisherian principle of statistical inference that Allan Birnbaum formally defined and studied in his 1962

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article. Informally, the conditionality principle can be taken as the claim that experiments which were not actually performed are statistically irrelevant. Together with the

sufficiency principle In statistics, a statistic is ''sufficient'' with respect to a statistical model and its associated unknown parameter if "no other statistic that can be calculated from the same sample (statistics), sample provides any additional information as to ...

, Birnbaum's version of the principle implies the famous

likelihood principle In statistics, the likelihood principle is the proposition that, given a statistical model, all the evidence in a sample relevant to model parameters is contained in the likelihood function. A likelihood function arises from a probability density ...

. Although the relevance of the proof to data analysis remains controversial among statisticians, many

Bayesians Thomas Bayes (/beɪz/; c. 1701 – 1761) was an English statistician, philosopher, and Presbyterian minister. Bayesian () refers either to a range of concepts and approaches that relate to statistical methods based on Bayes' theorem, or a follower ...

and

likelihoodist Likelihoodist statistics or likelihoodism is an approach to statistics that exclusively or primarily uses the likelihood function. Likelihoodist statistics is a more minor school than the main approaches of Bayesian statistics and frequentist statis ...

s consider the likelihood principle foundational for statistical inference.

Formulation

The conditionality principle makes an assertion about an experiment ''E'' that can be described as a mixture of several component experiments ''E''_h where ''h'' is an ancillary statistic (i.e. a statistic whose probability distribution does not depend on unknown parameter values). This means that observing a specific outcome ''x'' of experiment ''E'' is equivalent to observing the value of ''h'' and taking an observation ''x''_h from the component experiment ''E''_h, for example, rolling a

dice Dice (singular die or dice) are small, throwable objects with marked sides that can rest in multiple positions. They are used for generating random values, commonly as part of tabletop games, including dice games, board games, role-playing ...

(whose value is ''h'' = 1 ... 6) to determine which of six experiments to conduct (experiment ''E'' ... ''E''). The conditionality principle can be formally stated thus: :Conditionality Principle: If ''E'' is any experiment having the form of a mixture of component experiments ''E''_h, then for each outcome

(E_h, x_h)

of ''E'', the evidential meaning of any outcome ''x'' of any mixture experiment ''E'' is the same as that of the corresponding outcome ''x''_h of the corresponding component experiment ''E''_h actually conducted, ignoring the overall structure of the mixed experiment (see ). An illustration of the conditionality principle, in a

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context, is given by .

References

* * * ''(With discussion.)''

Formulation

References

Further reading