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, .

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

1. 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”.

Formulation

is some ancillary statistic, i.e. a statistic whose probability distribution does not depend on any unknown parameter

The conditionality principle can be formally stated thus:

1. Birnbaum's Conditionality Principle:

2. actually conducted, ignoring the overall structure of the mixed experiment; see .

Examples

An illustration of the conditionality principle, in a bioinformatics context, is given by .

1. Example scenario:

could be the roll of die is the one actually conducted to obtain the study's data.

that might is unaffected by any aspect of the other five sub-experiments that were not carried out, and only the procedures and experimental design the sub-experiment that was had any bearing on the statistical analysis the outcome, regardless of the fact that the experimental designs for the experiments which might and might just as likely been performed.

must be excluded from the statistical analysis of the actual

Citations

References