 Then formula_53 can be regarded as an unmeasurable (since formula_21 is unknown) random variable, whose distribution is uniform between 0 and 1 independent of formula_21.If the test is unbiased then the outcome formula_52 implies

from which, similarly to conditioning on formula_43 in the previous case, one obtains

The arguments given above can be viewed as following the spirit of the conditionality principle of statistical inference, although they express a more generalized notion of conditionality which do not require the existence of an ancillary statistic.The conditionality principle however, already in its original more restricted version, formally implies the likelihood principle, a result famously shown by Birnbaum.