A generalisation of the tail-based P-value to characterise the conformity of trinomial proportions to prescribed norms

Abstract

The traditional concept of a P-value comparing an observed binomial probability to a prescribed value is extended to the ordered trinomial case in which target proportions have been specified for `excellent', `acceptable' and `unacceptable' quality. The resulting trinomial probabilities are summarised by calculating two aggregate probabilities, relating to outcomes unequivocally better than, and unequivocally worse than, that actually observed, based on these assumed target proportions. Accumulations of exactly calculated tail probabilities on a mid-P basis are recommended.