SIMPLE COUNTEREXAMPLES AGAINST THE CONDITIONALITY PRINCIPLE

The famous theorem of Birnbaum, stating that the likelihood principle follows from the conditionality principle together with the sufficienc y principle, has caused much discussion among statisticians. Briefly, many writers dislike the consequences of the likelihood principle (amo ng other things, confidence coefficients and levels of tests are dismi ssed as meaningless), but at the same time they feel that both the con ditionality principle and the sufficiency principle are intuitively ob vious. In the present article we give examples to show that the condit ionality principle should not be taken to be of universal validity, an d we discuss some consequences of these examples.