Canadian Journal of Statistics

On principles and arguments to likelihood

Journal Article


Birnbaum (1962a) argued that the conditionality principle (C) and the sufficiency principle (S) implied the likelihood principle (L); he then argued (Birnbaum 1972) that C and a mathematical equivalence principle M implied L. Evans, Fraser, and Monette (1985a) gave reference details, and this paper gives proof that C alone implies L. The level of support by the profession for L is sharply less than that for S or even for C; thus the paradoxical nature of these results. In this regard, we elaborate on the Monette example (Fraser, Monette, and Ng 1984), which provides a strong case against L. We also examine closely the various proofs linking the principles and find that S and C can each be used operationally to suppress information otherwise deemed relevant. From another viewpoint this says that S and C can each be used in contexts that directly conflict with the original examples and motivations supporting them; the principles can thus be viewed as inappropriately used, or more strongly, as invalid. In either case, the result that C and S imply L or that C implies L can be regarded as noneffective in the context of discriminating applications. A resolution of the apparent anomalies can be obtained by allowing the statistical model to include ingredients additional to those usually present (particularly for subsequent use with conditionality), or alternatively by restricting the application of the principles to contexts where the conflicts would seem not to arise.

Related Topics

Related Publications

Related Content

Site Footer


This website is provided by John Wiley & Sons Limited, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ (Company No: 00641132, VAT No: 376766987)

Published features on are checked for statistical accuracy by a panel from the European Network for Business and Industrial Statistics (ENBIS)   to whom Wiley and express their gratitude. This panel are: Ron Kenett, David Steinberg, Shirley Coleman, Irena Ograjenšek, Fabrizio Ruggeri, Rainer Göb, Philippe Castagliola, Xavier Tort-Martorell, Bart De Ketelaere, Antonio Pievatolo, Martina Vandebroek, Lance Mitchell, Gilbert Saporta, Helmut Waldl and Stelios Psarakis.