Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

On the Foundations of Statistical Inference

Allan Birnbaum
Journal of the American Statistical Association
Vol. 57, No. 298 (Jun., 1962), pp. 269-306
DOI: 10.2307/2281640
Stable URL: http://www.jstor.org/stable/2281640
Page Count: 38
  • Download ($14.00)
  • Cite this Item
On the Foundations of Statistical Inference
Preview not available

Abstract

The concept of conditional experimental frames of reference has a significance for the general theory of statistical inference which has been emphasized by R. A. Fisher, D. R. Cox, J. W. Tukey, and others. This concept is formulated as a principle of conditionality, from which some general consequences are deduced mathematically. These include the likelihood principle, which has not hitherto been very widely accepted, in contrast with the conditionality concept which many statisticians are inclined to accept for purposes of "informative inference." The likelihood principle states that the "evidential meaning" of experimental results is characterized fully by the likelihood function, without other reference to the structure of an experiment, in contrast with standard methods in which significance and confidence levels are based on the complete experimental model. The principal writers supporting the likelihood principle have been Fisher and G. A. Barnard, in addition to Bayesian writers for whom it represents the "directly empirical" part of their standpoint. The likelihood principle suggests certain systematic reinterpretations and revisions of standard methods, including "intrinsic significance and confidence levels" and "intrinsic standard errors," which are developed and illustrated. The close relations between non-Bayesian likelihood methods and Bayesian methods are discussed.

Page Thumbnails

  • Thumbnail: Page 
269
    269
  • Thumbnail: Page 
270
    270
  • Thumbnail: Page 
271
    271
  • Thumbnail: Page 
272
    272
  • Thumbnail: Page 
273
    273
  • Thumbnail: Page 
274
    274
  • Thumbnail: Page 
275
    275
  • Thumbnail: Page 
276
    276
  • Thumbnail: Page 
277
    277
  • Thumbnail: Page 
278
    278
  • Thumbnail: Page 
279
    279
  • Thumbnail: Page 
280
    280
  • Thumbnail: Page 
281
    281
  • Thumbnail: Page 
282
    282
  • Thumbnail: Page 
283
    283
  • Thumbnail: Page 
284
    284
  • Thumbnail: Page 
285
    285
  • Thumbnail: Page 
286
    286
  • Thumbnail: Page 
287
    287
  • Thumbnail: Page 
288
    288
  • Thumbnail: Page 
289
    289
  • Thumbnail: Page 
290
    290
  • Thumbnail: Page 
291
    291
  • Thumbnail: Page 
292
    292
  • Thumbnail: Page 
293
    293
  • Thumbnail: Page 
294
    294
  • Thumbnail: Page 
295
    295
  • Thumbnail: Page 
296
    296
  • Thumbnail: Page 
297
    297
  • Thumbnail: Page 
298
    298
  • Thumbnail: Page 
299
    299
  • Thumbnail: Page 
300
    300
  • Thumbnail: Page 
301
    301
  • Thumbnail: Page 
302
    302
  • Thumbnail: Page 
303
    303
  • Thumbnail: Page 
304
    304
  • Thumbnail: Page 
305
    305
  • Thumbnail: Page 
306
    306