The fisher, Neyman–Pearson theories of testing hypotheses: One theory or two?

Journal of the American Statistical Association

Volumn 88, Issue 424, 1993, Pages 1242-1249

  Lehmann, E L ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Behrens Fisher problem; Conditioning; P value; Power; Significance level

Indexed keywords

EID: 0013396289     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1993.10476404     Document Type: Article

References (69)

1. Agresti, A. (1992), “A Survey of Exact Inference for Contingency Tables” (with discussion), Statistical Science, 7, 131–177.
2. Barnard, G. A. (1989), “On Alleged Gains in Power from Lower p Values,” Statistics in Medicine, 8, 1469–1477.
3. Barnett, V. (1982), Comparative Statistical Inference (2nd ed.), New York: John Wiley.
4. Bartlett, M. S. (1984), “Discussion of ‘Tests of Significance for2 × 2 Contingency Tables,’ by F. Yates.” Journal of the Royal Statistical Society, Ser. A, 147, 453.
5. Bennett, J. H. (1990), Statistical Inference and Analysis (Selected Correspondence of R. A. Fisher), Oxford, U.K.: Clarendon Press.
6. Braithwaite, R. B. (1953), Scientific Explanation, Cambridge, U.K.: Cambridge University Press.
7. Brown, L. (1967), “The Conditional Level of Student’s t Test,” Annals of Mathematical Statistics, 38, 1068–1071.
8. Carlson, R. (1976), “The Logic of Tests of Significance” (with discussion), Philosophy of Science, 43, 116–128.
9. Carnap, R. (1962), Logical Foundations of Probability (2nd ed.), Chicago: the University of Chicago Press.
10. Cowles, M., and Davis, C. (1982), “On the Origins of the .05 Level of Statistical Significance,” American Psychologist, 37, 553–558.
11. Cox, D. R. (1958), “Some Problems Connected With Statistical Inference,” Annals of Mathematical Statistics, 29, 357–372.
12. Cox, D. R., and Hinkley, D. V. (1974), Theoretical Statistics, London: Chapman and Hall.
13. Fisher, R. A. (1925) (10th ed., 1946), Statistical Methods for Research Workers, Edinburgh: Oliver & Boyd.
14. —— (1932), “Inverse Probability and the Use of Likelihood,” Proceedings of the Cambridge Philosophical Society, 28, 257–261.
15. —— (1935a), “The Logic of Inductive Inference,” Journal of the Royal Statistical Society, 98, 39–54.
16. —— (1935b), “Statistical Tests,” Nature, 136, 474.
17. —— (1935c) (4th ed., 1947), The Design of Experiments, Edinburgh: Oliver & Boyd.
18. —— (1939), “Student,” Annals of Engenics, 9, 1–9.
19. —— (1947), The Design of Experiments (4th ed.), New York: Hafner Press.
20. —— (1955), “Statistical Methods and Scientific Induction,” Journal of the Royal Statistical Society, Ser. B, 17, 69–78.
21. —— (1956), “On a Test of Significance in Pearson’s Biometrika Tables (No. 11), Journal of the Royal Statistical Society, Ser. B, 18, 56–60.
22. —— (1958), “The Nature of Probability,” Centennial Review, 2, 261–274.
23. —— (1959), “Mathematical Probability in the Natural Sciences,” Technometrics, 1, 21–29.
24. —— (1960), “Scientific Thought and the Refinement of Human Reason,” Journal of the Operations Research Society of Japan, 3, 1–10.
25. —— (1973), Statistical Methods and Scientific Inference, (3rd ed.) London: Collins Macmillan.
26. Gigerenzer, G., et al. (1989), The Empire of Chance, New York: Cambridge University Press.
27. Hacking, I. (1965), Logic of Statistical Inference, New York: Cambridge University Press.
28. Hall, P., and Selinger, B. (1986), “Statistical Significance: Balancing Evidence Against Doubt,” Australian Journal of Statistics, 28, 354–370.
29. Hedges, L., and Olkin, I. (1985), Statistical Methods for Meta-Analysis, Orlando, FL: Academic Press.
30. Hockberg, Y., and Tamhane, A. C. (1987), Multiple Comparison Procedures, New York: John Wiley.
31. Kendall, M. G. (1963), “Ronald Aylmer Fisher, 1890–1962,” Biometrika, 50, 1–15.
32. Kyburg, H. E., Jr. (1974), The Logical Foundations of Statistical Inference, Boston: D. Reidel.
33. Linhart, H., and Zucchini, W. (1986), Model Selection, New York: John Wiley.
34. Linssen, H. N. (1991), “A Table for Solving the Behrens-Fisher Problem,” Statistics and Probability Letters, 11, 359–363.
35. Miller, R. G. (1981), Simultaneous Statistical Inference, (2nd ed.), New York: Springer-Verlag.
36. Morrison, D. E., and Henkel, R. E. (1970), The Significance Test Controversy, Chicago: Aldine.
37. Neyman, J. (1935), “Discussion of Fisher (1935a).” Journal of the Royal Statistical Society, 98, 74–75.
38. —— (1938), “L’Estimation Statistique Traitée Comme un Problème Classique de Probabilité,” Actualités Scientifiques et Industrielles, 739, 25–57.
39. —— (1952), Lectures and Conferences on Mathematical Statistics and Probability (2nd ed.), Graduate School, Washington, D.C.: U.S. Dept. of Agriculture.
40. —— (1955), “The Problem of Inductive Inference,” Communications in Pure and Applied Mathematics, 8, 13–46.
41. —— (1956), “Note on an Article by Sir Ronald Fisher,” Journal of the Royal Statistical Society, Ser. B, 18, 288–294.
42. —— (1957), “‘Inductive behavior’ as a Basic Concept of Philosophy of Science,” Review of the International Statistical Institute, 25, 7–22.
43. —— (1961), “Silver Jubilee of My Dispute With Fisher,” Journal of the Operations Research Society of Japan, 3, 145–154.
44. —— (1966), “Behavioristic Points of View on Mathematical Statistics,” in On Political Economy and Econometrics: Essays in Honour of Oscar Lange, Warsaw: Polish Scientific Publishers, pp. 445–462.
45. —— (1976), “Tests of Statistical Hypotheses and Their Use in Studies of Natural Phenomena,” Communications in Statistics, Part A—Theory and Methods, 5, 737–751.
46. —— (1977), “Frequentist Probability and Frequentist Statistics,” Synthèse, 36, 97–131.
47. Neyman, J., and Pearson, E. S. (1928), “On the Use and Interpretation of Certain Test Criteria for Purposes of Statistical Inference,” Biometrika, 20A, 175–240, 263–294.
48. —— (1933a), “On the Problem of the Most Efficient Tests of Statistical Hypotheses,” Philosophical Transactions of the Royal Society of London, Ser. A, 231, 289–337.
49. —— (1933b), “The Testing of Statistical Hypotheses in Relation to Probabilities A Priori,” Proceedings of the Cambridge Philosophical Society, 29, 492–510.
50. Oakes, M. (1986), Statistical Inference: A Comment for the Social and Behavioral Sciences, New York: John Wiley.
51. Pearson, E. S. (1955), “Statistical Concepts in Their Relation to Reality,” Journal of the Royal Statistical Society. Ser. B, 17, 204–207.
52. —— (1962), “Some Thoughts on Statistical Inference,” Annals of Mathematical Statistics, 33, 394–403.
53. —— (1974), “Memories of the Impact of Fisher’s Work in the 1920’s,” International Statistical Review, 42, 5–8.
54. Pearson, E. S., and Hartley, H. O. (1954), Biometrika Tables for Statisticians (Table No. 11), New York: Cambridge University Press.
55. Pedersen, J. G. (1978), “Fiducial Inference,” International Statistical Review, 46, 147–170.
56. Robinson, G. K. (1976), “Properties of Student’s t and of the Behrens–Fisher Solution to the Two-Means Problem,” The Annals of Statistics, 4, 963–971.
57. —— (1982), “Behrens-Fisher Problem,” in Encyclopedia of Statistical Sciences (Vol. 1, eds. S. Kotz and N. L. Johnson), New York: John Wiley, pp. 205–209.
58. Savage, L. J. (1976), “On Rereading R. A. Fisher” (with discussion), Annals of Statistics, 4, 441–500.
59. Schweder, T. (1988), “A Significance Version of the Basic Neyman-Pearson Theory for Scientific Hypothesis Testing,” Scandanavian Journal of Statistics, 15, 225–242.
60. Seidenfeld, T. (1979), Philosophical Problems of Statistical Inference, Boston: D. Reidel.
61. Spielman, S. (1974), “The Logic of Tests of Significance,” Philosophy of Science, 41, 211–226.
62. —— (1978), “Statistical Dogma and the Logic of Significance Testing,” Philosophy of Science, 45, 120–135.
63. Steger, J. A. (ed.) (1971), Readings in Statistics for the Behavioral Scientist, New York: Holt, Rinehart and Winston.
64. Stuart, A., and Ord, J. K. (1991), Kendall’s Advanced Theory of Statistics, Vol. II (5th ed.), New York: Oxford University Press.
65. Tukey, J. W. (1960), “Conclusions vs. Decisions,” Technometrics, 2, 424–432.
66. Upton, G. J. G. (1982), “A Comparison of Alternative Tests for the 2 × 2 Comparative Trial,” Journal of the Royal Statistical Society, Ser. A, 145, 86–105.
67. Wallace, D. L. (1980), “The Behrens-Fisher and Fieller-Creasy Problems,” in R A. Fisher: An Application, eds. S. E. Fienberg and D. V. Hinkley, New York: Springer-Verlag, pp. 119–147.
68. Yates, F. (1984), “Tests of Significance for 2 × 2 Contingency Tables” (with discussion), Journal of the Royal Statistical Society, Ser. A, 147, 426–463.
69. Zabell, S. L. (1992), “R. A. Fisher and the Fiducial Argument,” Statistical Science, 7, 369–387.