Hypothesis Testing: From p Values to Bayes Factors

Journal of the American Statistical Association

Volumn 95, Issue 452, 2000, Pages 1316-1320

  Marden, John I ^a  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0442277950     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.2000.10474339     Document Type: Article

References (77)

1. Akritas, M. G., and Arnold, S. F. (1994), “Fully Nonparametric Hypotheses for Factorial Designs, I: Multivariate Repeated Measures Designs,” Journal of the American Statistical Association, 89, 336-343.
2. Anderson, T. W. (1984), An Introduction to Multivariate Statistical Analysis (2nd ed.), New York: Wiley.
3. Andersson, S. (1975), “Invariant Normal Models,” The Annals of Statistics, 3, 132-154.
4. Andersson, S. (1982), “Distributions of Maximal Invariants Using Quotient Mea-sures,” The Annals of Statistics, 10, 955-961.
5. Andersson, S. A., and Perlman, M. D. (1993), “Lattice Models for Conditional Independence in a Multivariate Normal Distribution,” Annals of Statistics, 21, 1318-1358.
6. Barlow, R. E., Bartholomew, D. J., Bremner, J. M., and Brunk, H. D. (1972), Statistical Inference Under Order Restrictions, New York: Wiley.
7. Bartlett, M. S. (1937), “Properties of Sufficiency and Statistical Tests,” Proceedings of the Royal Society of London, Ser. A, 160, 268-282.
8. Beran, R., and Millar, P. W. (1987), “Stochastic Estimation and Testing,” The Annals of Statistics, 15, 1131-1154.
9. Berger, J. O., and Pericchi, L. R. (1996), “The Intrinsic Bayes Factor for Model Selection and Prediction,” Journal of the American Statistical Association, 91, 109-122.
10. Berger, J. O., and Sellke, T. (1987), “Testing a Point Null Hypothesis: The Irreconcilability of p Values and Evidence” (with discussion), Journal of the American Statistical Association, 82, 112-122.
11. Birnbaum, A. (1955), “Characterizations of Complete Classes of Tests of Some Multiparametric Hypotheses, With Applications to Likelihood Ratio Tests,” Annals of Mathematical Statistics, 26, 21-36.
12. Bishop, Y. M. M., Fienberg, S. E., and Holland, P. W. (1975), Discrete Multivariate Analysis: Theory and Practice. Cambridge, MA: MIT Press.
13. Box, G. E. P. (1980), “Sampling and Bayes’ Inference in Scientific Modelling and Robustness” (with discussion), Journal of the Royal Statistical Society, Ser. A, 143, 383-430.
14. Brown, L. D., Cohen, A., and Strawderman, W. E. (1976), “A Complete Class Theorem for Strict Monotone Likelihood Ratio With Applications,” The Annals of Statistics, 4, 712-722.
15. Brown, L. D., Cohen, A., and Strawderman, W. E. (1980), “Complete Classes for Sequential Tests of Hypotheses,” The Annals of Statistics, 8, 377-398, Corr. 17, 1414-1416.
16. Brown, L. D., and Marden, J. I. (1989), “Complete Class Results for Hypothesis Testing Problems With Simple Null Hypotheses,” The Annals of Statistics, 17, 209-235.
17. Casella, G., and Berger, R. L. (1987), “Reconciling Bayesian and Fre-quentist Evidence in the One-Sided Testing Problem,” Journal of the American Statistical Association, 82, 106-111.
18. Chakraborty, B., and Chaudhuri, P. (1999), “On Affine Invariant Sign and Rank Tests in One-and Two-Sample Multivariate Problems,” in Multivariate Analysis, Design of Experiments, and Survey Sampling, ed. S. Ghosh, New York, Marcel Dekker, pp. 499-522.
19. Chaudhuri, P., and Sengupta, D. (1993), “Sign Tests in Multidimension: Inference Based on the Geometry of the Point Cloud,” Journal of the American Statistical Association, 88, 1363-1370.
20. Choi, K. M., and Marden, J. I. (1997), “An Approach to Multivariate Rank Tests in Multivariate Analysis of Variance,” Journal of the American Statistical Association, 92, 1581-1590.
21. Cohen, A., and Sackrowitz, H. B. (1987), “Unbiasedness of Tests for Homogeneity,” The Annals of Statistics, 15, 805-816.
22. Cox, D. R. (1961), “Tests of Separate Families of Hypotheses,” Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, 1, 105-123.
23. Davison, A. C., and Hinkley, D. V. (1997), Bootstrap Methods and Their Application, Cambridge, U.K.: Cambridge University Press.
24. Diaconis, P. (1988), Group Representations in Probability and Statistics, Heyward, CA: Institute for Mathematical Statistics.
25. Eaton, M. L. (1970), “A Complete Class Theorem for Multidimensional One-Sided Alternatives,” Annals of Mathematical Statistics, 41, 1884-1888.
26. Edwards, W., Lindeman, H., and Savage, L. J. (1963), “Bayesian Statistical Inference for Psychological Research,” Psychological Review, 70, 193-242.
27. Farrell, R. H. (1968), “Towards a Theory of Generalized Bayes Tests,” Annals of Mathematical Statistics, 39, 1-22.
28. Fisher, R. A. (1925), Statistical Methods for Research Workers: London: Oliver and Boyd.
29. Fisher, R. A. (1935), Design of Experiments, London: Oliver and Boyd.
30. Friedman, J. H., and Rafsky, L. C. (1979), “Multivariate Generalizations of the Wald-Wolfowitz and Smirnov Two-Sample Tests,” The Annals of Statistics, 7, 697-717.
31. Gelman, A., Carlin, J., Stern, H., and Rubin, D. (1995), Bayesian Data Analysis, London: Chapman Hall.
32. Gibbons, J. D., and Chakraborti, S. (1992), Nonparametric Statistical Inference, New York: Marcel Dekker.
33. Good, I. J. (1987), Comments on “Testing a Point Null Hypothesis: The Irreconcilability of p Values and Evidence” by Berger and Sellke and “Reconciling Bayesian and Frequentist Evidence in the One-Sided Testing Problem” by Casella and Berger, Journal of the American Statistical Association, 82, 125-128.
34. Goodman, L. A. (1968), “The Analysis of Cross-Classified Data: Independence, Quasi-Independence, and Interactions in Contingency Tables With or Without Missing Entries,” Journal of the American Statistical Association, 63, 1091-1131.
35. Haberman, S. J. (1974), The Analysis of Frequency Data, Chicago: University of Chicago Press.
36. Hettmansperger, T. P., and McKean, J. W. (1998), Robust Nonparametric Statistical Methods, London: Arnold.
37. Hettmansperger, T. P., Möttönen, J., and Oja, H. (1997), “Affine-Invariant Multivariate One-Sample Signed-Rank Tests,” Journal of the American Statistical Association, 92, 1591-1600.
38. Hettmansperger, T. P., Nyblom, J., and Oja, H. (1994), “Affine Invariant Multivariate One-Sample Sign Tests,” Journal of the Royal Statistical Society, Ser. B, 56, 221-234.
39. Hotelling, H. (1931), “The Generalization of Student’s Ratio,” Annals of Mathematical Statistics, 2, 360-378.
40. Jeffreys, H. (1939), Theory of Probability, Oxford, U.K.: Clarendon Press.
41. Kass, R. E., and Raftery, A. E. (1995), “Bayes Factors,” Journal of the American Statistical Association, 90, 773-795.
42. Kass, R. E., and Wasserman, L. (1996), “The Selection of Prior Distributions by Formal Rules,” Journal of the American Statistical Association, 91, 1343-1370.
43. Kiefer, J., and Schwartz, R. (1965), “Admissible Bayes Character of T2-, R2-, and Other Fully Invariant Tests for Classical Multivariate Normal Problems,” Annals of Mathematical Statistics, 36, 747-770. Corr. 43, 1742.
44. Lauritzen, S. L. (1996), Graphical Models, Oxford, U.K.: Clarendon Press.
45. Lehmann, E. L. (1959), Testing Statistical Hypotheses. New York: Wiley.
46. Lindley, D. V. (1957), “A Statistical Paradox,” Biometrika, 44, 187-192.
47. Liu, R. Y., and Singh, K. (1993), “A Quality Index Based on Data Depth and Multivariate Rank Tests,” Journal of the American Statistical Association, 88, 252-260.
48. Liu, R. Y., and Singh, K. (1997), “Notions of Limiting p Values Based on Data Depth and Bootstrap,” Journal of the American Statistical Association, 92, 266-277.
49. Mahalanobis, P. C. (1930), “On Tests and Measures of Group Divergence,” Journal and Proceedings of the Asiatic Society of Bengal, 26, 541-588.
50. Marden, J. I. (1982), “Minimal Complete Classes of Tests of Hypotheses With Multivariate One-Sided Alternatives,” The Annals of Statistics, 10, 962-970.
51. Marden, J. I. (1999), “Multivariate Rank Tests,” in Multivariate Analysis, Design of Experiments, and Survey Sampling, ed. S. Ghosh, New York: Marcel Dekker, pp. 401-432.
52. Matthes, T. K., and Truax, D. R. (1967), “Test of Composite Hypotheses for the Multivariate Exponential Family,” Annals of Mathematical Statistics, 38, 681-697. Corr. 38, 1928.
53. Mosteller, F., and Wallace, D. L. (1984), Applied Bayesian and Classical Inference: The Case of the Federalist Papers, New York: Springer.
54. Neyman, J., and Pearson, E. (1928), “On the Use and Interpretation of Certain Test Criteria for Purposes of Statistical Inference. Part I,” Biometrika, 20A, 175-240.
55. Neyman, J., and Pearson, E. (1933), “On the Problem of the Most Efficient Tests of Statistical Hypotheses,” Philosophical Transactions of the Royal Society, Ser. A, 231, 289-337.
56. Patel, K. M., and Hoel, D. G. (1973), “A Nonparametric Test for Interaction in Factorial Experiments,” Journal of the American Statistical Association, 68, 615-620.
57. Pearson, K. (1900), “On the Criterion That a Given System of Deviations From the Probable in the Case of a Correlated System of Variables is Such That it can be Reasonably Supposed to Have Risen From Random Sampling,” Philosophical Magazine, 1, 157-175.
58. Perlman, M. D. (1980), “Unbiasedness of Multivariate Tests: Recent Results,” in Multivariate Analysis V, Amsterdam: North-Holland/Elsevier, pp. 413-432.
59. Perlman, M. D., and Olkin, I. (1980), “Unbiasedness of Invariant Tests for MANOVA and Other Multivariate Problems,” The Annals of Statistics, 8, 1326-1341.
60. Pratt, J. W. (1965), “Bayesian Interpretation of Standard Inference Statements,” Journal of the Royal Statistical Society, Ser. B, 27, 169-203.
61. Puri, M. L., and Sen, P. K. (1971), Nonparametric Methods in Multivariate Analysis, New York: Wiley.
62. Puri, M. L., and Sen, P. K. (1985), Nonparametric Methods in General Linear Models, New York: Wiley.
63. Raftery, A. E. (1995), “Bayesian Model Selection in Social Research,” in Sociological Methodology 1995, ed. P. V. Marsden, Oxford, U.K.: Blackwells, pp. 111-196.
64. Randles, R. H. (1989), “A Distribution-Free Multivariate Sign Test Based on Interdirections,” Journal of the American Statistical Association, 84, 1045-1050.
65. Rao, C. R. (1947), “Large-Sample Tests of Statistical Hypotheses Concerning Several Parameters With Applications to Problems of Estimation,” Proceedings of the Cambridge Philosophical Society, 44, 50-57.
66. Rao, C. R. (1973), Linear Statistical Inference and its Applications, New York: Wiley.
67. Robertson, T., Wright, F. T., and Dykstra, R. L. (1988), Order-Restricted Statistical Inference, New York: Wiley.
68. Roy, S. N. (1953), “On a Heuristic Method of Test Construction and Its Use in Multivariate Analysis,” Annals of Mathematical Statistics, 24, 220-238.
69. Serfling, R. (1980), Approximation Theorems of Mathematical Statistics, New York: Wiley.
70. Stein, C. (1956), “The Admissibility of Hotelling’s T2 Test,” Annals of Mathematical Statistics, 27, 616-623.
71. Student (1908), “The Probable Error of a Mean,” Biometrika, 6, 1-25.
72. Sun, J. (1991), “Significance Levels in Exploratory Projection Pursuit,” Biometrika, 78, 759-769.
73. Wald, A. (1943), “Tests of Statistical Hypotheses Concerning Several Parameters When the Number of Observations is Large,” Transactions of the American Mathematical Society, 54, 426-482.
74. Wald, A. (1950), Statistical Decision Functions, New York: Wiley.
75. Wermuth, N., and Cox, D. R. (1992), “Graphical Models for Dependencies and Associations,” Proceedings of the Tenth Symposium on Computational Statistics, 1, 235-249.
76. Whitaker, J. (1990), Graphical Models in Applied Multivariate Statistics, New York: Wiley.
77. Wijsman, R. A. (1967), “Cross-Sections of Orbits and Their Application to Densities of Maximal Invariants,” Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, 1, 389-400.