Elucidating the foundations of statistical inference with 2 × 2 Tables

PLoS ONE

Volumn 10, Issue 4, 2015, Pages

  Choi, Leena ^a   Blume, Jeffrey D ^a   Dupont, William D ^a  

^a VANDERBILT UNIVERSITY SCHOOL OF MEDICINE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CONTINGENCY TABLE; DATA ANALYSIS; FISHER EXACT TEST; STATISTICAL INFERENCE; STATISTICAL PARAMETERS; STATISTICAL SIGNIFICANCE; THEORETICAL MODEL;

MODELS, THEORETICAL;

EID: 84928914308     PISSN: None     EISSN: 19326203     Source Type: Journal    
DOI: 10.1371/journal.pone.0121263     Document Type: Article

References (65)

1. Yates F. Contingency tables involving small numbers and the ?2 test. Journal of the Royal Statistical Society, Suppl. 1984; 1:217-235. doi: 10.2307/2983604
2. Conover WJ. Some reasons for not using the Yates continuity correction on 2 × 2 contingency tables (C/R: P376-382). Journal of the American Statistical Association. 1974; 69:374-376. doi: 10.1080/ 01621459.1974.10482957
3. Yates F. Tests of significance for 2× 2 contingency table (with discussion). Journal of the Royal Statistical Society, Series A: General. 1984; 147:426-463. doi: 10.2307/2981577
4. Haviland MG. Yates's correction for continuity and the analysis of 2× 2 contingency tables (C/R: P369-383). Statistics in Medicine. 1990; 9:363-367. doi: 10.1002/sim.4780090403 PMID: 2362976
5. Barnard GA. In contradiction to J. Berkson's dispraise: Conditional tests can be more efficient. Journal of Statistical Planning and Inference. 1979; 3:181-188.
6. Basu D. Comments on Joseph Berkson's paper "In dispraise of the exact test". Journal of Statistical Planning and Inference. 1979; 3:189-192. doi: 10.1016/0378-3758(79)90010-7
7. Corsten LCA, de Kroon JPM. Comments on J. Berkson's paper "In dispraise of the exact test". Journal of Statistical Planning and Inference. 1979; 3:193-198. doi: 10.1016/0378-3758(79)90011-9
8. Kempthorne O. In dispraise of the exact test: Reactions. Journal of Statistical Planning and Inference. 1979; 3:199-214. doi: 10.1016/0378-3758(79)90012-0
9. Berkson J. In dispraise of the exact test. Journal of Statistical Planning and Inference. 1978; 2:27-42. doi: 10.1016/0378-3758(78)90019-8
10. Agresti A. Exact inference for categorical data: recent advances and continuing controversies. Statistics in Medicine. 2001; 20(17-18):2709-2722. doi: 10.1002/sim.738 PMID: 11523078
11. Kalbfleisch JD, Sprott DA. Marginal and conditional likelihoods. Sankhyâ, Series A. 1973; 35:311-328.
12. Plackett RL. The marginal totals of a 2× 2 table. Biometrika. 1977; 64:37-42. doi: 10.2307/2335767
13. Haber M. Do the marginal totals of a 2× 2 contingency table contain information regarding the table proportions? Communications in Statistics: Theory and Methods. 1989; 18:147-156. doi: 10.1080/ 03610928908829889
14. Zhu Y, Reid N. Information, ancillarity, and sufficiency in the presence of nuisance parameters. The Canadian Journal of Statistics / La Revue Canadienne de Statistique. 1994; 22:111-123. doi: 10.2307/ 3315827
15. D'Agostino RB, Chase W, Belanger A. The appropriateness of some common procedures for testing the equality of two independent binomial populations (C/R: 89V43 P187-188). The American Statistician. 1988; 42:198-202. doi: 10.2307/2685002
16. Grizzle JE. Continuity correction in the chi-squared test for 2× 2 tables. The American Statistician. 1967; 21(4):28-32. doi: 10.2307/2682103
17. Starmer CF, Grizzle JE, Sen PK. Comment on " Some reasons for not using the Yates continuity correction on 2× 2 contingency tables (C/R: P376-382)". Journal of the American Statistical Association. 1974; 69:376-378. doi: 10.2307/2285662
18. Plackett RL. The continuity correction in 2× 2 tables. Biometrika. 1964; 51:427-338. doi: 10.2307/ 2334138
19. Tocher KD. Extension of the Neyman-Pearson theory of tests to discontinuous variates. Biometrika. 1950; 37(1/2):130-144. doi: 10.2307/2332156 PMID: 15420258
20. Lancaster HO. Statistical control of counting experiments. Biometrika. 1952; 39:419-422. doi: 10.1093/ biomet/39.3-4.419
21. Stone M. The role of significance testing: some data with a message. Biometrika. 1969; 56:485-493. doi: 10.1093/biomet/56.3.485
22. Upton GJG. Fisher's exact test. Journal of the Royal Statistical Society, Series A: Statistics in Society. 1992; 155:395-402. doi: 10.2307/2982890
23. Agresti A. Dealing with discreteness: Making ' exact' confidence intervals for proportions, differences of proportions, and odds ratios more exact. Statistical Methods in Medical Research. 2003; 12(1):3-21. doi: 10.1191/0962280203sm311ra PMID: 12617505
24. Dupont WD. Sensitivity of Fisher's exact test to minor perturbations in 2× 2 contingency tables (C/R: V8 P243-245). Statistics in Medicine. 1986; 5:629-635. doi: 10.1002/sim.4780050610 PMID: 3823670
25. Pearson ES. The choice of statistical tests illustrated on the interpretation of data classed in a 2× 2 table. Biometrika. 1947; 34:139-167. doi: 10.1093/biomet/34.1-2.139 PMID: 20287827
26. Barnard GA. Significance tests for 2× 2 tables. Biometrika. 1947; 34:123-138. doi: 10.1093/biomet/34. 1-2.123 PMID: 20287826
27. Cormack RS, Mantel N. Fisher's exact test: The marginal totals as seen from two different angles. The Statistician: Journal of the Institute of Statisticians. 1991; 40:27-34. doi: 10.2307/2348221
28. Greenland S. On the logical justification of conditional tests for two-by-two contingency tables (C/R: 92V46 P163). The American Statistician. 1991; 45:248-251. doi: 10.1080/00031305.1991.10475813
29. Cox DR, Hinkley DV. Theoretical statistics. Chapman & Hall Ltd; 2000.
30. Casella G, Berger RL. Statistical inference. 2nd ed. Duxbury Press; 2002.
31. Reid N. The roles of conditioning in inference (Disc: P173-199). Statistical Science. 1995; 10:138-157. doi: 10.1214/ss/1177010027
32. Cox DR. Some problems connected with statistical inference. Annals of Mathematical Statistics. 1958; 29:357-372. doi: 10.1214/aoms/1177706618
33. McCullagh P, Nelder JA. Generalized linear models. Chapman & Hall Ltd; 1999.
34. Little RJA. Testing the equality of two independent binomial proportions (C/R: 90V44 P260-261). The American Statistician. 1989; 43:283-288. doi: 10.1080/00031305.1989.10475676
35. Cox DR. Discussion of Dr. Yates's paper. Journal of the Royal Statistical Society, Series A: General. 1984; 147:451.
36. Cox DR, Reid N. Parameter orthogonality and approximate conditional inference (with discussion). Journal of the Royal Statistical Society, Series B. 1987; 49:1-39.
37. Rothman KJe, Greenland Se. Modern epidemiology. Little, Brown and Co; 1998.
38. Blume JD. Likelihood and its evidential framework. In: Bandyopadhyay PS, Malcolm RF, editors. Philosophy of statistics (Handbook of the philosophy of science). vol. 7. North Holland; 2011. p. 493-512.
39. Blume JD. Likelihood methods for measuring statistical evidence. Statistics in Medicine. 2002; 21 (17):2563-2599. doi: 10.1002/sim.1216 PMID: 12205699
40. Cornfield J. Sequential trials, sequential analysis and the likelihood principle. The American Statistician. 1966; 20:18-23. doi: 10.2307/2682711
41. Goodman SN. P values, hypothesis tests, and likelihood: implications for epidemiology of a neglected historical debate. American Journal of Epidemiology. 1993; 137(5):485-496. PMID: 8465801
42. Royall RM. Statistical evidence: a likelihood paradigm. Chapman & Hall/CRC; 1997.
43. Blume JD, Peipert JF. What your statistician never told you about p-values. Journal of the American Association of Gynecologic Laparoscopists. 2003; 10:439-444. doi: 10.1016/S1074-3804(05)60143-0 PMID: 14738627
44. Agresti A. Categorical data analysis. 3rd ed. Wiley-Interscience; 2012.
45. Brazzale AR, Davison AC, Reid N. Applied asymptotics: case studies in small-sample statistics. Cambridge University Press; 2007.
46. Brown LD, Cai TT, DasGupta A. Interval estimation for a binomial proportion. Statistical Science. 2001; 16(2):101-133. doi: 10.1214/ss/1009213285
47. Hacking I. Logic of statistical inference. New York: Cambridge University Press; 1965.
48. Barnard GA. Statistical inference. Journal of the Royal Statistical Society, Series B: Methodological. 1949; 11:115-139.
49. Birnbaum A. On the foundations of statistical inference (Com: P307-326). Journal of the American Statistical Association. 1962; 57:269-306. doi: 10.1080/01621459.1962.10480660
50. Evans MJ, Fraser DAS, Monette G. On principles and arguments to likelihood. The Canadian Journal of Statistics / La Revue Canadienne de Statistique. 1986; 14(3):pp. 181-194. doi: 10.2307/3314794
51. Royall RM. On the probability of observing misleading statistical evidence (C/R: P768-780). Journal of the American Statistical Association. 2000; 95(451):760-768. doi: 10.1080/01621459.2000.10474264
52. Choi L, Caffo B, Rohde C. A survey of the likelihood approach to bioequivalence trials. Statistics in Medicine. 2008; 27(24):4874-4894. doi: 10.1002/sim.3334 PMID: 18618422
53. Barndorff-Nielsen OE. On a formula for the distribution of a maximum likelihood estimator. Biometrika. 1983; 70:343-365. doi: 10.1093/biomet/70.2.343
54. Berger JO, Liseo B, Wolpert RL. Integrated likelihood methods for eliminating nuisance parameters (Pkg: P1-28). Statistical Science. 1999; 14(1):1-22. doi: 10.1214/ss/1009211803
55. McCullagh P, Tibshirani R. A simple method for the adjustment of profile likelihoods. Journal of the Royal Statistical Society, Series B: Methodological. 1990; 52:325-344.
56. Fraser DAS. Likelihood for component parameters. Biometrika. 2003; 90(2):pp. 327-339. doi: 10.1093/ biomet/90.2.327
57. Severini TA. Likelihood methods in statistics. Oxford University Press; 2000.
58. Barndorff-Nielsen O. Discussion of the paper by Professors Cox and Reid. Journal of the Royal Statistical Society, Series B. 1987; 49:18-20.
59. Severini T. Likelihood functions for inference in the presence of a nuisance parameter. Biometrika. 1998 Sep; 85(3):507-522. doi: 10.1093/biomet/85.3.507
60. Sartori N, Salvan A, Pace L. A note on directed adjusted profile likelihoods. Journal of Statistical Planning and Inference. 2003; 110(1-2):1-9. doi: 10.1016/S0378-3758(01)00290-7
61. Fraser DAS, Reid N. Adjustments to profile likelihood. Biometrika. 1989; 76:477-488. doi: 10.1093/ biomet/76.3.477
62. Choi L. ProfileLikelihood: profile likelihood for a parameter in commonly used statistical models; 2011. R package version 1.1. Available from: http://CRAN.R-project.org/package=ProfileLikelihood.
63. Howard JV. The 2× 2 table: a discussion from a Bayesian viewpoint. Statistical Science. 1998; 13 (4):351-367. doi: 10.1214/ss/1028905830
64. Staicu AM, Reid NM. On probability matching priors. Canadian Journal of Statistics. 2008; 36(4):613-622. doi: 10.1002/cjs.5550360408
65. Gong G, Samaniego FJ. Pseudo maximum likelihood estimation: theory and applications. The Annals of Statistics. 1981; 9(4):861-869. doi: 10.1214/aos/1176345526