Statistics and Computing

, Volume 7, Issue 2, pp 137–143

# Simplifying the calculation of the P-value for Barnard's test and its derivatives

• A. Silva Mato
• A. Martín Andrés
Article

## Abstract

Unconditional non-asymptotic methods for comparing two independent binomial proportions have the drawback that they take a rather long time to compute. This problem is especially acute in the most powerful version of the method (Barnard, 1947). Thus, despite being the version which originated the method, it has hardly ever been used. This paper presents various properties which allow the computation time to be drastically reduced, thus enabling one to use not only the more traditional and simple versions given by McDonald et al. (1977) and Garside and Mack (1967), but also the more complex original version of Barnard (1947).

Barnard's test comparison of two proportions unconditional test × tables

## Preview

### References

1. Barnard, G. A. (1947) Significance tests for 2 x 2 tables. Biometrika, 34, 123–38.Google Scholar
2. Berger, R. L. (1996) More powerful tests from confidence interval p values. The American Statistician, 50 (4), 314–8.Google Scholar
3. Fisher, R. A. (1935) The logic of inductive inference. Journal of the Royal Statistical Society A, 98, 39–54.Google Scholar
4. Garside, G. R. and Mack, C. (1967) Correct confidence limits for the 2 x 2 homogeneity contingency table with small frequencies. New Journal of Statistics and Operations Research, 3(2), 1–25.Google Scholar
5. Haber, M. (1986) An exact unconditional test for the 2 x 2 comparative trial. Psychometrics Bull, 99 (1), 129–32.Google Scholar
6. Haber, M. (1987) A comparison of some conditional and unconditional exact tests for 2 x 2 contingency tables'. Communications in Statistics-Simulation and Computing, 16(4), 999–1013.Google Scholar
7. Liddell, D. (1976) Practical test of 2 x 2 tables. Statistician, 25(4), 295–304.Google Scholar
8. Martí n André s, A. (1991) A review of classic non-asymptotic methods for comparing two proportions by means of independent samples. Communications in Statistics-Simulation and Computation, 20 (2 & 3), 551–83.Google Scholar
9. Martí n André s, A. and Silva Mato, A. (1994) Choosing the optimal unconditioned test for comparing two independent proportions. Computational Statistics and Data Analysis, 17, 555–74.Google Scholar
10. McDonald, L. L., Davis, B. M. and Milliken, G. A. (1977) A non-randomized unconditional test for comparing two proportions in a 2 x 2 contingency table. Technometrics, 19, 145–50.Google Scholar
11. McDonald, L. L., Davis, B. M., Bauer, H. R.(III) and Laby, B. (1981) Algorithm AS161: Critical Regions of an unconditional non-randomized test of homogeneity in 2 x 2 contingency tables. Applied Statistics, 30(2), 182–9.Google Scholar
12. Richardson, J. T. E. (1994) The analysis of 2 x 1 and 2 x 2 contingency tables: an historical review. Statistical Methods in Medical Research, 3, 107–33.Google Scholar
13. Sahai, H. and Khurshid, A. (1995) On analysis of epidemiological data involving a 2 x 2 contingency table: an overview of Fisher's exact test and Yates' correction for continuity. Journal of Biopharmaceutical Statistics, 5(1), 43–70.Google Scholar
14. Schawe, D. (1977) Error probabilities for 2 x 2 contingency table American Statistician, 31(3), 134.Google Scholar
15. Shuster, J. J. (1988) EXACTB and CONF: Exact unconditional procedures for binomial data. The American Statistician, 42(3), 234.Google Scholar
16. Silva Mato, A. and Martí n André s, A. (1995) Optimal unconditional tables for comparing two independent proportions. Biometrical Journal, 37(7), 821–36.Google Scholar