Two-by-two References

Agresti, A. (2001). Exact inference for categorical data: recent advances and continuing controversies. Statist. Med., 20, 2709-2722.

Andersen, B. (1990) Methodological Errors in Medical Research. London: Blackwell Scientific Publications.

Armitage, P., Berry, G. and Matthews, J. N. S. (2002) Statistical Methods in Medical Research, 4th edn. Oxford: Blackwell.

Barnard, G. A. (1947a) Significance tests for 2 x 2 tables. Biometrika, 34, 123-138.

Barnard, G. A. (1947b) 2 x 2 tables: A note on E. S. Pearsons paper. Biometrika, 34, 168-169.

Barnard, G. A. (1979) In contradiction to J. Berksons dispraise: conditional tests can be more efficient. Journal of Statistical Planning and Inference, 3, 181-187.

Barnard, G. A. (1984) Discussion on Tests of significance for 2 x 2 contingency tables (by F. Yates). J. R. Statist. Soc. A, 147, 449-450.

Barnard, G. A. (1989) On alleged gains in power from lower P values. Statist. Med., 8, 1469-1477.

Berkson, J. (1978a) In dispraise of the exact test. Journal of Statistical Planning and Inference, 2, 27-42.

Berkson, J. (1978b) Do the marginal totals of the 2 x 2 table contain relevant information respecting the table proportions? Journal of Statistical Planning and Inference, 2, 43-44.

Berry, G. and Armitage, P. (1995) Mid-P confidence intervals: a brief review. Statistician, 44, 417-423.

Bradley, D. R. and Cutcomb, S. (1977) Monte Carlo simulations and the chi-square test of independence. Behaviour Research Methods and Instrumentation, 9, 193-201.

Camilli, G. (1990) The test of homogeneity for 2 x 2 contingency tables: a review of and some personal opinions on the controversy. Psychological Bulletin, 108, 135-145.

Camilli, G. and Hopkins, J. D. (1978) Applicability of chi-square to 2 x 2 contingency tables with small expected cell frequencies. Psychological Bulletin, 85, 163-167.

Camilli, G. and Hopkins, J. D. (1979) Testing for association in 2 x 2 contingency tables with very small sample sizes. Psychological Bulletin, 86, 1011-1014.

Campbell, I. (2007) Chi-squared and Fisher-Irwin tests of two-by-two tables with small sample recommendations. Statistics in Medicine, 26, 3661 - 3675.

Cochran, W. G. (1942) The χ2 correction for continuity. Iowa State Coll. Jour. Sci., 16, 421-436.

Cochran, W. G. (1952) The χ² test of goodness of fit. Ann. Math. Statist., 25, 315-345.

Cochran, W. G. (1954) Some methods for strengthening the common χ² tests. Biometrics, 10, 417-451.

Cormack, R. S. and Mantel, N. (1991) Fishers exact test: the marginal totals as seen from two different angles. Statistician, 40, 27-34.

DAgostino, R. B., Chase, B. and Belanger, A. (1988) The appropriateness of some common procedures for testing the equality of two independent binomial populations. American Statistician, 42, 198-202.

Dupont, W. D. (1986) Sensitivity of Fishers exact test to minor perturbations in 2 x 2 contingency tables Statist. Med., 5, 629-635.

Fisher, R. A. (1922) On the interpretation of χ² from contingency tables, and the calculation of P. J. R. Statist. Soc., 85, 87-94.

Fisher, R. A. (1935) The logic of inductive inference. J. R. Statist. Soc., 98, 39-54.

Fisher, R. A. (1945) The logical inversion of the notion of the random variable. Sankhya, 7, 129-132.

Fisher, R. A. (1973) Statistical Methods and Scientific Inference, 3rd edn. London. Collier Macmillan Publishers.

Fleiss, J. L. (1981) Statistical Methods for Rates and Proportions, 2nd edn. Chichester: John Wiley & Sons.

Garside, G. R. and Mack, C. (1976) Actual Type I error probabilities for various tests in the homogeneity case of the 2 x 2 contingency table. American Statistician, 30, 18-21.

Grizzle, J. E. (1967) Continuity correction in the χ²-test for 2 x 2 tables. American Statistician, 21, 28-32.

Haber, M. (1986) An exact unconditional test for the 2 x 2 comparative trial. Psychological Bulletin, 99, 129-132.

Hill, I. D. (1988) Discussion on A new probability model for determining exact P-values for 2 x 2 contingency tables when comparing binomial proportions (by W. R. Rice). Biometrics, 44, 1-22.

Hill, I. D. and Pike, M. C. (1965) Algorithm 4: TWOBYTWO Computer Bulletin, 9, 56-63.

Hirji, K. F., Tan, S. and Elashoff, R. M. (1991) A quasi-exact test for comparing two binomial proportions. Statist. Med., 10, 1137-1153.

Hwang, J. T. G. and Yang, M.-C. (2001) An optimality theory for mid p-values in 2 ### UNKNOWN CHARACTER CODED BY d7 ###2 contingency tables. Statistica Sinica, 11, 807-826.

Irwin, J. O. (1935) Tests of significance for differences between percentages based on small numbers. Metron, 12, 83-94.

Jagger, G. (1984) Discussion on tests of significance for 2 x 2 contingency tables (by F. Yates). J. R. Statist. Soc. A, 147, 455.

Kempthorne, O. (1979) In dispraise of the exact test: reactions Journal of Statistical Planning and Inference, 3, 199-213.

Kurtz, T. E. (1968) A role of time-sharing computing in statistical research. The American Statistician, 22, 19-21.

Larntz, K. (1978) Small-sample comparisons of exact levels for chi-squared goodness-of-fit statistics. J. Am. Statist. Ass. 73, 235-245.

Little, R. J. A. (1989) Testing the equality of two independent binomial proportions. American Statistician, 43, 283-288.

Martin Andres, A. and Herranz Tejedor, I. (2000). On the minimum expected quantity for the validity of the chi-squared test in 2 x 2 tables. Appl. Statist. 27, 807-820.

Martin Andres, A., Sanchez Quevedo, M. J.and Silva Mato, A. (2002) Asymptotical tests in 2 x 2 comparative trials (unconditional approach). Computational Statistics and Data Analysis, 40, 339 - 354.

Overall, J. E., Rhoades, M. and Starbuck, R. R. (1987) Small-sample tests for homogeneity of response probabilities in 2 x 2 contingency tables. Psychological Bulletin, 102, 307-314.

Pearson, E. S. (1947) The choice of statistical tests illustrated on the interpretation of data classed in a 2 x 2 table. Biometrika, 34, 139-167.

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 arisen from random sampling. Philos. Mag. Series 5, 50, 157-172.

Plackett, R. L. (1964) The continuity correction in 2 x 2 tables. Biometrika, 51, 327-337.

Plackett, R. L. (1984) Discussion on Tests of significance for 2 x 2 contingency tables (by F. Yates). J. R. Statist. Soc. A, 147, 458.

Rhoades, H. M. and Overall, J. E. (1982) A sample size correction for Pearson chi-square in 2 x 2 contingency tables. Psychological Bulletin, 91, 418-423.

Rice, W. R. (1988) A new probability model for determining exact P-values for 2 x 2 contingency tables when comparing binomial proportions. Biometrics, 44, 1-22.

Richardson, J. T. E. (1990) Variants of chi-square for 2 x 2 contingency tables. British Journal of Mathematical and Statistical Psychology, 43, 309-326.

Richardson, J. T. E. (1994) The analysis of 2 x 1 and 2 x 2 contingency tables: a historical review Statistical Methods in Medical Research, 3, 107-134.

Roscoe, J. T. and Byars, J. A. (1971) An investigation of the restraints with respect to sample size commonly imposed on the use of the chi-square statistic. J. Am. Statist. Ass., 66, 755-759.

Sahai, H. and Khurshid, A. (1995) On analysis of epidemiological data involving a 2 x 2 contingency table: an overview of Fishers exact test and Yates correction for continuity. Journal of Biopharmaceutical Statistics, 5, 43-70.

Schouten, H. J. A., Molenaar, I. W., van Strik, R. and Boomsma, A. (1980) Comparing two independent binomial proportions by a modified chi square test. Biometrical Journal, 22, 241-248.

Seneta, E. and Phipps, M. C. (2001) On the comparison of two observed frequencies. Biometrical Journal, 43, 23-43.

Storer, B. E. and Kim, C. (1990) Exact properties of some exact test statistics for comparing two binomial proportions. J. Am. Statist. Ass., 85, 146-155.

Stuart, A., Ord, J. K. and Arnold, S. (1999) Kendalls Advanced Theory of Statistics, Vol. 2A, 6th edn. London: Arnold.

Suissa, S. and Shuster, J. J. (1985) Exact unconditional sample sizes for the 2 x 2 binomial trial. J. R. Statist. Soc. A, 148, 317-327.

Tocher, K. D. (1950) Extension of the Neyman-Pearson theory of tests to discontinuous variates. Biometrika, 37, 130-144.

Upton, G. J. G. (1982). A comparison of alternative tests for the 2 x 2 comparative trial. J. R. Statist. Soc. A, 145, 86-105.

Upton, G. J. G. (1984). Discussion on Tests of significance for 2 x 2 contingency tables (by F. Yates). J. R. Statist. Soc. A, 147, 451-452.

Upton, G. J. G. (1992). Fishers exact test. J. R. Statist. Soc. A, 155, 395-402.

Yates, F. (1934) Contingency tables involving small numbers and the χ² test. J. R. Statist. Soc. Suppl., 1, 217-235.

Yates, F. (1984). Tests of significance for 2 x 2 contingency tables (with discussion) J. R. Statist. Soc. A, 147, 426-463.

Back to top