Subroutines to calculate exact chi-square and Fisher's exact probability tests are presented for 3 by 2 cross-classification tables. A nondirectional probability value for each test is computed recursively. The use of an arbitrary starting value in each recursion eliminates the cumbersome computation of initial probability values based on the hypergeometric distribution.
Get full access to this article
View all access options for this article.
References
1.
Agresti, A. and Wackerly, D. (1977). Some exact conditional tests of independence for r x c cross-classification tables. Psychometrika, 42, 111-125.
2.
Baker, R. J. (1978). AS-122: Exact distributions derived from two-way tables. Applied Statistics, 1977, 26, 199-206. Correction, 27, 109.
3.
Bedian A. G. and Armenakis, A. A. (1977). A program for computing Fisher's exact probability test and the coefficient of association A for n x m contingency tables. Educational and Psychological Measurement, 37, 253-256.
4.
Berry, K. J. and Mielke, P. W. (1985). Subroutines for computing exact chi-square and Fisher's exact probability tests. Educational and Psychological Measurement, 45, 153-159.
5.
Berry, K. J. and Mielke, P. W. (1986). R by C chi-square analyses with small expected cell frequencies. Educational and Psychological Measurement, 46, 169-173.
6.
Boulton, D. M. (1974). Remark on algorithm 434. Communications of the ACM, 17, 326.
7.
Fisher, R. A. (1922). On the interpretation of x2, when used as a test of homogeneity, when expectations are small. Biometrika, 31, 346-355.
8.
Fisher, R. A. (1934). Statistical methods for research workers. Edinburgh: Oliver and Boyd.
9.
Fleishman, A. I. (1977). A program for calculating the exact probability along with exploration of M x N contingency tables. Educational and Psychological Measurement, 37, 799-803.
10.
Howell, D. C. and Gordon, L. R. (1976). Computing the exact probability of an r x c contingency table with fixed marginal totals. Behavior Research Methods and Instrumentation, 8, 317.
11.
March, D. L. (1972). Algorithm 434: Exact probabilities for R x C contingency tables. Communications of the ACM, 15, 991-992.
12.
Mielke, P. W. and Berry, K. J. (1985). Non-asymptotic inferences based on the chi-square statistic for r by c contingency tables. Journal of Statistical Planning and Inference, 12, 41-45.
13.
Pierce, A. (1970). Fundamentals of nonparametric statistics. Belmont, Calif.,: Dickenson.
14.
Radlow, R. and Alf, E. F. (1975). An alternate multinomial assessment of the accuracy of the x2 test of goodness of fit. Journal of the American Statistical Association, 80, 811-813.
15.
Romesburg, H. C. , Marshall, K., and Mauk, T. P. (1981). FITEST: A computer program for "exact chi-square" goodness-of-fit significance tests. Computers and Geosciences, 7, 47-58.