A FORTRAN program to calculate exact probabilities for first- and second-order interactions in 2 x 2 x 2 contingency tables with fixed marginals is presented. Computational speed and accuracy are ensured with the use of an arbitrary constant for the initial table and recursively defined values for all subsequent tables.
Get full access to this article
View all access options for this article.
References
1.
Bartlett, M. S. (1935). Contingency table interactions. Journal of the Royal Statistical Society Supplement, 2, 248-252.
2.
Berry, K. J. , & Mielke, P. W. (1985). Subroutines for computing exact chi-square and Fisher's exact probability tests. Educational and Psychological Measurement, 45, 153-159.
3.
Darroch, J. N. (1962). Interactions in multi-factor contingency tables. Journal of the Royal Statistical Society, B, 24, 251-263.
4.
Darroch, J. N. (1974). Multiplicative and additive interaction in contingency tables. Biometrika, 61, 207-214.
5.
Haber, M. (1983). Sample sizes for the exact test of "no interaction" in 2 x 2 x 2 tables. Biometrics, 39, 493-498.
6.
Haber, M. (1984). A comparison of tests for the hypothesis of no three-factor interaction in 2 x 2 x 2 contingency tables. Journal of Statistical Computing and Simulation, 20, 205-215.
7.
Mielke, P. W. , & Berry, K. J. (1992). Fisher's exact probability test for cross-classification tables. Educational and Psychological Measurement, 52, 97-101.
8.
Mielke, P. W. , Berry, K. J., & Zelterman, D. (1994). Fisher's exact test of mutual independence for 2 x 2 x 2 cross-classification tables. Educational and Psychological Measurement, 54, 110-114.
9.
Odoroff, C. L. (1970). A comparison of minimum logit chi-square estimation and maximum likelihood estimation in 2 x 2 x 2 and 3 x 2 x 2 contingency tables: Tests for interaction. Journal of the American Statistical Association, 65, 1617-1631.
10.
O'Neill, M. E. (1982). A comparison of the additive and multiplicative definitions of second-order interaction in 2 x 2 x 2 contingency tables. Journal of Statistical Computing and Simulation, 15, 33-50.
11.
Plackett, R. L. (1962). A note on interactions in contingency tables. Journal of the Royal Statistical Society, B, 24, 162-166.
12.
Pomar, M. I. (1984). Demystifying loglinear analysis: Four ways to assess interaction. Sociological Perspectives, 27, 111-135.
13.
Quetelet, M. A. (1849). Letters addressed to H.R.H. the Grand Duke of Saxe Coburg and Gotha on the theory of probabilities as applied to the moral and political sciences (O. G. Downes, Trans.). London: Charles & Edwin Layton.
14.
Simpson, E. H. (1951). The interpretation of interaction in contingency tables. Journal of the Royal Statistical Society, B, 13, 238-241.
15.
Zachs, S. , & Solomon, H. (1976). On testing and estimating the interaction between treatments and environmental conditions in binomial experiments: The case of two stations. Communications in Statistics: Theory and Methods, A, 5, 197-223.
