On uniform generation of two-way tables with fixed margins and the conditional volume test of Diaconis and Efron. (English) Zbl 0888.62060

Summary: Two efficient Monte Carlo algorithms are proposed for uniformly generating two-way contingency tables with fixed margins. These permit some improvements on recent work of P. Diaconis, B. Efron and A. Gangolli [Ann. Stat. 13, 845-913 (1985; Zbl 0593.62040); IMA Vol. Math. Appl. 72, 15-41 (1995; Zbl 0839.05005)], especially concerning estimates of the total number of such tables.


62H17 Contingency tables
62G99 Nonparametric inference
Full Text: DOI


[1] DIACONIS, P. and EFRON, B. 1985. Testing for independence in a two-way table: new interpretations of the chi-square statistic. Ann. Statist. 13 845 874. · Zbl 0593.62040 · doi:10.1214/aos/1176349634
[2] DIACONIS, P. and GANGOLLI, A. 1995. Rectangular array s with fixed margins. In Discrete Z. Probability and Algorithms D. Aldous, P. Diaconis, J. Spencer and J. M. Steele, eds. Springer, New York. · Zbl 0839.05005
[3] MEHTA, C. and PATEL, N. 1983. A network algorithm for performing Fisher’s exact test in r c contingency tables. J. Amer. Statist. Assoc. 78 427 434. JSTOR: · Zbl 0545.62039 · doi:10.2307/2288652
[4] SNEE, R. 1974. Graphical display of two-way contingency tables. Amer. Statist. 38 9 12. · Zbl 0361.62037 · doi:10.2307/2683520
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