An Algorithm for Generating Two-way Contingency Tables with Fixed Marginal Totals and Arbitrary Mean Proportions Using Sequentially Assigned Counts

• Activity Number: 80
• Type: Contributed
• Date/Time: Monday, August 12, 2002 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section*
• Author(s): Craig Borkowf*+
• Affiliation(s): National Cancer Institute
• Keywords: contingency table ; multivariate extended hypergeometric distribution ; quasi-independence ; iterative proportion fitting ; permutation test ; structural zero

Abstract

We present a new algorithm for generating two-way contingency tables with fixed marginal totals with arbitrary mean proportions, including structural zeros. This algorithm sequentially assigns counts to tables using probabilities that are repeatedly updated by iterative proportion fitting to reflect the current marginal totals. We say that tables generated in this manner have the "sequentially assigned restricted counts" (SARC) distribution. We argue that the SARC distribution is the natural distribution to employ for modeling certain types of data and the optimal distribution for testing certain hypotheses. We also note that the SARC and multivariate extended hypergeometric (MXH) distributions are identical under quasi-independence and converge to the same asymptotic multivariate normal distribution otherwise. Thus, one can simulate SARC tables to approximate the results of permutation tests, which essentially enumerate MXH tables, under arbitrary hypotheses, which is particularly useful when permutation tests become computationally prohibitive. Finally, we illustrate the use of the SARC algorithm developed here on an application from mathematical anthropology.