Exact tests for interaction in several 2 . 2 tables

The investigation of interaction in a series of 2 . 2 tables is warranted in a variety of research endeavors. Though many large-sample approaches for such investigations are available, the exact analysis of the problem has been formulated for the probability statistic only. We present several alternative statistics applicable in this context. We also give an efficient polynomial multiplication algorithm to compute exact distributions and tail areas for the family of stratum-additive statistics. Besides the probability statistic, these include the score, likelihood ratio, and other statistics. In addition to comparing, in empirical terms, the diverse computational strategies for exact interaction analysis, we also explore the theoretical linkages between them. Data from published papers are used for illustration.