Smallsample And Sparsedata Inference

The test statistics presented in this article are large-sample statistics. For chi-squared statistics, the convergence to chi-squared distributions tends to be faster for statistics having smaller values of d.f., such as the single-degree-of-freedom statistics.

For any particular statistic referring to the two-way contingency table of dose by ordinal response, one can construct a small-sample 'exact' test using the generalized hypergeometric distribution that results from conditioning on the row and column totals. This approach generalizes Fisher's exact test for 2-by-2 tables, with the conditioning argument yielding a distribution not depending on unknown nuisance parameters. Exact tests are available in StatXact22 for several statistics, including the Jonchkeere-Terpstra statistic and correlation-type statistics with fixed or rank scores.47 (The correlation-type statistics use the 'linear-by-linear' option in StatXact.) Currently these tests are restricted to the single-stratum case.

For stratified data, only the case of two dose groups is currently addressed by standard software, using the CMH correlation type approach for a set of fixed or midrank response scores (StatXact). In principle, though, the methodology of small-sample exact tests extends directly to the more general case of several dose groups.48 Specialized FORTRAN programs exist for these analyses.

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