Using Monte-Carlo-algorithms for the estimation of ß-error: alternative inference strategies for multidimensional contingency tables

Abstract

Small samples and sparse cell frequencies cause major problems for statistical modelling with categorical data: Sampling zeros or small expected frequencies can lead to situations where asymptotic approximations of test statistics will be inadequate. In such cases one resorts to the use of exact tests or Monte-Carlo-simulations. But also in this ease, inference can yield problematie results, as the power of tests is often extremely low and will therefore lead to the rejection of theoretically plausible hypotheses on the base of poor empirical material. In this paper an alternative modeHing strategy for small samples using Monte-Carlo-algorithms is presented. This strategy is extending the asymptotic power approximations presented by Cohen (1977) or Agresti (1990).