Most Possible Estimates and Maximum Likelihood Estimates

Testing for independence in two-way contingency tables [ILLEGIBLE][ILLEGIBLE] using a chi-square test that measures the goodness of fit between the observed data and the expected values. This article examines the expected values normally employed in such analyses. It first notes that the usually derived expected values are based on assumptions about the distributional form of an underlying probability density function that may not always be well-founded. Then the article presents an alternative method of estimating expected values, the most possible estimate approach, that does not rely on a priori assumptions about the distributional form. Finally, by establishing that the most possible estimates approximate maximum likelihood estimates, the robustness of the standard maximum likelihood estimator is demonstrated and the researcher is thereby assured of safety in using it without attending to distributional assumptions. The analysis is applied to 3 × 3 tables in this article.