Simplified Freeman-Tukey test statistics for testing probabilities in contingency tables

Abstract

This paper presents the simplified version of the Freeman-Tukey test statistic for testing hypothesis about multinomial probabilities in one, two and multidimensional contingency tables that does not require calculating the expected cell frequencies before test of significance. The simplified method established new criteria of collapsing cells whose frequency are less than 5. Illustrated examples compared favourably the new method with Pearson, Neyman and Likelihood ratio chi- squared statistics. Apart from being faster, the simplified version provides more accurate result since the problem of figure approximation is reduced.

Keywords: Freeman-Tukey statistic, dimension, contingency table, multinomial probabilities, expected cell frequencies