A study on Freeman-Tukey test statistic under the symmetry model for square contingency tables

The symmetry model is the basic in analysis of square contingency tables. Multiple test statistics have been developed for goodness fit test. Freeman-Tukey appropriate to be used large samples. However, required sample size use not clear. In this paper, asymptotic properties statistic are discussed via extensive Monte-Carlo simulation study. compared with members power-divergence family under model. results study evaluated based on Type-I error and power a artificial data show that Freeman-Tukey’s T^2 does converge chi-squared distribution both sparse non-sparse