The symmetry model is the basic model in the analysis of square contingency tables. Multiple test statistics have been developed for the goodness of fit test. Freeman-Tukey test statistics is appropriate to be used in large samples. However, the required sample size to use the Freeman-Tukey test statistics is not clear. In this paper, the asymptotic properties of Freeman-Tukey test statistic are discussed via extensive Monte-Carlo simulation study. The Freeman-Tukey test statistic is compared with members of power-divergence family test statistic under the symmetry model. The results of simulation study are evaluated based on the Type-I error and power of a test. The results of simulation study and artificial data study show that Freeman-Tukey’s T^2 test statistic does not converge to chi-squared distribution for both sparse and non-sparse square contingency tables.
Freeman-Tukey test statistic Power-divergence family Goodness-of-fit test statistics Square contingency tables Symmetry model
Primary Language | English |
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Subjects | Statistics |
Journal Section | Natural Sciences |
Authors | |
Publication Date | June 30, 2021 |
Submission Date | December 2, 2020 |
Acceptance Date | March 31, 2021 |
Published in Issue | Year 2021Volume: 42 Issue: 2 |