In this paper we introduce a family of test statistics for testing complete symmetry in three-dimensional contingency tables based on phis- divergence families. These test statistics yield the likelihood ratio test and the Pearson test statistics as special cases. Asymptotic distribution
for the new test statistics are derived under both the null and the alternative hypotheses. A simulation study is presented to show that some new statistics offer an attractive alternative to the classical Pearson and likelihood ratio test statistics for this problem of complete symmetry.
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