A distribution-free test for symmetry in hierarchical data

Distribution-free tests for permutational symmetry of correlated variables have been offered recently in the literature. However, situations arise when all the planned measurements are available only on some subjects, while others drop out at various stages of the experiment. The present paper offers a distribution-free statistic for testing permutational symmetry of correlated variables in such hierarchical data, and develops a large-sample chi-square approximation. Explicit expressions for the test statistic have been provided for some special cases.