Statistical tests under Dallal’s model: Asymptotic and exact methods

This paper proposes asymptotic and exact methods for testing the equality of correlations for multiple bilateral data under Dallal’s model. Three asymptotic test statistics are derived for large samples. Since they are not applicable to small data, several conditional and unconditional exact methods are proposed based on these three statistics. Numerical studies are conducted to compare all these methods with regard to type I error rates (TIEs) and powers. The results show that the asymptotic score test is the most robust, and two exact tests have satisfactory TIEs and powers. Some real examples are provided to illustrate the effectiveness of these tests.