Testing the equality of two normal percentiles
T. F. Cox, Khalifa Hmood Jaber · Communications in Statistics - Simulation and Computation · 1985
Two statistics are suggested for testing the equality of two normal percentiles where population means and variances are unknown. The first is based on the generalized likelihood ratio test (LRT), the second on Cochran's statistic used in the Behrens-Fisher problem. Size and power comparisons are made by using simulation and asympototic theory.