Comparison of quantiles for several normal populations

For the purpose of comparison between several independent populations, many procedures exist for testing equality of means or medians among the groups. However, the mean or the median do not determine the entire distribution. This paper addresses the problem of testing the equality of quantiles of several normal distributions. We propose an approximate test based on large sample method and an exact procedure based on a generalized p-value. An extensive simulation study was conducted to evaluate the size and powers of these two tests. Simulation results show that the generalized p-value approach performs very satisfactorily even for small samples while the approximate method exhibits poor Type I error control. A robustness study was done for power-exponential distribution and t-distribution. Finally, the proposed methods are applied to two real examples.