Testing Ratios of Means to Standard Deviations from Normal Populations under Order Restrictions with Generalized p Values

A procedure for testing ratios of means to standard deviations from normal populations under semi-order restriction and tree order restriction is developed. The testing is performed on the basis of the generalized p value approach and U-I test and involves a one-dimensional numerical integration. The problem is always encountered in biology, medication, business investment, telecommunication, and so on. We propose the generalized test variable and obtain the generalized p values of the testing problem. Finally, simulation results are given.