Modified p-values for one-sided testing in restricted parameter spaces

For testing the mean of a normal distribution, the p-value, derived from the uniformly most powerful test, is usually used as evidence against the null hypothesis. However, the p-value only depends on the hypothesis assumption, but not on the bounds of the parameter space. When the parameter space is restricted, the information of the restriction will not be sufficiently utilized if we still use the usual p-value as evidence against the null hypothesis. In this paper, a modified p-value, based on the bounds of the parameter space for one-sided hypothesis testing, is proposed. Theoretical and simulation studies show that the modified p-value has better performance than the usual p-value from theoretical and simulation studies.