  One class of statistical hypothesis testing procedures is the indisputable
equivalence tests, whose main objective is to establish practical equivalence
rather than the usual statistical significant difference. These hypothesis
tests are prone in bioequivalence studies, where one would wish to show that,
for example, an existing drug and a new one under development have the same
therapeutic effect. In this article, we consider a two-stage randomized (RAND2)
p-value utilizing the uniformly most powerful (UMP) p-value in the first stage
when multiple two-one-sided hypotheses are of interest. We investigate the
behavior of the distribution functions of the two p-values when there are
changes in the boundaries of the null or alternative hypothesis or when the
chosen parameters are too close to these boundaries. We also consider the
behavior of the power functions to an increase in sample size. Specifically, we
investigate the level of conservativity to the sample sizes to see if we
control the type I error rate when using either of the two p-values for any
sample size. In multiple tests, we evaluate the performance of the two p-values
in estimating the proportion of true null hypotheses. We conduct a family-wise
error rate control using an adaptive Bonferroni procedure with a plug-in
estimator to account for the multiplicity that arises from the multiple
hypotheses under consideration. We verify the various claims in this research
using simulation study and real-world data analysis.
