This article is concerned with the comparison between posterior probability and p-value in two-parameter exponential distribution when the location parameter is considered as extra (nuisance) parameter. It has been shown that for a fixed p-value the posterior probability is increases as the number of observations gets large value. It means that it may be different results between classical and Bayesian point of view. This irreconcilability between classical evidence and Bayesian evidence is remained if we compare the lower bound of posterior probability under a class of reasonable prior distributions.

The coefficient of variation is often used for comparing the dispersions of populations that have different measurement systems. In this study, the problem of testing the equality of coefficients of variation of several Normal populations is considered and a new test procedure based on Wald test and parametric bootstrap approach is developed. Since all the proposed tests for this problem are approximate, it is important to investigate how well each test controls the type I error rate. Therefore, via a simulation study, first the type I error rate of our new test is compared with some recently proposed tests. Then, the power of our proposed test is compared with others.