Some One-Sided Tests for Change in Level

We consider tests based on one observation on each of N ≥ 2 random variables X l, …, XN to decide if the means μ of the xi 's are all equal against the one-sided alternative that a shift has occurred at some unknown point γ, (i.e. μ1, = μ2 = … = μ r < μ r+1 = … = μ N ). The x i 's are considered to be normally distributed with a common unknown variance. Bayesian tests as well as a test based on the maximum likelihood estimate of γ are considered and their powers are compared by Monte Carlo methods. The exact distribution of a Bayesian test statistic is derived. A simple application using traffic accident data is presented.