Simple Approximations for the Size of the Gauss Test and the Power of aPreliminary Test of Variance

摘要

For testing the mean of a normal population one can use the one-sample t-test,but if the variance is known, the power can be improved by using the Gauss test with prescribed variance. However, if one is not sure, the choice between these two tests can be based on a preliminary test on the variance. Although this seems an attractive procedure, numerical evaluations of exact probabilities show that for realistic numbers of observations, the power of the pre-test is too small to detect many cases where the significance level of the Gauss test is destroyed. Higher order asympototics are used to obtain simple expressions for the power of the pre-test and the size of the Gauss test, which explain the numerical results rather well.