Comparison of several means: A fiducial based approach

To study the equality of several normal means when the variances are unknown and unequal, we propose a fiducial based test, and theoretically examine the frequentist property of the proposed test. We numerically compare the performance of the proposed approach with several tests, recently developed such as the generalized F-test by Weerahandi (1995a), the trimmed mean-based test by Lix and Keselman (1998), and the parametric bootstrap test by Krishnamoorthy et al. (2007). The simulation results indicate that the proposed approach can provide a reasonable p-value via a few straightforward simulation steps. Finally, the proposed approach is applied to an analysis of two real data sets for illustration.