Construction and comparisons of simultaneous confidence intervals for the mean difference of multivariate normal distributions

In this paper, Scheff, and Simplified Scheff, simultaneous confidence intervals are first constructed for mean difference of several multivariate normal distributions. Then the authors theoretically prove that when there are only two populations, Bonferroni bounds and Simplified Scheff, bounds are the same and they are shorter than Scheff, bounds for p a parts per thousand currency sign 10. In the case for 3 a parts per thousand currency sign k a parts per thousand currency sign 10 and 2 a parts per thousand currency sign p a parts per thousand currency sign 10, there exists n(p, k) such that Bonferroni method is better than Simplified Scheff, procedure for n a parts per thousand yen n(p, k), otherwise Simplified Scheff, procedure is better. Finally, the authors find out that neither of Scheff, critical values nor Simplified Scheff, critical values are always larger than another through numerical calculation.