Exactly simultaneous confidence interval for the case of four means using TK procedure

Abstract

The problem of simultaneously estimating the pairwise differences of means of four independent normal populations with equal variances is considered. A statistical computing procedure involving a trivariate t density constructs the exact confidence intervals with simultaneous coverage probability equal to 1- $\alpha$. For equal sample sizes, the new procedure is the same as the Tukey studentized range procedure. With unequal sample sizes, in the sense of efficiency for the confidence interval lengths and experiment wise error rates, the procedure is superior to the various generalized Tukey procedures. The values of the probability points is presented for small sample sizes which is less than 30.