We consider the problem of constructing simultaneous fixed-width confidence intervals for all pairwise treatment differences μi – μj in the presence of k(≥2) independent populations Np(μi, Σ), 1≤ i ≠ j ≤ k. Appropriate purely sequential, accelerated sequential and three-stage sampling strategies have been developed and various first-order asymptotic properties are then derived when Σp×p is completely unknown, but positive definite (p.d.). In the two special cases when the largest component variance in Σ is a known multiple of one of the variances or Σ = α2H where σ(>0) is unknown, but Hpxp is known and p.d., the original multistage sampling strategies are specialized. Under such special circumstances, associated second-order characteristics are then developed. It is to be noted that our present formulation and the methodologies fill important voids in the context of multivariate multiple comparisons which is a challenging area that has not yet been fully explored. Moderate sample performances of the proposed techniques were very encouraging and detailed remarks on these were included in an earlier paper.
