Egbert Biesheuvel (Solvay Pharmaceuticals, The Netherlands),

Ludwig Hothorn (University of Hannover, Germany)

Many-to-one comparisons in a stratified design maintaining the overall alpha level

Dunnett (1955) described a multiple comparison procedure for many-to-one comparisons in the one-way layout assuming normal distributed data. Cheung and Holland (1991) extented the Dunnett procedure to the situation of a stratified design. In this latter situation, the correlation matrix has a block product-moment structure. Nowadays different algorithms exist to handle multivariate t-distributions. Percentage points, confidence intervals and power can be computed/calculated within SAS, even in case of unbalanced data. The performance of this method in comparison to resampling techniques (bootstrap, permutation and parametric simulation) is investigated for different kind of data. The bootstrap and permutation techniques are calculated within PROC MULTTEST and the Edwards and Berry %-rejection method within PROC MIXED. In addition, a proposal of a non-parametical technique for many-to-one comparisons in a stratified design will be discussed. Extentions to a step-down procedure and how to proceed in situations with a non product-moment correlation structure will be briefly mentioned.


  1. Cheung, S.H. and Holland, B. Extension of Dunnett’s multiple comparison procedure to the case of several groups. Biometrics, 47, 21-32 (1991)
  2. Dunnett, C.W. A multiple comparison procedure for comparing several treatments with a control. Journal of the American Statistical Association, 50, 1096-1121 (1955)
  3. Edwards, D. and Berry, J.J. The efficiency of simulation-based multiple comparisons. Biometrics, 43, 913-928 (1987)
  4. Genz, A. and Bretz, F. Numerical computation of multivariate t-probabilities with application to power calculations of multiple contrasts. Working paper (1999)