1 Testing marginal homogeneity against stochastic order in multivariate ordinal data B. Klingenberg 1,∗ , A. Solari 2 , L. Salmaso 3 , and F. Pesarin 2 , 1 Department of Mathematics and Statistics, Williams College Williamstown, MA 01267, U.S.A. 2 Department of Statistics, University of Padova, Via Cesare Battisti, 241/243, 35121 Padova, Italy 3 Department of Management and Engineering, University of Padova, Stradella San Nicola, 3, 36100 Vicenza, Italy ∗ email: bklingen@williams.edu SUMMARY: Many assessment instruments used in the evaluation of toxicity, safety, pain or disease progression consider multiple ordinal endpoints to fully capture the presence and severity of treatment effects. Contingency tables underlying these correlated responses are often sparse and imbalanced, rendering asymptotic results unreliable or model fitting pro- hibitively complex without overly simplistic assumptions on the marginal and joint distribu- tion. Instead of a modeling approach, we look at stochastic order and marginal inhomogeneity as an expression or manifestation of a treatment effect under much weaker assumptions. Of- ten, endpoints are grouped together into physiological domains or by the body function they describe. We derive tests based on these subgroups which might supplement or replace the individual endpoint analysis because they are more powerful. The permutation or bootstrap distribution is used throughout to obtain global, subgroup and individual significance levels as they naturally incorporate the correlation among endpoints. We provide a theorem that establishes a connection between marginal homogeneity and the stronger exchangeability assumption under the permutation approach. Multiplicity adjustments for the individual