In　clinical　studies,　pairwise　comparisons　are　frequently　performed　to　examine　differences　in　efficacy　between　treatments.　The　statistical　methods　of　pairwise　comparisons　are　available　when　treatment　responses　are　measured　on　an　ordinal　scale.　The　Wilcoxon-Mann-Whitney　test　and　the　latent　normal　model　are　popular　examples.　However,　these　procedures　cannot　be　used　to　compare　treatments　in　parallel　groups　(a　two-way　design)　when　overall　type　I　error　must　be　controlled.　In　this　paper,　we　explore　statistical　approaches　to　the　pairwise　testing　of　treatments　that　satisfy　the　requirements　of　a　two-way　layout.　The　results　of　our　simulation　indicate　that　the　latent　normal　approach　is　superior　to　the　Wilcoxon-Mann-Whitney　test.　Clinical　examples　are　used　to　illustrate　our　suggested　testing　methods.