For clinical trials based on the one-way experimental design, powerful statistical multiple comparison methods are available: Tukey's method of all-pairwise comparisons (MCA), the principal investigator's method for multiple comparisons with the best treatment (MCB), and Dunnett's method for multiple comparisons with a control (MCC). They are accessible through the popular statistical packages SAS (since 1986) and MINITAB (in 1989). However, clinical trials often incorporate blocking factors (e.g., """"""""patient"""""""") and/or covariates (e.g., """"""""sex"""""""", """"""""age""""""""). Then the one-way model is insufficient, and the problem of treatments comparison becomes one of simultaneous statistical inference in a General Linear Model (GLM) Y=X beta + E, or extensions of the GLM. Our research has revealed that existing statistical methods applicable to GLM are either very conservative or, in the case of the MEANS option for multiple comparisons in PROC GLM of SAS, wrong. By making novel uses of dimension reduction algorithms in Factor Analysis, we propose to develop new extensions to MCB and MCC that will be applicable to the General Linear Model. These new methods will provide statistically correct inference, and will be much sharper than the existing conservative procedures. In addition, using the rank regression approach, we propose to develop robust MCB and MCC methods applicable to GLM with non-normal errors. Further, for clinical trials with blocking factors and/or covariates, and discrete treatment response variables (e.g., success/failure, cell counts), MCB and MCC will be extended to the Generalized Linear Iterative Model (GLIM), providing sharper statistical inference than the traditional X2 based comparison methods. As has been done in the current project, computer implementation of these new statistical methods will be contributed to SAS and MINITAB whenever possible.