New procedures are developed and illustrated for the analysis of experimental data with particular emphasis on MANOVA and MANCOVA designs. The authors begin with one-way designs, including overall tests of significance, step-down analyses, and the use of latent variables. Next they describe a general test of homogeneity and consider a procedure that is applicable even under conditions of heterogeneity. Two-way designs then are derived as special cases of the more general n-way case. Finally, advantages and disadvantages of the new methods are considered.