ABSTRACT
The main difference between the analysis of a one-way treatment structure and that of a two-way treatment structure is that the sums of squares for intercepts and slopes can be partitioned into row treatment effects, column treatment effects, and row treatment by column treatment interaction effects. One of the objectives of a good analysis is to determine if a different slope is needed for each treatment combination and, if not, to determine whether a different slope is needed for each row treatment and whether a different slope is needed for each column treatment. Once an adequate model has been determined in terms of the slope parameters, the analysis is completed by making comparisons of interest between the planes or lines at various selected values of the covariate. If there are unequal slopes for the levels of the row treatments or column treatments or both, the analysis of the intercepts provides a comparison of the regression surfaces at the value of the covariate equal to zero. Great care must be used in the interpretation of results when there are unequal slopes in two-way and higher order treatment structures. Several examples involving one covariate are used to demonstrate these concepts.
