Make a decomposition of the observations for the poisons-treatments example. There should be six tables of elements associated ·with the original observations-the grand average, the poison main effects, the treatment main effects, the interaction, and the residuals. Confirm to your own satisfaction that (a) the various components are orthogonal, (b) the sums of squares of the individual elements in the tables correctly give the sums of squares of the ANOVA table, and (c) the allocated numbers of degrees of freedom are logical.