ANOVA with equal cell frequencies: In higher-way ANOVA, as in twoway ANOVA, when cell frequencies are equal, the sum of squares for each set of effects can be calculated directly from the parameter...

ANOVA with equal cell frequencies: In higher-way ANOVA, as in twoway ANOVA, when cell frequencies are equal, the sum of squares for each set of effects can be calculated directly from the parameter estimates for the full model or, equivalently, in terms of cell and marginal means. To get the sum of squares for a particular set of effects, we simply need to square the parameter estimate associated with each cell, sum over all cells, and multiply by the common cell frequency, n’ . For example, for a balanced three-way ANOVA,

Write out similar expressions for SS(α_A) and SS(α_ABC) in three-way ANOVA. Show that

Where

is the variance in cell j; k; m of the design.