 Two-factor normal linear model

A two-factor normal linear model describes independent responses with factor-specific means and common normal error variance. The additive mean $\mu +{\alpha }_a+{\gamma }_j$ assumes no interaction term; the full mean $\mu +{\alpha }_a+{\gamma }_j+{\delta }_{aj}$ permits the first factor effect to vary with the second. Constraints or treatment coding identify the parameters. In a balanced two-by-five design the full model has ten free cell means.