Example 11.4.4

In the balanced two-factor ANOVA model (ie, nijn0), the estimates are much simpler when one uses the following notations

Y-=n0ab1ijkYijk,Y-i=n0b1jkYijk,Y-j=n0a1ikYijk,andY-ij=n01kYijk.

si260_e

With these notations

μ^=Y-,α^i=Y-iY-,β^j=Y-jY-,αβ^ij=Y-ijY-iY-j+Y-,andYijkμ^=α^i+β^j+αβ^ij+ε^ijk,

si261_e

where ε^ijk=YijkY-ijsi262_e are the residuals. If both sides are squared and summed over i, j, and

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