= Center-point curvature contrast
{title2=$\widehat\gamma=\bar Y_F-\bar Y_0$}
In a two-factor design with four corner observations and $n_0$ independent center replicates, the difference between the corner mean and center mean has <variance> $\sigma^2(1/4+1/n_0)$. Under a full <quadratic regression> surface it estimates $\beta_{11}+\beta_{22}$; the linear and interaction terms average to zero at the corners. With $n_0\geq2$, the center <pure error> estimate makes its squared standardized contrast an $F_{1,n_0-1}$ test under a first-order mean model. Zero contrast does not exclude curvature, since the two squared-term coefficients may cancel.
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