The general Nature of Saturated Designs
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In a full two-level factorial experiment the design matrix is a Hadamard matrix H. The OLS estimator of the full set of parameters β ( the mean, the main effects and interactions) is given by β̂ = 1/NH^TY.Thus the estimator of each parameter except the mean is a contrast. That is H^T1_N = < b m a t r i x >. In this paper we show this result not only holds for Hadamard matrices but also holds for any saturated design matrix D in the two-level factorial experiment set-up.
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