Abstract
Summary Some of the problems of asymmetrical factorial experiments using incomplete block designs of equal block size are considered. A set of conditions is established under which a non-orthogonal design for an m × n factorial experiment will give an orthogonal analysis of the main effects and interaction. These conditions are based upon the variances and covariances of the estimated treatment effects in the basic design, and cover all known classes of designs that give an orthogonal analysis. Simple expressions for the adjusted main effects and interaction sums of squares are obtained.
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