Main Effects Designs Research Articles

Non-Orthogonal Main-Effect Designs for Asymmetrical Factorial Experiments

Summary Two techniques are presented for constructing efficient non-orthogonal main-effect designs. The first technique is an extended method of collapsing that permits non-orthogonality in the derived design. The second technique is a modification of the fold-over method of design construction to produce new main-effect plans. The designs in this paper supplement the major work on orthogonal asymmetrical main-effect plans by Addelman and Kempthorne. The new designs require fewer observations than the corresponding Addelman–Kempthorne plans; this advantage is gained at a sacrifice of orthogonality. The new plans are potentially useful in exploratory studies involving a few multi-level factors plus many two-level factors. Being more nearly saturated than the Addelman–Kempthorne plans, the new designs usually require graphical analysis or testing via a valid external measure of variability. The relationship of some of the new designs to Latin squares and Graeco-Latin squares is also discussed briefly.