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Abstract:
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Many methods have been proposed in literature for classifying and ranking experimental designs. Complete classification and ranking is desirable, as equivalent designs share the same statistical properties, but nonequivalent designs might have different statistical properties under different models. We discuss equivalence of regular and nonregular fractional factorial symmetric designs. We examine combinatorial equivalence, which is appropriate for qualitative factors. Clark and Dean (2001) gave a necessary and sufficient condition for combinatorial equivalence. Since then, a number of authors have suggested alternative methods, which are supposedly faster than the Clark and Dean method, but, as we show, none yields a sufficient condition for equivalence. We examine the efficiency of candidate methods as fast screens for nonequivalent designs.
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