FRACTIONAL FACTORIAL-DESIGNS FOR FACTORS WITH A PRIME NUMBER OF QUANTITATIVE LEVELS

A technique for single degree of freedom partitioning of canonical con trasts for prime level factorials with quantitative levels is reviewed . The relationship between canonical contrasts and the polynomial cont rasts of response function models is discussed. Aliasing of canonical contrasts in fractional factorials is examined and alias sets from pri ncipal fractions are shown to have a particularly simple structure. Se cond-order response function designs built from single principal fract ions or from sums of two or four different principal fractions are dis cussed. The accommodation of nuisance trend effects in experiments wit h quantitative factor effects is exemplified. Tables of fractional fac torial designs for factors with three or five quantitative levels are presented.