Equivalence of factorial designs with qualitative and quantitative factors

► Equivalent symmetric fractional factorial design with both qualitative and quantitative factor have same statistical properties. ► The provided necessary and sufficient conditions for equivalence allow classification of designs in equivalence classes. ► Necessary criteria for equivalence of designs with only qualitative factors provide a quick check for non-equivalence. ► Results extend to asymmetric fractional factorial designs with both qualitative and quantitative factors.