A NOTE ON AUGMENTING RESOLUTION-III DESIGNS

Box and Draper suggested two methods for augmenting resolution III fra ctional replications of a 2(n) experiment. One method identifies a par ticular factor of interest and augments the design to obtain estimates of the corresponding main effect and all two-factor interactions invo lving that factor so that they are not aliased with other two-factor i nteractions. The second method provides an augmented design that allow s one to estimate all main effects unaliased with two-factor interacti ons. In particular, the second method provides foldover designs. Both methods consist of adding another fraction to the original design. The purpose of this note is to show how these augmentation methods can be obtained as fractional replications of a larger design involving an a dditional blocking factor. This provides both a simple justification o f the blocking methods and a basis for discussing hidden block effects .