Sequences of Fractional Replicates in the 2 ^{<i>p</i> – <i>q</i>} Series

Abstract

Abstract The confounding of effects and of interactions in experiments in the 2 p–q series is usually resolved by doing other fractions of the same size as the first one. This paper gives augmenting fractions which require fewer runs. If only one ambiguity is present, it is possible that one more run may resolve it. If more than one ambiguity is suspected, then more runs will be required. Some pairs of fractional replicates are given that require fewer runs than the usual single fractions. The estimates of effects, of two-factor interactions, of their variances and of their covariances are computed by direct methods, simpler than matrix inversion.