Analyzing a designed experiment with a dispersion response and many replicates per condition

Abstract

AbstractMost designed experiments (DOEs) seek to shift a mean response, but a few aim to minimize the dispersion of a response, using the standard deviation (STD) of replicates at each condition. Obtaining sufficient statistical power is often a challenge; dozens of replicates may well be needed to detect a substantial reduction in dispersion. For the problem which motivated this paper, many replicates were feasible, since the two‐level factorial DOE studied a highly automated gage for measuring the axial strength of a mass‐produced metal object. After 30 replicates per condition had been collected, the question arose whether to calculate one dispersion estimate per condition (based on 30 raw data), two estimates per condition (15 raw data each), three estimates (10 each) etc.? A Monte Carlo simulation showed that the best arrangement of the raw data is often one that approximately balances the number of dispersion estimates and the dispersion subgroup size per each condition (e.g., five dispersion estimates of subgroup size 6) for all but the most severely skewed raw data distributions. The authors provide free access to a simulator which may be used by the reader to explore a variety of two‐level factorial DOEs, as needed. This enables experimenters in any subject domain to design such DOEs with sufficient power, while making best use of the raw data in the analysis.