Dispersion-effects detection after screening for location effects in unreplicated two-level experiments

Abstract

Prior to calculating test statistics, methods to detect dispersion effects in an unreplicated two-level design exclude the contrasts that correspond with active location effects. In many examples from the literature, these location effects are detected with simple screening devices. In this paper, we study the impact of initial detection of location effects with a robust scale estimator on dispersion-effects detection by F-ratios of squared null contrasts. Recent literature shows a severe sensitivity of the dispersion F-test to unidentified location effects, to the link function for the variance, and to the presence of other dispersion effects. We derive conditions for which the reported sensitivity might be less severe. Using unreplicated resolution III designs is not compatible with these conditions. Designs with higher resolution are considered more closely by simulation under various true models for location and dispersion. The simulations confirm the validity of the above conditions. For 16-run experiments with 5 or more factors, the power to detect a single dispersion effect doubling the standard deviation roughly equals the Type I error for null effects. For 32-run experiments with 7 or more factors, further research is needed to alleviate the restrictions needed to control the Type I error.