An improved Lenth’s method with applications to second-order designs

The main goal in the analysis of a screening experiment is to correctly identify the set of active factors. Lenth’s method (Lenth 1989) has become a standard approach for the analysis of saturated, two-level orthogonal screening designs due to its power and ease of implementation. Although various modifications and alternatives have been proposed in the intervening years, Lenth’s method remains a primary option in standard statistical software for the analysis of experiments. Despite its widespread use, limitations to Lenth’s method include (1) its inapplicability to nonorthogonal saturated screening designs such as many optimal saturated main effects designs and orthogonal designs with missing observations, and (2) its restrictive reliance on a “pseudo” standard error. This work provides an alternative to Lenth’s method that is applicable to both orthogonal and nonorthogonal designs. It’s effectiveness relies in part on a novel approach to estimating the error variance (and by extension the standard errors of the regression coefficients). Simulation studies reveal the superiority of our approach to current best alternatives.