Inference for Effect-Saturated Fractional Factorials

Abstract

Industrial scientists and engineers often use experimental designs in which all degrees of freedom are used to estimate effects and consequently no classical estimate of the error is possible. Robust scale estimates provide an alternative measure of the error. In this study, several such scale estimators are evaluated based on the power or related significance tests. The pseudo standard error method of Lenth provides the best overall performance. Lenth's t approximation for critical values was found to be inaccurate, however, so new tables are provided. Additional recommendations are made according to the experimenter's prior belief in the number of likely important factors.