Selecting significant effects in factorial designs: Lenth's method versus using negligible interactions

Among the many analytical techniques that have been published to analyze the significance of the effects in the absence of replications, two have emerged as the most widely used in text books as well as statistical software packages: The Lenth's method and the estimation of the variance of the effects from the values of those considered negligible. This article shows that neither is better than the other in all cases, and by analyzing the results obtained in a wide variety of situations it provides guidelines on when it is preferable to use one or the other technique.