Selecting significant effects in factorial designs: Lenth’s method versus the Box-Meyer approach

ABSTRACT

The Lenth method is conceptually simple and probably the most common approach to analyzing the significance of the effects in factorial designs. Here, we compare it with a Bayesian approach proposed by Box and Meyer and which does not appear in the usual software packages. The comparison is made by simulating the results of 4, 8 and 16 run designs in a set of scenarios that mirror practical situations and analyzing the results provided by both methods. Although the results depend on the number of runs and the scenario considered, the use of the Box and Meyer method generally produces better results.

KEYWORDS:

• Factorial design
• significant effects
• Lenth method
• Box-Meyer method
• four-run experiments

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. R.V. Lenth was aware that his method could not be applied to 4 run designs and in his paper never tries to do that. Unfortunately several statistical packages apply it to all two level designs independently of the number of runs.