Testing Multiple Dispersion Effects in Unreplicated Fractional Factorial Designs

Abstract

In unreplicated 2^k−p designs, the assumption of constant variance is commonly made. When the variance of the response differs between the two levels of a column in the effect matrix, that column produces a dispersion effect. In this article we show that two active dispersion effects may create a spurious dispersion effect in their interaction column. Most existing methods for dispersion-effect testing in unreplicated fractional factorial designs are subject to these spurious effects. We propose a method of dispersion-effect testing based on geometric means of residual sample variances. We show through examples from the literature and simulations that the proposed test has many desirable properties that are lacking in other tests.

KEY WORDS :

• Experimental design
• Geometric mean
• Multiple effects
• Robust design
• Screening experiments
• Variance