Quick, Easy, and Powerful Analysis of Unreplicated Factorial Designs

ABSTRACT

Lenth (1989) introduced a quick, easy, and powerful method for assessing the sizes of contrasts of unreplicated 2 ^p factorial designs. The computations of this method are easy to carry out by hand, and together with the advantage that it uses the original numerical measurements which makes the analysis easier to explain. This article suggests a different competing scheme that is also quick, easy, and more powerful. The proposed method is an adaptation of an M-estimator for scale based on the median of the absolute deviation (MAD). The solution uses the concept of the influence function for scale. Critical values and power-tables for three sample sizes often used have been empirically computed in order to conduct several illustrative comparisons between the two methods.

Key Words:

• Fractional factorials
• Influence function
• M-estimators for scale
• Powers

Mathematics Subject Classification:

• Primary 62K15, 62F35
• Secondary 62N10