Analysis of orthogonal saturated designs

Abstract

This chapter provides a review of special methods for analyzing data from screening experiments conducted using regular fractional factorial designs. The methods considered are robust to the presence of multiple nonzero effects. Of special interest are methods that try to adapt effectively to the unknown number of nonzero effects. Emphasis is on the development of adaptive methods of analysis of orthogonal saturated designs that rigorously control Type I error rates of tests or confidence levels of confidence intervals under standard linear model assumptions. The robust, adaptive method of Lenth (1989) is used to illustrate the basic problem. Then nonadaptive and adaptive robust methods of testing and confidence interval estimation known to control error rates are introduced and illustrated. Although the focus is on Type I error rates and orthogonal saturated designs, Type II error rates, nonorthogonal designs, and supersaturated designs are also discussed briefly.