Generalization and efficient computation of the box-meyer analysis for orthogonal designs

Abstract

Box and Meyer (1986) [1] proposed a Bayesian analysis for saturated orthogonal dedigns, based on the widely-used method of examining normal plots of effects estimates. Stephenson, Hulting, and Moore (1989) [5] give an algorithm for computing this analysis, but it can be quite slow for even 2⁵ designs. In this paper we extend the technique to cover all orthogonal factorial designs, rather than just saturated ones, and we show how the computational algorithm can be greatly improved, both in terms of accuracy and speed. With these extensions and improvements the Box-Meyer method becomes viable as a technique for interactive analysis of any orthogonal factorial design, not just small, saturated ones.