Yates Analysis

In statistics, a Yates analysis is an approach to analysing data obtained from a designed experiment, where a factorial design has been used. Full- and fractional-factorial designs are common in designed experiments for engineering and scientific applications. In these designs, each factor is assigned two levels. These are typically called the low and high levels. For computational purposes, the factors are scaled so that the low level is assigned a value of -1 and the high level is assigned a value of +1. These are also commonly referred to as "-" and "+".

A full factorial design contains all possible combinations of low/high levels for all the factors. A fractional factorial design contains a carefully chosen subset of these combinations. The criterion for choosing the subsets is discussed in detail in the fractional factorial designs article.

Formalized by Frank Yates, a Yates analysis exploits the special structure of these designs to generate least squares estimates for factor effects for all factors and all relevant interactions. The Yates analysis can be used to answer the following questions:

1. What is the ranked list of factors?
2. What is the goodness-of-fit (as measured by the residual standard deviation) for the various models?

The mathematical details of the Yates analysis are given in chapter 10 of Box, Hunter, and Hunter (1978).

The Yates analysis is typically complemented by a number of graphical techniques such as the dex mean plot and the dex contour plot ("dex" stands for "design of experiments").