Yates analysis

In statistics, a Yates analysis is an approach to analyzing 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:

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").

Before performing a Yates analysis, the data should be arranged in "Yates order". That is, given k factors, the k^th column consists of 2^{(k - 1)} minus signs (i.e., the low level of the factor) followed by 2^{(k - 1)} plus signs (i.e., the high level of the factor). For example, for a full factorial design with three factors, the design matrix is

Determining the Yates order for fractional factorial designs requires knowledge of the confounding structure of the fractional factorial design.

A Yates analysis generates the following output.

where e is the estimated factor effect and s_e is the standard deviation of the estimated factor effect.

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