Design of Experiments—Factorial Designs
Designs are often described by the number of factors. Chapter 6, “OneWay Analysis of Variance” , discusses designs with one factor. Chapter 12, “Two-Way Analysis of Variance” , discusses designs with two factors. More generally, we speak of “three-way” or “higher-way” designs and talk about main effects (one factor), two-way interactions (two factors), three-way interactions, four-way interactions, and so forth. Factors can have crossed or nested relationships. A factor can be fixed or random. When interaction is significant, its nature must be carefully investigated. If higher-order interactions, meaning those involving more than two factors, can be assumed to be negligible, it is often possible to design experiments that require observations on only a fraction of all possible treatment combinations.
KeywordsSimple Effect ANOVA Table Conditional Test Concomitant Variable Model Formula
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