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Factorial designs allow the effects of a factor to be estimated at several levels of the other factors, yielding conclusions that are valid over a range of experimental conditions. The main disadvantage of the full factorial design is its sample size requirement, which grows exponentially with the number of factors or inputs considered. [6]
In the design of experiments, a between-group design is an experiment that has two or more groups of subjects each being tested by a different testing factor simultaneously. This design is usually used in place of, or in some cases in conjunction with, the within-subject design , which applies the same variations of conditions to each subject ...
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In the statistical analysis of the results from factorial experiments, the sparsity-of-effects principle states that a system is usually dominated by main effects and low-order interactions. Thus it is most likely that main (single factor) effects and two-factor interactions are the most significant responses in a factorial experiment.
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 ...
A fractional factorial design is said to have resolution if every -factor effect [note 5] is unaliased with every effect having fewer than factors. For example, a design has resolution R = 3 {\displaystyle R=3} if main effects are unaliased with each other (taking p = 1 ) {\displaystyle p=1)} , though it allows main effects to be aliased with ...
The design with 7 factors was found first while looking for a design having the desired property concerning estimation variance, and then similar designs were found for other numbers of factors. Each design can be thought of as a combination of a two-level (full or fractional) factorial design with an incomplete block design. In each block, a ...
Plackett–Burman designs are experimental designs presented in 1946 by Robin L. Plackett and J. P. Burman while working in the British Ministry of Supply. [1] Their goal was to find experimental designs for investigating the dependence of some measured quantity on a number of independent variables (factors), each taking L levels, in such a way as to minimize the variance of the estimates of ...