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An important characteristic of a fractional design is the defining relation, which gives the set of interaction columns equal in the design matrix to a column of plus signs, denoted by I. For the above example, since D = AB and E = AC, then ABD and ACE are both columns of plus signs, and consequently so is BDCE: D*D = AB*D = I. E*E = AC*E = I
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 4] 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 ...
List of basic statistics topics – redirects to Outline of statistics; List of convolutions of probability distributions; List of graphical methods; List of information graphics software; List of probability topics; List of random number generators; List of scientific journals in statistics; List of statistical packages; List of statisticians ...
The design matrix for a central composite design experiment involving k factors is derived from a matrix, d, containing the following three different parts corresponding to the three types of experimental runs: The matrix F obtained from the factorial experiment. The factor levels are scaled so that its entries are coded as +1 and −1.
Designed experiments with full factorial design (left), response surface with second-degree polynomial (right) In statistics, a full factorial experiment is an experiment whose design consists of two or more factors, each with discrete possible values or "levels", and whose experimental units take on all possible combinations of these levels across all such factors.
Design Point: A single combination of settings for the independent variables of an experiment. A Design of Experiments will result in a set of design points, and each design point is designed to be executed one or more times, with the number of iterations based on the required statistical significance for the experiment.
The use of a sequence of experiments, where the design of each may depend on the results of previous experiments, including the possible decision to stop experimenting, is within the scope of sequential analysis, a field that was pioneered [12] by Abraham Wald in the context of sequential tests of statistical hypotheses. [13]