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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 of experiments with full factorial design (left), response surface with second-degree polynomial (right) The design of experiments , also known as experiment design or experimental design , is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation.
Factorial designs carry labels that specify the number of independent variables and the number of levels of each independent variable there are in the design. For example, a 2x3 factorial design has two independent variables (because there are two numbers in the description), the first variable having two levels and the second having three.
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 ...
In such a case, the design is also said to be orthogonal, allowing to fully distinguish the effects of both factors. We hence can write ∀ i , j n i j = K {\displaystyle \forall i,j\;n_{ij}=K} , and ∀ i , j n i j = n i + ⋅ n + j n {\displaystyle \forall i,j\;n_{ij}={\frac {n_{i+}\cdot n_{+j}}{n}}} .
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 ...
Factorial experimental design software drastically simplifies previously laborious hand calculations needed before the use of computers. During World War II, a more sophisticated form of DOE, called factorial design, became a big weapon for speeding up industrial development for the Allied forces. These designs can be quite compact, involving a
A way to design psychological experiments using both designs exists and is sometimes known as "mixed factorial design". [3] In this design setup, there are multiple variables, some classified as within-subject variables, and some classified as between-group variables. [3] One example study combined both variables.