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Factorial experiments are described by two things: the number of factors, and the number of levels of each factor. For example, a 2×3 factorial experiment has two factors, the first at 2 levels and the second at 3 levels. Such an experiment has 2×3=6 treatment combinations or cells.
In the 2 × 3 experiment illustrated here, the expression is a contrast that compares the mean responses of the treatment combinations 11 and 12. (The coefficients here are 1 and –1.) The effects in a factorial experiment are expressed in terms of contrasts. [19] [20] In the above example, the contrast
The results of that example may be used to simulate a fractional factorial experiment using a half-fraction of the original 2 4 = 16 run design. The table shows the 2 4-1 = 8 run half-fraction experiment design and the resulting filtration rate, extracted from the table for the full 16 run factorial experiment.
Design of experiments with full factorial design (left), response surface with second-degree polynomial (right) The design of experiments ( DOE ), [ 1 ] 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 ...
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.
In the design of experiments and analysis of variance, a main effect is the effect of an independent variable on a dependent variable averaged across the levels of any other independent variables. The term is frequently used in the context of factorial designs and regression models to distinguish main effects from interaction effects.
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.
Some research has been done regarding whether it is possible to design an experiment that combines within-subject design and between-group design, or if they are distinct methods. A way to design psychological experiments using both designs exists and is sometimes known as "mixed factorial design". [3]