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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 .
In a fractional factorial experiment, the contrast vectors belonging to a given effect are restricted to the treatment combinations in the fraction. Thus, in the half-fraction {11, 12, 13} in the 2 × 3 example, the three effects may be represented by the column vectors in the following table:
In statistics, a Yates analysis is an approach to analyzing data obtained from a designed experiment, where a factorial design has been used. Full- and fractional-factorial designs are common in designed experiments for engineering and scientific applications.
If a full factorial design becomes too complex due to the sheer number of combinations, researchers can use a fractional factorial design. This method strategically omits some combinations (usually at least half) to make the experiment more manageable.
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.
Designed experiments with full factorial design (left), response surface with second-degree polynomial (right) In statistics, response surface methodology (RSM) explores the relationships between several explanatory variables and one or more response variables. RSM is an empirical model which employs the use of mathematical and statistical ...
An orthogonal array can be used to design a fractional factorial experiment. The columns represent the various factors and the entries are the levels at which the factors are observed. An experimental run is a row of the orthogonal array, that is, a specific combination of factor levels.
A factorial (perhaps fractional) design in the factors studied, each having two levels; A set of center points, experimental runs whose values of each factor are the medians of the values used in the factorial portion. This point is often replicated in order to improve the precision of the experiment;