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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.
Statisticians [2] [3] describe stronger multifactorial DOE methods as being more “robust”: see Experimental design. As DOE software advancements gave rise to solving complex factorial statistical equations, statisticians began in earnest to design experiments with more than one factor (multifactor) being tested at a time.
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.
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.
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
Replication in statistics evaluates the consistency of experiment results across different trials to ensure external validity, while repetition measures precision and internal consistency within the same or similar experiments. [5] Replicates Example: Testing a new drug's effect on blood pressure in separate groups on different days.
An experimental nasal spray has helped clear toxic protein buildups in the brains of mouse models of Alzheimer's. Its developers believe the spray may help delay Alzheimer's by at least a decade.
(where ! denotes factorial) possible run sequences (or ways to order the experimental trials). Because of the replication , the number of unique orderings is 90 (since 90 = 6!/(2!*2!*2!)). An example of an unrandomized design would be to always run 2 replications for the first level, then 2 for the second level, and finally 2 for the third level.