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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.
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
Huck, S. W. & McLean, R. A. (1975). "Using a repeated measures ANOVA to analyze the data from a pretest-posttest design: A potentially confusing task". Psychological Bulletin, 82, 511–518. Pollatsek, A. & Well, A. D. (1995). "On the use of counterbalanced designs in cognitive research: A suggestion for a better and more powerful analysis".
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.
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}}} .
Design–Expert offers test matrices for screening up to 50 factors. A power calculator helps establish the number of test runs needed. ANOVA is provided to establish statistical significance. Based on the validated predictive models, a numerical optimizer helps the user determine the ideal values for each of the factors in the experiment. [7]
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 ...
To enable efficient estimation of driving and modulatory effects, a 2x2 factorial experimental design is often used - with one factor serving as the driving input and the other as the modulatory input. [2] Resting state experiments have no experimental manipulations within the period of the neuroimaging recording.