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Factorial designs allow the effects of a factor to be estimated at several levels of the other factors, yielding conclusions that are valid over a range of experimental conditions. The main disadvantage of the full factorial design is its sample size requirement, which grows exponentially with the number of factors or inputs considered. [6]
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.
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Regular designs have run size that equal a power of two, and only full aliasing is present. Non-regular designs, sometimes known as Plackett-Burman designs, are designs where run size is a multiple of 4; these designs introduce partial aliasing, and generalized resolution is used as design criterion instead of the resolution described previously.
The design with 7 factors was found first while looking for a design having the desired property concerning estimation variance, and then similar designs were found for other numbers of factors. Each design can be thought of as a combination of a two-level (full or fractional) factorial design with an incomplete block design. In each block, a ...
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 ...
Plackett–Burman designs are experimental designs presented in 1946 by Robin L. Plackett and J. P. Burman while working in the British Ministry of Supply. [1] Their goal was to find experimental designs for investigating the dependence of some measured quantity on a number of independent variables (factors), each taking L levels, in such a way as to minimize the variance of the estimates of ...
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".