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The word "factorial" (originally French: factorielle) was first used in 1800 by Louis François Antoine Arbogast, [18] in the first work on Faà di Bruno's formula, [19] but referring to a more general concept of products of arithmetic progressions. The "factors" that this name refers to are the terms of the product formula for the factorial. [20]
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.
Comparison of Stirling's approximation with the factorial. In mathematics, Stirling's approximation (or Stirling's formula) is an asymptotic approximation for factorials. It is a good approximation, leading to accurate results even for small values of .
Principal component analysis (PCA) is a widely used method for factor extraction, which is the first phase of EFA. [4] Factor weights are computed to extract the maximum possible variance, with successive factoring continuing until there is no further meaningful variance left. [4]
A fractional factorial design is said to have resolution if every -factor effect [note 4] is unaliased with every effect having fewer than factors. For example, a design has resolution R = 3 {\displaystyle R=3} if main effects are unaliased with each other (taking p = 1 ) {\displaystyle p=1)} , though it allows main effects to be aliased with ...
Factor loadings indicate how strongly the factor influences the measured variable. In order to label the factors in the model, researchers should examine the factor pattern to see which items load highly on which factors and then determine what those items have in common. [2] Whatever the items have in common will indicate the meaning of the ...
A representation of factors from separate analyses. The small size and simplicity of the example allow simple validation of the rules of interpretation. But the method will be more valuable when the data set is large and complex. Other methods suitable for this type of data are available. Procrustes analysis is compared to the MFA in. [2]
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.