Sparsity-of-effects principle
Encyclopedia
The sparsity-of-effects principle states that a system is usually dominated by main effect
s and low-order interactions. Thus it is most likely that main (single factor) effects and two-factor interactions are the most significant responses (see factorial experiment
). In other words, higher order interactions such as three-factor interactions are very rare. Formally, C.F. Jeff Wu
and Hamada (2000, page 112) refer to this as the hierarchical ordering principle. They state that the effect sparsity principle actually refers to the idea that only a few effects in a factorial experiment will be statistically significant.
Note: the Wu Hamada principle is only valid on the assumption of a factor space far from a stationary point (Statistics for experimenters; Box, Hunter, Hunter 2005; page 208)
Main effect
In the design of experiments and analysis of variance, a main effect is the effect of an independent variable on a dependent variable averaging across the levels of any other independent variables...
s and low-order interactions. Thus it is most likely that main (single factor) effects and two-factor interactions are the most significant responses (see factorial experiment
Factorial experiment
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. A full factorial design may also be...
). In other words, higher order interactions such as three-factor interactions are very rare. Formally, C.F. Jeff Wu
C.F. Jeff Wu
C.F. Jeff Wu is a statistician known for his work on the convergence of the EM algorithm,resampling methods like bootstrap and jackknife, design of experiments, and robust parameter design .- Notes and references :*- Sources and links :*...
and Hamada (2000, page 112) refer to this as the hierarchical ordering principle. They state that the effect sparsity principle actually refers to the idea that only a few effects in a factorial experiment will be statistically significant.
Note: the Wu Hamada principle is only valid on the assumption of a factor space far from a stationary point (Statistics for experimenters; Box, Hunter, Hunter 2005; page 208)