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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 (see factorial experiment). In other words, higher order interactions such as three-factor interactions are very rare. Formally, 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.


  • Wu, C. F. Jeff and Hamada, Michael (2000) Experiments: Planning, analysis, and parameter design optimization, New York: Wiley, ISBN 0-471-25511-4.

See also

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