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Sparsity of Effects

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The principle of Sparsity or parsimony of effects states that a system/process is essentially driven by a few, key effects and that these effects are more likely to be simple Main Effects and lower-order Interactions rather than the more complex three-factor and higher-order Interactions.


The Effect sparsity principle derives from the maxim known as Occam’s Razor, which states that all things being equal, the simplest explanation is usually the best. It has found widespread application in the field of data-modeling. In fact, the analysis of fractional factorial designs takes advantage of this principle. Such designs study the effects of a large number of factors in less than the complete set of runs, and as a result, lower–order (main and two-factor) effects are confounded/aliased with higher-order (three-factor) effects. But this is not a big problem if we assume that only about 20% of the effects will be significant and that the remaining 80% of the (mainly higher-order) effects are negligible, so that any significant effects basically estimate the main or two-factor effects in the aliased pairs.