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  "body": "\n## Summary\n\nA fractional factorial design runs only a chosen fraction of the combinations of a [[factorial experiment|EHJ3R589ZX]].\nAn example is $2^{k-p}$ of the $2^k$ runs of a two-level design.\nThe fraction is chosen by a defining relation, so that the main effects and low-order interactions can still be estimated.\nThe price is that they are aliased with higher-order interactions.\nThe resolution of the design measures how severe the aliasing is.\nSuch designs make screening experiments with many factors affordable, on the assumption that high-order interactions are negligible.\n\n## Explanations\n\n### L1 human\n\nWith seven factors at two levels, a full factorial needs $128$ runs, often far too many.\nA well chosen eighth of it, $16$ runs, still measures each factor's main effect.\nThe price is that some effects become indistinguishable: in the data, a main effect looks exactly like a certain interaction of other factors.\nIf those interactions are small, nothing important is lost.\n",
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