= Aliasing in a fractional factorial design
{title2=$\chi_{AG}=s_G\chi_A$}
Two <factorial contrasts> are aliased if their columns are proportional on the selected <fractional factorial design>. A word $G$ that has fixed sign $s_G$ gives $\chi_{AG}=s_G\chi_A$. Conversely, averaging a character over the fraction vanishes unless its word belongs to the <defining contrast subgroup>, so every alias class is exactly a subgroup coset. In a half fraction each class has two distinct words; their separate coefficients cannot be identified without assumptions or additional runs.
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