Defining contrast subgroup
= Defining contrast subgroup
{title2=$\mathcal H=\langle G_1,\ldots,G_k\rangle$}
Factor subsets multiply by <symmetric difference>; their sign columns multiply pointwise. The subgroup generated by independent defining words has $2^k$ elements. On a selected <fractional factorial design>, every word in this subgroup is constant, with sign determined by the chosen generator signs. The cosets classify identical or opposite contrast columns.