. Author manuscript; available in PMC: 2010 Sep 1.

Published in final edited form as: Food Chem Toxicol. 2009 Jun 6;47(9):2183–2188. doi: 10.1016/j.fct.2009.06.003

Table 5.

Aliasing structure between each main effect and two-factor interactions in the quaternary-code design used in Study 2.

\begin{matrix} E ({\hat{β}}_{For}) = & β_{For} + \frac{1}{2} (β_{MC \times Asp} + β_{MC \times Lop} - β_{MC \times Sper} + β_{MC \times DEHP} \\ - β_{Asp \times CC} + β_{Asp \times Sn} + β_{Asp \times BHA} + β_{CC \times Lop} \\ + β_{CC \times Sper} + β_{CC \times DEHP} + β_{Sn \times Lop} + β_{Sn \times Sper} \\ - β_{Sn \times DEHP} - β_{Lop \times BHA} + β_{Sper \times BHA} + β_{BHA \times DEHA}) \end{matrix}

E ({\hat{β}}_{MC}) = β_{MC} + \frac{1}{2} (β_{For \times Asp} + β_{For \times Lop} - β_{For \times Sper} + β_{For \times DEHP})

E ({\hat{β}}_{Asp}) = β_{Asp} + \frac{1}{2} (β_{For \times MC} - β_{For \times CC} + β_{For \times Sn} + β_{For \times BHA})

E ({\hat{β}}_{CC}) = β_{CC} + \frac{1}{2} (- β_{For \times Asp} + β_{For \times Lop} + β_{For \times Sper} + β_{For \times DEHP})

E ({\hat{β}}_{Sn}) = β_{Sn} + \frac{1}{2} (β_{For \times Asp} + β_{For \times Lop} + β_{For \times Sper} - β_{For \times DEHP})

E ({\hat{β}}_{Lop}) = β_{Lop} + \frac{1}{2} (β_{For \times MC} + β_{For \times CC} + β_{For \times Sn} - β_{For \times BHA})

E ({\hat{β}}_{Sper}) = β_{Sper} + \frac{1}{2} (- β_{For \times MC} + β_{For \times CC} + β_{For \times Sn} + β_{For \times BHA})

E ({\hat{β}}_{BHA}) = β_{BHA} + \frac{1}{2} (β_{For \times Asp} - β_{For \times Lop} + β_{For \times Sper} + β_{For \times DEHP})

E ({\hat{β}}_{DEHP}) = β_{DEHP} + \frac{1}{2} (β_{For \times MC} + β_{For \times CC} - β_{For \times Sn} + β_{For \times BHA})