Confounding and Blocking
Linear Combination Method
Video 6 demonstrates the linear combination method for blocking and confounding using the 0/1 coding system.
Using the 0/1 coding system, the linear combinations of the defining relation of all factors are used as in Equation 2.
For a 23 factorial design,
therefore, the Equation 2 becomes Equation 3 for confounding the ABC effect.
To determine the associated block for a treatment combination, simply following steps can be performed provided in Table 11.
1. Add the codes for the factors as in the L column.
2. As the summation values bounce between 0 and 1 coding (known as modulus 2 system or mod 2), value 2 becomes 0, 3 becomes 1, 4 becomes 0, 5 becomes 1 and so on.
3. Finally, assign the treatment combination to one block for all same codes, such as block # 1 for the 0 codes while block #2 for the 1 codes.
Table 11. Assignment of Two Blocks for One Confounding Effect Using 0/1 Coding System