Video 6. Blocking and Confounding Explained in 2K Factorial Design of Experiments DOE Using MS Excel 

Using the 0/1 coding system, the linear combinations of the defining relation of all factors are used as in Equation 2. 

Equation 2

For a 23 factorial design,  

therefore, the Equation 2 becomes Equation 3 for confounding the ABC effect.  

Equation 3

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