Video 5. How to Confound Three or More Effects in Eight or More Blocks in 2K Design of Experiments Explained.

If the experiment is designed for five variables, which requires 32 experimental units to complete a full replication. However, if there are only four samples/experimental units can be prepared from one batch, a total of 8 numbers of batches is required to produce 32 samples (4X8) to complete one full replication. Three higher-order interaction terms are needed to be confounded with 8 blocks because three factors (higher-order interaction terms in this case) produce a total of eight treatment combinations like a 2³ full factorial design (Table 3). Any three higher-order interaction terms can be chosen for the purpose of confounding with 8 blocks. Table 9 shows confounding technique for three higher-order interaction ABCD, ABCE, and ABDE. Their generalized interactions of ABCD*ABCE=DE, ABCD*ABDE=CE, ABCE*ABDE=CD, & ABCD*ABCE*ABDE=ABE are also confounded with blocks, resulting in a total of 7 effects, including three higher-order interactions and their generalized interactions of a total of 4, cannot be distinguished from the block effects. The seven indistinguishable effects can also be understood by the seven degrees of freedom for the block effects (7=8-1).

Table 9. Block Assignment for Three Confounded Effects to Produce 8 Blocks in -1/+1 Coding System.

The complete assignment of the 8 blocks for three confounding effects can be found in Table 10. Similarly, any desired number of confounding and their associated blocks can be developed.

Table 10. Assignment of Eight Blocks for Three Confounding Effects in a 2⁵ Factorial Design of Experiments