Confound an Effect
-1/+1 Coding System Method
Video 2 demonstrates the process of confounding and blocking using the -1/+1 coding system.
Using the -1/+1 coding system, the confounding can be performed as described in the following steps.
1. Produce the signs -1/+1 for the effect of ABC interaction column by simply multiplying the main effect columns of A, B, and C.
2. Multiply the effect ABC effect column with the treatment combination column to find the contrast of ABC.
3. Run all the positive treatment combinations in one block and all negative ones in another block.
Table 4. The 23 Factorial Design of Experiments with two blocks
With this +1/-1 coding system, it is not really necessary to produce the contrast. Simply, all the positive signs go into one block, and all negative signs go into another block. However, visually, it is easier to understand why the effect of the ABC interaction cannot be determined from this experiment. Figure 1 shows the graphical representation of the 23 design with ABC confounded with block. As all the “highs” of ABC are run in block #1, and all the “lows” of ABC are run in block #2, it won’t be possible to distinguish whether the effect of ABC is due to the block or by its own. Therefore, the name confounding is appropriately justified for the ABC interaction effect in this design.
Figure 1. Graphical Representation of Blocking and Confounding in a 23 Design with ABC Confounded with Block.