Video 7 demonstrates the complete vs partial confounding in 2k designs, and their appropriate use.

If the replications are possible with confounding and blocking experiments, the confounding can be performed either completely or partially depending on the interest of the research questions or hypothesis. For an example, the ABC interaction is completely confounded with blocks in Figure 2 (Kempthorne 1952; Yates 1978; Montgomery 2013). In this situation, the three-way ABC interaction is not an interest of the experiment. In this design, no information can be retrieved for the ABC interaction. However, all the main effects and the second-order interaction can be obtained 100%.

However, if some information is useful for the ABC interaction, it could be partially confounded as in Figure 3. In this situation, the ABC, AB, AC, and BC are confounded with blocks in the replication I, II, III, and IV, respectively. Therefore, 3/4th (75%) information can be retrieved for each of the interaction terms. For an example, the AB interaction effect can be obtained from replication I, III, and IV. This confounding process is known as partial confounding (Yates 1978; Hinkelmann and Kempthorne 2005; Montgomery 2013). Nevertheless, three-way interaction ABC effect is rarely a practical interest. Therefore, complete confounding of higher-order interactions for the interest of the lower-order interactions would be preferable.

Figure 2. Complete Confounding: ABC Interaction Confounded with Blocks in All Four Replications

Figure 3. Partial Confounding: ABC, AB, AC, and BC are Confounded with Blocks in Replication I, II, III, and IV, respectively

ANOVA Table for a Partially Confounded 23 Design