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Extra info for Six sigma and beyond. / Vol. 5, Design of experiments
In the case of two-factor models, the general case is Yijk = µ + Ai + Bj + ABij + ε k(ij) where I = 1, 2,…a; j = 1, 2,…b; k = 1, 2,…n provided the design is completely randomized. In this model, it is again assumed 2 that µ is a fixed constant and ε k(ij)s are NID (0, σ ε ). If both A and B are at fixed levels, the model is a fixed model. If both are at random levels, the model is a random model, and if one is at fixed levels and the other at random levels, the model is a mixed model. 11. In the assumptions for the mixed model, the fact that summing the interaction term over the fixed factor (∑i) is zero but summing it over the random factor (∑ j) is not zero affects the expected mean squares, as seen in item 3 on the table for EMS.
That is, something depends on something else and the results are somewhat (sometimes quite significant) different, from what they would have been had the factors involved been evaluated separately. Interaction then is the influence that two or more factors have in combination toward an outcome (result). The classic warning against taking certain medications and drinking alcohol is perhaps the most famous interaction of them all. Whereas the medication does benefit the individual if taken as directed, and the alcohol in moderation can contribute to a “good time,” the combination of the two may prove deadly.
It is important to note that, if treatment A has p © 2002 by CRC Press LLC SL3143_Frame_book Page 11 Tuesday, September 17, 2002 4:28 PM Introduction 11 levels and B has q levels a total of pq groups of experimental subjects is required. If one or more of the treatment variables in a factorial design is a classification variable used for blocking experimental subjects into relatively homogeneous strata, the design is also described as a randomized block design. This type of design can also be represented in the same way as a factorial design.