9.4 Are Interactions Important?
Many of us have learned that, when experimenting with several factors, we must investigate one factor at a time, keeping all others fixed. This method makes it all but impossible to detect factor interactions. A common response to this is that interactions are not important and, in the rare cases when they do matter, we can get rid of them by suitable variable transformations. Statistician George Box inimitably dismisses of these statements in the following, imaginary rabbit breeding experiment .
If we do not know anything about breeding rabbits we may start by an appropriate control case with no rabbits in the hutch, to confirm that this case produces no rabbits. Adding a doe to the hutch we find that this single factor fails to produce any rabbits. Since we have learned to experiment with one factor at a time we now take the doe out and replace it with a buck. After waiting for some time things begin to look black and we might conclude that it is simply not possible to breed rabbits. We have now tried all the combinations in Figure 9.6 except the upper right one. Adding this last case, combining a doe and a buck, we do not only produce a full factorial experiment but a number of little rabbits as well!
The important message is that many important phenomena depend on a combination of factors; ...