Interpretation of data showing something has one effect sometimes and a different effect in other circumstances: Theories of interaction of factors

A possible explanation of interaction is that quantities derived from the independent variables separately add together, but then a curvilinear relationship intervenes between their total and the dependent variable observed. It is shown that two different theories of this type are always available to explain crossover interaction in a 2x2 table. For example, one theory may say that a good outcome occurs when there is an approximate match between values associated with the independent variables, and the other theory that a good outcome occurs when the total of values associated with the independent variables is either decisively small or large, with poorer outcome resulting from intermediate values.T. P. Hutchinso