Interactions (More...)

How can we summarize these results? Is it appropriate to conclude that (1) challenging tests make students work harder, (2) achievement-oriented students work harder than achievement-avoiders? None of these statements captures the essence of this clearly systematic pattern of means. The appropriate way to summarize the result would be to say that challenging tests make only achievement-oriented students work harder, while easy tests make only achievement-avoiders work harder. In other words, the relation between the type of test and effort is positive in one group but negative in the other group. Thus, the type of achievement orientation and test difficulty interact in their effect on effort; specifically, this is an example of a two-way interaction between achievement orientation and test difficulty. (Note that statements 1 and 2 above would describe so-called main effects.)
For more information regarding interactions, see Interaction Effects in the ANOVA chapter.