With any factorial design, one possible outcome of the analysis is a significant interaction. If this occurs, it must not be ignored. Whether or not the main effects are significant, these will be unable to provide an adequate summary of the results by themselves. In addition, interpreting an interaction by eye is also inadequate. This is illustrated in Figure 10.1. Suppose that you were predicting the pattern of data on the top left-hand side, but instead obtained the data on the top right-hand side. The circled cell means were predicted not to be significantly different, but appear to be different on the graph. The only way to determine whether or not this unexpected difference is significant is to conduct the follow-up tests to be described in this chapter. As a further example, consider that a
large expected difference on the bottom left-hand graph in Figure 10.1 has turned out to be slightly smaller than expected, as shown by the circled cell means on the bottom right-hand graph. Again, without further statistical tests, there is no way of knowing whether or not the outcome has gone against the prediction.