I'm actually reading the book "A handbook of statistical analysis using SAS"
When talking about an ANOVA analysis the author discuss the results of a model in which a dependent variable is analyzed with the three independent variables diet, biofeed and drug:
The diet, biofeed, and drug main effects are all significant beyond the 5% level. None of the first-order interactions are significant, but the three-way, second-order interaction of diet, drug, and biofeedback is significant. Just what does such an effect imply, and what are its implications for interpreting the analysis of variance results? First, a significant second-order interaction implies that the first-order interaction between two of the variables differs in form or magnitude in the different levels of the remaining variable. Second, the presence of a significant second-order interaction means that there is little point in drawing conclusions about either the non-significant first-order interactions or the significant main effects.
I can't understand the interaction explanation. I know that the interaction coefficient is statistically significant when the magnitude of the effect vary across the values of the covariates but what about the second order interaction term?