The printout you receive for a log linear analysis is similar to that of an ANOVA, but the interpretation differs somewhat. The test of the A effect is essentially a goodness of fit for that particular variable. A significant A effect would mean that the proportions of cases in each category are not equal on that variable. What would be a significant interaction for an ANOVA (such as AC), would mean in a log linear analysis that a relationship exists between A and C. This is really analogous to a main effect for A, since one variable acts as if it were a dependent variable. By the same logic, a significant ABC effect in log linear demonstrates a significant relationship between A and B on the nominal dependent variable C.

When testing effects in log linear analysis, the goal is to reduce the number of significant effects that it takes to explain the data. Thus, the log linear analysis is not finished until it reaches non-significance for the level of effect you are testing. For example, test ABC first. If it is significant, all effects are necessary to explain the relationships between variables. If it is not significant, test all lower level effects. In the end, the equation should contain only those effects which have been found to be significant (or necessary components of significant effects).