I've just read a paper which uses a 2x2 ANOVA on two between subjects independent variables. Effectively they have Factor A (Yes/No) and Factor B (Yes/No) with different participants in each group. They report that both factors show main effects and that there is also an interaction. However the graphical plotting of their data clearly shows that the value of the dependent variable only changes when both factor A AND factor B = yes. The value of the dependent variable is nearly identical for the other three conditions. To me this suggests that there is just an interaction effect - i.e. the factors on their own don't create an effect, only their presence in unison does.

To check whether this wasn't just some effect of their graph being misleading I created some dummy data in SPSS for the same test, such that the mean value of three of the groups was identical, and the value of the fourth was much higher. When I ran the ANOVA I also got both main effects as significant (graph and effects table of data shown - is very similar to that found in the paper).

I'm having some trouble interpreting the results from the paper. Surely they clearly indicate that you need an interaction of the two factors to get an effect, but the authors claim that each factor on it's own causes an effect because of the main effects they found. Can someone explain where either myself or the authors are going wrong in our interpretation?

Thanks

Rob