I've just started on a project. The existing experiment is looking at the effect of factor B on factor A. Both factors have only 2 levels (for ease lets say these relate to presence or absence of the factor). Now normally one would design such an experiment to be fully factorial so that you could perform a 2x2 ANOVA. i.e.
Where A+ = factor A present, and A- = factor A absent etc.
However the actual design of the experiment is as follows:
So there is no condition where both factor B and factor A are absent, factor B only occurs when A is also present. The experiment uses a full repeated-measures design (i.e. all participants contribute to all conditions).
My questions are
1) How do you go about analyzing the data from this 'unbalanced' design? I would have thought you couldn't really use an ANOVA because the design isn't fully factorial, and therefore you effectively can't have a 'factor B'. Is that correct? The only alternative I can think of is to calculate the effect of factor A separately for the two conditions, and then do a t-test of the difference in these effects of factor A.
i.e. T-test of [A+B+ - A-B-] vs [A+B- - A-B-]
2) At a descriptive level, what is the difference between what the fully factorial design would do, and what the current, unbalanced experiment is doing? My thoughts are that the interaction for the fully factorial design would show how the effect of Factor A is influenced by occuring in the context of factor B (or vice versa), whereas in the unbalanced design you are seeing how the presence of factor B alongside factor A effects the impact of the presence of factor A! Can anyone shed any light on whether this is correct.
Thanks in advance.