I am wondering about the correct statistical analysis for an experiment involving 2 independent variables (treatment A, 4 levels and treatment B, 2 levels) and one dependent variable (C, score). Because subjects undergo all levels of both treatments, I am assuming a two-way within-subject (repeated-measures) ANOVA (4x2) should be used.
However, there is a complicating factor: we used a setup in which we measured C for 2 subjects together, according to the following scheme:
\begin{array}{| l | c | r |} \hline & \text{B level 1} & \text{B level 2}\\ \hline \text{A level 1} & \text{Subject 1} & \text{Subject 2}\\ \text{A level 2} & \text{Subject 2} & \text{Subject 1}\\ \text{A level 3} & \text{Subject 1} & \text{Subject 2}\\ \text{A level 4} & \text{Subject 2} & \text{Subject 1}\\ \hline \end{array}
When looking at treatment A, all subjects undergo levels 1 to 4, so within-subject design. Also, when looking at treatment B, all subjects undergo levels 1 and 2, so again within-subject design.
However, it is not the case that all subjects undergo all levels of A in conjunction with all levels of B, e.g. subject 1 has undergone A level 1 in conjunction with B level1, but not with B level 2. And vice versa for subject 2.
Hence, I am inclined to think that regarding interaction between treatment A and B, a within-subject design might not be correct. Any suggestions would be appreciated.