In my current experiment, I designed a 2 x 2 repeated measures factorial design.
Suppose that first condition has levels of (a / b), and the second condition has levels of (1 / 2). Thus, my factorial design has four groups (a1, a2, b1, b2). When I ran a statistical test, there were main effects of both conditions but no interaction effect.
However, I recently found that one confounding variable exists in my design. Suppose that the confounding variable has three levels (A / B / C). With the confounder added, my design was found to be four groups as (Aa2, Ba1, Bb2, Cb1).
Are there any methods for adjusting the confounding variables in my design? Or, are there any tests for finding the effect of the confounder?
It looks impossible but I cannot logically conclude. Any help would be appreciated!