I measured a variable during pre- and post-sessions and my research question is whether the change from pre to post is different across various conditions (e.g. (c=1,a=1), (c=2,a=1), (c=1,a=2), (c=2,a=2) etc) and if so, across which.
How can I test whether the differences between pre- and post are significantly different across conditions?
This may sound easy, however, the pre- and post-session measurements are not paired in any meaningful way. Hence, using an arbitrary pairing to compute the differences and then performing an ANOVA for the differences across conditions does not make full use of the dataset.
Alternatively, I think a multi-way ANOVA could be applied with factors (pre/post), c and a (for the above example). In that case, however, it is unclear to me how to figure out across which of the conditions the change from pre to post is significantly different. Posthoc pairwise comparisons would not directly provide such information.
Thank you very much in advance for any help!