I have a small number (<10) surveys given to a small number of respondents (<10) before and after a program of instruction. The survey responses are on a Likert scale, and the results of all questions are summed to produce a raw score (one per survey/respondent pair).
I want to infer whether the difference in mean for these scores are equal for each survey. I am not comfortable with assuming that the variances (or distributions, for that matter) are the same across surveys.
Since the number of respondents is very low, it is not feasible to conduct a test per survey--I'd like an omnibus test to improve power.
Is there a hierarchical version of (or corollary to) the Wilcoxon signed rank test available that will handle this situation?
Something implemented in R would be excellent :-)