I have 20 human subjects doing a task under 2 different difficulty conditions. (So it's a repeated measures design)
Each person has a different performance in each of the task difficulty conditions, so I can rank-order them. I want to test whether there are differences between the ranking of performaces between conditions.
I'm essentially looking for a test that would give me a significant result when there is no correlation between measures.
EDIT: To clarify, I want to see if the rank order 1 2 3 4 5 6 7 8 9 10 is different from the rank order 1 3 4 5 2 8 9 6 7 10
The Wilcoxon signed-rank test -and other rank-based statistics- won't do, because their null hypothesis (unless I'm mistaken) is that the median of the two ranks is equal. This allows to test overall differences in rank order (when the two conditions are ranked together). What I need is a test that will compare whether the order itself changes.
Can anybody point me to a test that has the null hipothesis that the rank orders are equal?