Let's say I studied the shoulders of 10 individuals, and I scored the presence/absence of a criteria (ex: arthrosis, presence=0;absence=1) on the left side and the right side.
I need to test the bilateral asymmetry, to evaluate if there is a statistically significant difference between the left and right side.
So I am dealing with categorical/binary data, which are paired, and there are 4 different possibilities for one individual : no arthrosis at all (0 0); arthrosis on both sides (1 1); arthrosis on the left but not on the right (1 0); and the contrary (0 1).
Considering the nature of data, I assumed the McNemar test was the solution, but if I have for example five pairs with presence on the left and absence on the right (1 0), and the five others with absence on the left and presence on the right (0 1), then McNemar test gives a p value of 1.
If I'm correct, this would mean that there is no significant difference between both sides, while the fact is that there is 100% of bilateral asymmetry since no pair share the same value (no ties).
So maybe the test was not appropriate and I would need to use a Chi square/Fisher's exact test instead? But then, how to make these tests compare the pairs and not globally both sides?(a contingency table from the same example also gives a p value of 1, because there are five 0s and five 1s for each side). Or should I consider the data as ordinal and use Wilcoxon signed-ranks test instead?
I have been looking for a solution for a very long time but have not succeeded. Thank you very much for your help.