I have a problem trying to figure out why the mean of a/b is not the same as the mean of b/a and if there is an interpretation to that.
Basically, I am trying to compare the relative size of a to b for sample X to the relative size of a to b for sample Y. The result is the relative size of a to b in sample X is larger than that of Y.
When I do the reverse by using relative size of b to a, I expect that sample Y is now larger than X but my result showed that sample X is still larger than Y. Which in my opinion does not make sense and I could no longer interpret the reason behind it. Thereafter, I calculated the mean of a/b and mean of b/a and they are not the simply the reverse of each other - maybe the reason behind it will enlighten me.
If anyone can explain this to me, it would be greatly appreciated!