I have seen some other posts related to using the ratio of means vs. the mean of ratios, but I'm still confused about some things and hoping to get a little more clarity.
First, from what I've read, I've (perhaps mistakenly) drawn the conclusion that the ratio of means may be better if you have sampled an entire population and the mean of ratios better if you have sampled a sample of the population -- any truth to this?
Second, I read a few things that seemed to indicate that outliers will affect the ratio of means more because higher denominators are weighted more, whereas in the mean of ratios, each observation is weighted equally. Is this accurate? I then found this great paper and it seems to suggest the opposite.
Finally, I was hoping someone could maybe explain some of this in examples I am much more acquainted with. I've seen some examples given on various forums using economics terms and those make sense when I read them. But when I try to apply it to other ratios I've worked with I still can't quite grasp it. I am working with fisheries data right now and I also have experience in terrestrial biogeochemistry, so a couple of relevant ratios to me are:
$$ \text{fishing effort} = \frac{\text{catch}}{\text{angler}\text{ day}} $$
$$\text{N:P ratio} = \frac{N_\text{concentration in a leaf}}{P_\text{concentration in a leaf}}$$
My instinct is to use the mean of ratios for both of these but I couldn't tell you why.
Any help is very much appreciated.
