I understand what you're saying, but it's highly flawed. You don't know how many people in general live in each area, and that is probably not something which be calculated merely upon size of the area.
Thank you for taking the time read and understand the methodology. It is genuinely appreciated. I really do welcome criticism that addresses the specifics, and criticism that may uncover specific flaws in the method.
To take you up on your point, which is a good point: when I was thinking this through in my mind, as far as I can see, it does not matter what the population density is within each 500 meter radius circle. The only thing that matters is that on average, there is a uniform population density within each 500 meter circle.
A 500 meter circle in the center of a city will tend to have a higher population density than the same circle in the suburban areas. But in either case, the population density will likely be uniform inside the 500 meter circle, on average. That's the key assumption I have based my analysis on.
When you are dealing with a 500 meter circle with uniform population density, you would expect that on average, the incidence of ME/CFS in the inner 300 meter circle would be proportional to its area, and likewise for the outer 300 to 500 meter annulus, the incidence would be proportional to its area.
As I mentioned, the ratio of these two areas is 0.56, so you would expect the ratio of incidence of ME/CFS in these areas to be 0.56 (assuming the null hypothesis, that proximity to base stations is not a risk factor for triggering ME/CFS).
But if you get results that differ from this ratio, with a higher than expected incidence of ME/CFS in the inner 300 meter circle, then by the logic of my analysis, that indicates proximity to base stations may be a risk for ME/CFS.
I'd be concerned about selection bias, this is not a random sample of PWME, those who know they live near a mast may have been much more inclined to click on this thread.
I agree, and I did think about that shortcoming. The self-selecting nature of forum polls responses is problematic in this respect, and I agree, people who know they live near a mobile phone mast may be more inclined to respond to this poll, thereby introducing bias.
But the method I've used should to an extent prevent this bias: because I am only analysing the data of people who live close to (within 500 meters) a base station anyway. I am discarding the data of people who live 500 meters or further from a base station.