I'm trying to figure out what the most robust way to compare two ratios is. What I have is a set of proportions between two or more quantities. For example, it might be 0.5:0.5, or 0.45:0.2:0.35. Then I have some measurements of those quantities, for example, I might have 47, 21, 32. What I'm doing is converting those quantities into proportions (so in this case it'll be 0.47, 0.21 and 0.32 - i.e. they add up to 1) and then comparing it to the expected ratio (0.45:0.2:0.35).
0.47:0.21:0.32 is probably close enough to 0.45:0.2:0.35, but what's the best equation for comparing these with an adjustable tolerance?
What I'm currently doing is to take each number in my observed ratio and dividing it by the expected value. Then if the result is within the range of 0.9...1.1, I'm saying it's close enough. Then if all numbers are within this range, then the ratio is close enough. However, the weakness here is that the smallest number in the ratio (in my example, the 0.20) ends up being the most important since it'll end up with the tightest range.
Is there an established way to do this kind of comparison?