My statistics classes are far behind me, so bear with me going forward.
Let A and B be positive real numbers. B is always an offset of A, to a small margin of error.
B = A + offset ± margin
We can measure A and B repeatedly, but with the following caveats:
- Any measurements of A and B will be with a resolution r. That is, we can only ever know the integer n for which A is within [n·r,(n+1)·r[. The exact value of r is known and does not change.
- True value of A and B will change between measurements, although the offset stays the same. The distribution is even.
An example:
margin = 1
r = 10
1st set: we measure A to be within [20,30[ and B to be within [40,50[
2nd set: we measure A to be within [20,30[ and B to be within [30,40[
3rd set: we measure A to be within [10,20[ and B to be within [30,40[
...
Nth set: we measure A to be within [20,20[ and B to be within [40,50[
Given enough sets (a big enough N), we should be able to approximate offset through probabilities, to a certain confidence interval.
How to calculate N for a desired confidence interval p? Or how to calculate p for a given N?
What is giving me trouble is the facts that the distribution is even and that there is an upper limit to the error in the approximation of offset, given by the resolution r. Also not sure how margin interacts here, but it is small enough that it could probably be disregarded.