[Hps-analysis] combined errors

[Timothy Nelson]

Stepan,

When combining multiple independent measurements of a quantity, the error on the combined value depends only on the errors of the individual measurements and the number of measurements, and not on any systematic shift between the two independent techniques. I understand that it is natural to think otherwise, but this is basic statistics.

To make this more intuitive, consider the following thought experiment:

- I have two perfectly precise methods for measuring a length, but they are systematically different by 10%
- I use those methods to measure something that is exactly one meter long.
- Therefore, one technique always gives exactly 1.0 meters and the other technique always gives exactly 1.1 meters
- When I combine those two measurements, the combination is always exactly 1.05 meters, no more, no less.

Obviously, from this extreme example, one can see that a systematic shift, even one that is infinitely larger than the error of either measurement alone, does not result in a wider distribution for the combined result.

Tim