- #1
kelly0303
- 563
- 33
Hello! If I have a measurement of a (dimensionless) parameter, ##a##, say 998 +/- 3 and the theoretical prediction of that parameter (assuming known physics) is 1000 +/- 4. Let's say that I want to set limits on a new parameter (not included in the theoretical calculations), call it ##\alpha##, that would contribute additively to ##a##. By comparing the experiment with the theory, I get a = 2 +/- 5 (the errors are all gaussian and I added them in quadrature). I want to set, let's say, a 95% upper bound on the value of a. In general, I could just say a < 12. However, in my case I know that ##a## has to be positive. How would I define the upper bound in this case, knowing that part of the range allowed by a = 2 +/- 5 is in practice not allowed by the physical theory? Also, I am not totally sure if my range would be (1000-998) +/- 5 = 2 +/- 5 or (998-1000) +/- 5 = -2 +/- 5. How do I decide which one to use. The first one would be the conservative choice, but I am not sure if it is not too conservative). Thank you!