I have a question regarding the output of the ROOT macro
StandardHypoTestInvDemo.C, which I am using to carry out an inverted hypothesis test.
As you might know, the value of the expected upper limit using the median of the alternate model (for sensitivity studies) is given by the crossing point between the
(1-CL) horizontal line and the median line in the p-value plot (see figure attached). The 1sigma and 2sigma expected limits are also calculated from this plot, and although I can see clearly where the values for the (-1 sig), (+1 sig) and (+2sig) expected limits come from, I am finding difficult to understand how the (-2sig) point is actually calculated.
As you can see in the example attached, the red horizontal line is crossing the 1sigma green band and the upper part of the 2sigma band. However, what is happening for the lower part of the 2 sigma band? For this particular example I am getting the following results:
expected limit (median) 6.618925
expected limit (-1 sig) 3.913686
expected limit (+1 sig) 12.378785
expected limit (-2 sig) 2.281817
expected limit (+2 sig) 18.912360
What is the program doing to get a value which is different from 0 for the expected limit (-2 sig)?
Also, if the right answer is actually 0, do you have any recommendation on how to calculate this lower 2 sigma limit properly to avoid the 0 (which will result in a limit with an error bar that goes all the way to 0)?
Thanks and kind regards,