the simulation result should be expressed by: sample mean +- S/sqrt(n), where sample mean is sum/n, and S is square root of sample variance, and n is number of events. Here S/sqrt(n) is the standard error of the sample mean. However, the simulation result in N03 and N03Con is expressed by: sample mean +- S. My suggestion is please correct some statements in the RunAction.cc for example, rmsEAbs = std::sqrt(rmsEAbs); should be: rmsEAbs = std::sqrt(rmsEAbs)/std::sqrt(NbOfEvents); other three statements, like rmsEGap should also be corrected. For examples\extended\analysis\N03Con, it has the same problem. Actually, the calculation in G4ConvergenceTester() is correct.
Done. As results are printed, you are right. However, in HEP, S is also a quantity of interest: it is related to the intrinsic resolution of the calorimeter. This was the initial motivation of the example.