怎样计算两个正态分布之间的置信水平 (tension)

转自：https://physics.stackexchange.com/questions/366367/how-to-calculate-the-sigma-level-between-two-normal-distribution

问题：

Recently, the improved local measurement km sMpc from Riess et al. 2016 (hereafter R16) exhibits a stronger tension with the Planck 2016 release km sMpc (hereafter P15) at the level. ... The value of the Hubble constant is consistent with the P15’s result at the confidence level.

How do we figure and level out?

解决：

Trivially, if you have and , then can be determined (assuming the usual approximations of independent uncertainties that are normally distributed) with a precision of .
In this case, the difference in the two determinations of is km/s per Mpc. i.e. different from zero by 3.4 error bars. The σ refers to the size of the uncertainty ; or more specifically, it represents the 68% confidence interval in a normal distribution.

计算过程：