## How to quantify the discrepancy between two observational results with errors?

Yun-He Li
Posts: 2
Joined: March 16 2012
Affiliation: Northeast University of China

### How to quantify the discrepancy between two observational re

When reading the original papers from Planck Collaboration, I am always confused by the sentence like that ''this measument ($H_0=73.8\pm2.4$ km/s/Mpc) is discrepant with the planck estimate ($H_0=67.3\pm1.2$ km/s/Mpc) at about the 2.5$\sigma$.''

Here, how is the value of 2.5$\sigma$ calculated?

I have tried many ways to get this result, but none of them satisfies me. Can anybody enlighten me?

Antony Lewis
Posts: 1484
Joined: September 23 2004
Affiliation: University of Sussex
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### Re: How to quantify the discrepancy between two observationa

If you have two independent measurements of H, H1 and H2, with Gaussian errors, then you'd expect mean(H1-H2)=0, with variance \sigma^2=\sigma_{H1}^2 + \sigma_{H2}^2. In this case |H1-H2| ~ 6.5, \sigma^2~2.68, and hence |H1-H2| ~ 2.4 sigma.

Yun-He Li
Posts: 2
Joined: March 16 2012
Affiliation: Northeast University of China

### Re: How to quantify the discrepancy between two observationa

Antony Lewis wrote:If you have two independent measurements of H, H1 and H2, with Gaussian errors, then you'd expect mean(H1-H2)=0, with variance \sigma^2=\sigma_{H1}^2 + \sigma_{H2}^2. In this case |H1-H2| ~ 6.5, \sigma^2~2.68, and hence |H1-H2| ~ 2.4 sigma.
Although this approach give a slightly different value, it is definitely a scientific approach. Now I can decide which way to use. Thanks a lot!