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How to quantify the discrepancy between two observational results with errors?
 
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Yun-He Li



Joined: 16 Mar 2012
Posts: 2
Affiliation: Northeast University of China

PostPosted: June 18 2014  Reply with quote

When reading the original papers from Planck Collaboration, I am always confused by the sentence like that ''this measument (H0 = 73.8±2.4 km/s/Mpc) is discrepant with the planck estimate (H0 = 67.3±1.2 km/s/Mpc) at about the 2.5σ.''

Here, how is the value of 2.5σ calculated?

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



Joined: 23 Sep 2004
Posts: 1300
Affiliation: University of Sussex

PostPosted: June 19 2014  Reply with quote

If you have two independent measurements of H, H1 and H2, with Gaussian errors, then you'd expect mean(H1-H2)=0, with variance σ2=σH12 + σH22. In this case |H1-H2| ~ 6.5, σ2~2.68, and hence |H1-H2| ~ 2.4 sigma.
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Yun-He Li



Joined: 16 Mar 2012
Posts: 2
Affiliation: Northeast University of China

PostPosted: June 20 2014  Reply with quote

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 σ2=σH12 + σH22. In this case |H1-H2| ~ 6.5, σ2~2.68, 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!
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