CosmoCoffee

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

Here, how is the value of 2.5[tex]\sigma[/tex] calculated?

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

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.

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!