1. Order of Kilopi
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## hubble constant

Could use some help understanding the terms in the Hubble constant. Ho = 69.8 ± 0.6 (stat) ± 1.6 (sys) what is the plus minus 0.6, which I assume is one sigma vs the 1.6 sys? Thanks for any help.

2. kzb
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Originally Posted by Copernicus
Could use some help understanding the terms in the Hubble constant. Ho = 69.8 ± 0.6 (stat) ± 1.6 (sys) what is the plus minus 0.6, which I assume is one sigma vs the 1.6 sys? Thanks for any help.
I wonder if they have followed the ISO Guide on Uncertainty of Measurement (the GUM). It appears not, because random and systematic uncertainties in the GUM are combined in the same way, so that you end up with a single figure for the uncertainty.

3. No, the whole point is to distinguish purely statistical uncertainties (often traceable to 1/square root (sample size), and therefore amenable to shrinkage purely from a larger sample) from identifiable uncertainties due to external unknowns, which cannot be improved just by growing the sample size. This immediately points to areas where further work would be fruitful. Examples in some approaches for the Hubble constant would be the effect of chemical composition on the Leavitt law relating Cepheid periods and luminosity, different amounts of blending of the light of the Cepheids and surrounding star clusters with distance, the extent to which spiral galaxies avoid the center of galaxy clusters and this do not necessarily sample their mean distances... Contemporaneous projects using different samples may share the same systematics, so separating these pieces of the uncertainty budget also make that sort of comparison more clear.

4. Order of Kilopi
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What would be the combined uncertainty, one sigma, two sigma, three sigma, or can't that be done.

5. kzb
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Originally Posted by Copernicus
What would be the combined uncertainty, one sigma, two sigma, three sigma, or can't that be done.

It can be done in principle but we need to know a few things first:

the confidence level of the stated uncertainties and degrees of freedom.

the distribution shape of the "systematic" uncertainty. For example, if this number is a combination of several different uncertainties, we can probably assume it is normally distributed. Or maybe it is a range limit, with every value between the limits equally probable.

If we can sort these out there are standard rules for combining the uncertainties.

6. Order of Kilopi
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Originally Posted by kzb
It can be done in principle but we need to know a few things first:

the confidence level of the stated uncertainties and degrees of freedom.

the distribution shape of the "systematic" uncertainty. For example, if this number is a combination of several different uncertainties, we can probably assume it is normally distributed. Or maybe it is a range limit, with every value between the limits equally probable.

If we can sort these out there are standard rules for combining the uncertainties.
Thanks!

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