From: Chris Lidman (clidman@eso.org)
Date: Tue Mar 09 2004 - 12:38:52 PST
Hi Serena,
Thanks for re-computing the standard deviations for each sample
separately. I think this is the statistic that should appear in column
5 of table 4.
One final question. What is the reason for the slight increase in the
dispersion for the CfA2 sample. Is this because you use the denominator
n(n-1) in computing the standard deviation for the first case
(as the means is determined from a fit to the same sample) and n^2
in computing the standard deviation for the second case (as the mean
is determined from the fit to all samples)?
Cheers, Chris.
On Tue, 2004-03-09 at 09:58, Serena Nobili wrote:
> Hi Chris,
>
> I have build the Hubble diagram for each of the data sets separately, as
> you asked. The results are not very different from what we already know,
> within uncertainties, although as you said the Calan/Tololo show a slight
> decrease in the weighted standard deviation (0.14 +- 0.06 instead of
> 0.16 +- 0.06)
>
> First column is the dispersion about the fit made on each of the sets, and
> the second column is the dispersion about the line fitted in the whole
> set (column 5 of table 4 of the paper).
>
> sigma_w sigma_w(paper)
> CT 0.14 +- 0.06 0.16 +- 0.06
> CfA 0.27 +- 0.06 0.27 +- 0.06
> CfA2 0.15 +- 0.05 0.14 +- 0.04
>
> Cheers,
>
>
> Serena
>
>
>
> On 3 Mar 2004, Chris Lidman wrote:
>
> >>
> >> >In relation to the numbered items.
> >> >
> >> >1) There was concern for the way the dispersion in the Hubble diagram
> >> > is computed. Serena should compute the weighted r.m.s.
> >> >
> >> >Serena's reply ...
> >> >
> >> >I have done this. The weighted r.m.s. gives about the same values as
> >> >the non-weighted r.m.s. due to the uncertainties, which are about the same
> >> >for all the points. However, Table 4 now includes the weighted r.m.s. as
> >> >well as the weighted average for each of the samples. I have also added a
> >> >discussion in section 3 about the differences between the data sets.
> >> >
> >> >Chris' comment ...
> >> >
> >> >I think that we were also interested in seeing the RMS scatter about
> >> >the individual Hubble lines and not the scatter about the Hubble line
> >> >that is derived from the entire data set. Was the RMS calculated in
> >> >this way? It is not 100% clear in the paper.
> >> >
> >>
> >> I think the mean value of the residuals for each data set (column 4 of
> >> Table 4) should be taken as an indication that differences are not
> >> important. Although I could run the fit on each data set separately, I
> >> don't think this is really relevant, given the low statistics of each of
> >> them separately, e.g. only 6 SNe are in the CfA sample. For the same
> >> reason I think any claims on differences between the data sets
> >> (which I don't clearly see anyway), should be done very carefully.
> >>
> >
> >Nevertheless, I think it should be done. I understand that the sample
> >size is small, but I expect that you'll find that the RMS for the
> >Calan/Tololo sample will show a significant decrease. I do not
> >expect there to be much of a change for the CfA and CfA2 samples.
> >
>
>
>
>
>
>
> ----------------------------------------------------------------------
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>
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>
>
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