Re: French's Primordial Study and Schramm & Turner, 1997

From: Franz Heymann (notfranz.heymann_at_btopenworld.com)
Date: 06/22/04 

Date: Tue, 22 Jun 2004 21:23:43 +0000 (UTC)

"greywolf42" <mingstb@marssim-ss.com> wrote in message
news:10dgs7c2ouu98b6@corp.supernews.com...
> Franz Heymann <notfranz.heymann@btopenworld.com> wrote in message
> news:cb8r6j$akd$1@hercules.btinternet.com...
> >
> > "greywolf42" <mingstb@marssim-ss.com> wrote in message
> > news:10deshvq6vtcd06@corp.supernews.com...
> > > Joseph Lazio <jlazio@adams.patriot.net> wrote in message
> > > news:ll8yei4vnb.fsf@adams.patriot.net...
>
> {snip higher levels}
>
> > > > Of course the fact that the uncertainty on every point is
larger
> > > > than the total range of the data does not prevent one from
> > > > determining the mean of the data fairly well. In general, if
the
> > > > typical uncertainty on a datum is s, then the uncertainty on
the
> > > > mean of the data derived from N data is s/\sqrt(N). For data
> > > > samples containing, say, 20 data, that means that the mean
> > > > can be derived with about 5 times less uncertainty than the
> > > > individual data.
> > >
> > > This is theoretically true, but only in Bayesian statistics.
> >
> > That is incorrect.
> > Lazio's statement is correct in the case of ordinary old
fashioned
> > least squares analysis.
>
> How did you determine that the relationship was linear, Franz? This
isn't a
> case of simply finding the mean of several measurements of a single
value.
> (Which I believe Joseph understood, even though he used the improper
term
> 'mean of the data.')
>
> > > My point is
> > > that there is no support in such a noisy distribution for a
linear
> > > fit.
> >
> > You are wrong.
> > If the errors for the individual measurements are known, (as they
are
> > in the case under discussion) a correctly applied least squares
fit to
> > the data will yield no only the values of the parameters, the
> > uncertainties associated with the errors, but also an estimator as
to
> > the significance of the expression used to parametrise the data.
>
> How did you determine that the relationship was linear, Franz?

Very simple. Fit a hypothesis that the relaionship contains a square
term as well and study the values of the fitted parameters and their
associated errors. If your square term is insignificant, its
magnitude will be swamped by its error.
>
> > > Certainly one can impress a linear fit to the data. However,
there
> > > is no experimental support *FOR* the linear fit in this case.
One can
> > > draw *any* straight line they wish through a shotgun scatter
plot --
> > > and get 'uncertainty of the mean'.
> >
> > You are once again wrong. A good experimenter will determine the
> > chi-squared parameter of the fit. If the straight line was not a
> > statistically valid form for the parametrisation, the value
obtained
> > for chi-squared would tell you so.
>
> A chi-squared value can be obtained for any straight line drawn
through
> otherwise random (or even non-random) data. Now, one can pick the
'best' of
> the infinite number of fits. But this was not done. The assumption
of the
> Big Bang was used to determine the line (a Bayesian prior), then
selected
> data was used (with discordant data thrown out).

I was not commenting on a specific case of fitting parameters to a
specific set of data.
I was merely pointing out that you were burbling when you said

"This is theoretically true, but only in Bayesian statistics."
>
> At least Joseph was trying to address the science issues. You are
simply
> frothing at the mouth (as usual).

If telling you that you are bullshitting is frothing at the mouth,
then so be it.

Franz

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