On Tue, 25 May 1999 [EMAIL PROTECTED] wrote:
> Not necessarily. In order to get the ESD, the variance-covariance matrix is
> multiplied by chi^2, and the roots of the diagonal elements are taken.
The justification for multiplying by chi^2 is to assume that the
systematic errors are really just due to overestimated counting statistics
and you can rescale the weight of each data point accordingly. A question
arises as to whether you should rescale each pattern's esds according to
the individual patterns chi^2 or do you have to use the overall chi^2 for
both together?
Thinking of an (over-determined) D20 data and an (under-determined) lab
x-ray data set then it makes sense to rescale errors for the D20 data but
not the x-ray (common sense?!). It seems as if the method for calculating
the esd's is nonsense - surely one can only justify rescaling the weights
on a per dataset basis. The systematic errors which are being accounted
for in each dataset are different. Fullprof (multipattern) does give a
chi^2 per pattern although I don't know how it gets the esd's, GSAS
doesn't so I assume it degrades the esd's. (I read that the multiplication
by chi^2 has no basis in statistics anyway :)
So is it compulsory to multiply by the overall chi^2? If not then I see no
reason for a degradation unless the individual fits get worse due to a
disagreement over a parameter.
> Therefore, if the chi^2 of the combined refinement is worse than that of the
> individual ones, the ESD will automatically be worsened. I think this is by
> far the commonest case.
Agreed although I'm interpreting it as an odd method for estimating an
error. Is it set in stone?
> .... Also, by adding reflections that are insensitive to
> a given parameter my feeling is that you increase the esd on that parameter
> even if chi^2=1, but the proof of this is too tedious.
Can you direct me to a text with this tedious proof? My feeling is that if
the derivative of a data point w.r.t a parameter is small or zero then it
does not affect the LSQ calculation unless it alters the chi^2. If the
chi^2 is 1 then how do an extra bunch of zero derivatives affect an
esd??? For example adding or excluding background regions shouldn't alter
the esd's on positions provided the chi^2 is unchanged.
Is there anything other than GSAS for doing combined fits anyway?
Apologies to the list if I am displaying my ignorance, sometimes it's the
quickest way to learn.
Jon Wright
PS: Sorry to pick at your comments Paolo, it's a shame I'm not at RAL at
the moment. Could have discussed it out over a coffee...
