[Ifeffit] Double dipping

[Scott Calvin]

Hi all,

Interesting discussion. It seems to me that one issue of importance 
in these cases is the uncertainty in the difference of the parameters 
between sites. In Shelly's case, it certainly seems reasonable to say 
that the coordination number decreases from set 3 to 4 to 5, with the 
difference between 3 and 4 being statistically significant, and the 
difference between 4 and 5 being borderline. Fixing S02 introduces a 
very similar fractional error to every determination of N, and thus 
does not affect determinations of difference. The same may be true of 
sigma2, although it also possible that changes in coordination number 
are accompanied by changes in sigma2 that are not being allowed under 
this scheme.

If your willing to believe that the sigma2 is similar for all 
samples, it seems reasonably conservative to me to assume the 
uncertainties found in the constrained fits are independent and add 
them in quadrature to get the uncertainties in the differences: Ncas4 
- NCas3 = -0.7 +/- 0.4; Ncas5 - Ncas4 = -0.5 +/- 0.6. It would then 
be reasonable to assign an uncertainty of +/- 0.9 to the absolute 
value of Ncas3, although the relative values are known more 
precisely. Comments?

--Scott


>Hi Matt,
>
>I think that your reply sounds reasonable.  Lets talk some more about this.
>>  The other side of this is that I think it's more difficult than
>>  generally acknowleged to over-interpret data.  Most of the cases
>>  I've seen are due to blatantly ignore the confidence limits or do
>>  completely unfair things like fitting So2 to get 0.9+/-0.1, then
>>  fix So2 to 0.90, fitting N, and claiming N to better than 10%.
>>  Those are serious, but are the normal mistakes in analysis that
>>  can happen with any data.
>
>If you fix s02 and then you fit N and get a error lets call it dn.  Then the
>more generous estimation of the uncertainty for N is d(s02*n) = ds02*n +
>s02*dn.  How would you estimate the error for N if you fix s02, R and
>sigma2? 
>
>I will try to be more specific to my original problem.  lets say that the
>original data set (s3) gives these results for the Ca shell. 
>Ncas3=3.4+/-0.9
>Rcas3=4.01+/-0.01
>sigma2cas3=0.006+/-0.3
>s02s3=1.05+/-0.10
>
>Now I run another fit and I fix all the parameters except for Nca. This time
>I fit three data sets s3, s4 and s5 together and I get these results.
>Ncas3 = 3.2+/-0.1
>Ncas4 = 2.5+/-0.4
>Ncas5 = 2.0+/-0.4
>What would you think would be an "appropriate" uncertainty?  Surely 0.1 is
>too small for Ncas3 but 0.9 seems rather huge.  So we have some limits but
>can I do any better than that?  The difference is between these to extremes
>is quite profound.  In one case we see a change in the value for Nca in the
>other we see nothing.
>
>Shelly
>
>

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