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
--