# [Ifeffit] R-factor uncertainty

Scott Calvin SCalvin at slc.edu
Fri Jan 5 12:19:17 CST 2007

```Hi Lisa,

>At 07:23 AM 1/5/2007, you wrote:
>
>I have a question about the R factor: how can I decide if the
>difference between the R factors of 2 fits is statistically
>significant, i.e, how can I calculate the uncertainty which has to
>be associated to the R factor?
>

As I understand it, you can't. The R-factor is not a proper
statistical measure, as it doesn't incorporate any measure of data
quality. That's the great weakness of this measure of quality-of-fit.
It is also its strength, as estimating the uncertainty in EXAFS data
is notoriously problematic.

The complementary statistic is reduced chi-square. It does
incorporate a measure of data quality. By default, ifeffit uses noise
from high in the FT to estimate this. That's a reasonable idea, but
can be problematic. It has been shown (by Matt and/or Shelly, as I
recall), that there may in some cases be signal in the part of the FT
ifeffit is using to estimate noise. There are also cases where the
noise may not be "white," that is, the noise high in the FT may be a
poor estimate of the noise low in the FT. Ifeffit does allow you to
specify a value of the measurement uncertainty instead, so if you
think you have a way of doing this, go ahead.

What does all this mean in practice? It means, in my opinion, that
the actual =value= of the reduced chi-square statistic is usually
meaningless, unless you have a good way of coming up with the
measurement uncertainty (for example, your sample may be so dilute
that errors are dominated by counting statistics). But reduced
chi-square is a great statistic for comparing two fits to a given set
of data, particularly if the k-range, k-weighting, and k-window are
the same for the two fits. For example, you can apply statistical
tests of significance, if you'd like. The R-factor then provides the
reality check that the fit is "good" at all. The R-factor isn't doing
anything other than what you can see by looking at a graph, but is a
nice shorthand for tables showing the results of many fits and
similar applications. If there's a big R-factor (say, 0.20), the
question of statistical significance isn't necessary to tell you that
you haven't got a conclusive positive result: maybe the R-factor is
big because the fitting model is lousy, or maybe it's big because the
data quality is lousy, but either way the fit shouldn't be trusted.

I'd also add that your eye tells you considerably more than the
R-factor, because you can tell the character of the mismatch. Is it
in the high part of the FT, low, or evenly throughout? Is the miss
primarily in amplitude, or phase? I often find I choose a fit with an
R-factor of 0.03 over one with 0.01, if, for example, the 0.03
reproduces qualitatively all the features in the data but has small
errors in the amplitude of the peaks, while the 0.01 fits the first
part of the spectrum perfectly but misses some peak altogether.

Hope that helps...

--Scott Calvin
Sarah Lawrence College

```