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