On Mar 14, 2008, at 5:41 AM, Franz Werner wrote:
w=1/Yo**2 [weighting] is proposed ("By using the new weighting scheme, the accuracy of positional parameters of the test sample was significantly improved relative to the weight function 1/Yo, which weights the medium and strong intensities more heavily, is in accordance with statistical theory and gives a better overall fit between the observed and calculated powder patterns.").
I'll give my stock comment in response. For fitting of data with only statistical errors, you obtain the smallest uncertainties on the fit parameters when weighting is w = sigma**-2. This requires that you know the experimental uncertainties (no image plates or other non- quanta counting detectors). Further, if your data have only statistical errors, then chi**2 ~= 1. Any other weighting scheme is effectively throwing away data.
In cases where there are non-statistical error sources, then you do gain by down-weighting the data most effected by systematic errors. However, be aware that the systematic error you are choosing to reject could be trying to tell you that really would want to know: e.g. the model you are using is incomplete or even wrong.
If you have reason to believe that your measurements are inaccurate in a particular way (for example uncorrected deadtime, sample roughness, or funky peak shapes, etc) it might make sense to change the weighting function, but I personally don't think there is a generic source of error in all diffraction measurements that would make it appropriate to use the same weighting change for all types of data and materials.
Brian
