On 1 June 2012 03:22, Edward A. Berry <[log in to unmask]> wrote:
> Leo will probably answer better than I can, but I would say I/SigI counts
> only
> the present reflection, so eliminating noise by anisotropic truncation
> should
> improve it, raising the average I/SigI in the last shell.
We always include unmeasured reflections with I/sigma(I) = 0 in the
calculation of the mean I/sigma(I) (i.e. we divide the sum of
I/sigma(I) for measureds by the predicted total no of reflections incl
unmeasureds), since for unmeasureds I is (almost) completely unknown
and therefore sigma(I) is effectively infinite (or at least finite but
large since you do have some idea of what range I must fall in). A
shell with <I/sigma(I)> = 2 and 50% completeness clearly doesn't carry
the same information content as one with the same <I/sigma(I)> and
100% complete; therefore IMO it's very misleading to quote
<I/sigma(I)> including only the measured reflections. This also means
we can use a single cutoff criterion (we use mean I/sigma(I) > 1),
and we don't need another arbitrary cutoff criterion for
completeness. As many others seem to be doing now, we don't use
Rmerge, Rpim etc as criteria to estimate resolution, they're just too
unreliable  Rmerge is indeed dead and buried!
Actually a mean value of I/sigma(I) of 2 is highly statistically
significant, i.e. very unlikely to have arisen by chance variations,
and the significance threshold for the mean must be much closer to 1
than to 2. Taking an average always increases the statistical
significance, therefore it's not valid to compare an _average_ value
of I/sigma(I) = 2 with a _single_ value of I/sigma(I) = 3 (taking 3
sigma as the threshold of statistical significance of an individual
measurement): that's a case of "comparing apples with pears". In
other words in the outer shell you would need a lot of highly
significant individual values >> 3 to attain an overall average of 2
since the majority of individual values will be < 1.
> F/sigF is expected to be better than I/sigI because dx^2 = 2Xdx,
> dx^2/x^2 = 2dx/x, dI/I = 2* dF/F (or approaches that in the limit . . .)
That depends on what you mean by 'better': every metric must be
compared with a criterion appropriate to that metric. So if we are
comparing I/sigma(I) with a criterion value = 3, then we must compare
F/sigma(F) with criterion value = 6 ('in the limit' of zero I), in
which case the comparison is no 'better' (in terms of information
content) with I than with F: they are entirely equivalent. It's
meaningless to compare F/sigma(F) with the criterion value appropriate
to I/sigma(I): again that's "comparing apples and pears"!
Cheers
 Ian
