Hi Roberto,

for my taste the answers so far have not mentioned (or I did not understand 
them) that there is a distinction between indicators of the precision of merged 
data, and those for the precision of unmerged data.

It is not possible to directly compare (or equate) indicators of one category 
with those of the other category. This would be like comparing apples to 
oranges, and is, in my experience, the biggest source of confusion in 
crystallographic statistics, _and_ not clearly explained in writing. The only 
way to do such a comparison numerically is to include a factor of sqrt(n) where 
n is the multiplicity - the ratio of the number of observations and the number 
of unique reflections.

Indicators of precision of unmerged data are: [Rsym=Rmerge (which should be 
deprecated),] Rmeas and the <I/sigma(I)> of individual observations, as given 
in the first long table in XDS' CORRECT.LP which is fine-grained in resolution. 
Aimless also has this, but it is _not_ the quantity labeled Mn(I)/sd(Mn(I)).

Indicators of precision of merged data are: CC1/2, Rpim and the <I/sigma(I)> of 
unique reflections after averaging, as given in the repeated (by DATA_RANGE) 
tables in XDS' CORRECT.LP. In aimless, the average signal/noise after averaging 
symmetry-related observations < <I>/σ(<I>) >is labelled Mn(I)/sd(Mn(I)).

For both categories, there is not much difference in <I>/<sigma(I)> and 
<I/sigma(I)>; in particular at high resolution, these are becoming equal.

Thus, 
Rmerge ≈ 0.8/<I/σ(I)>
can only hold for unmerged data (i.e. observations), not for merged data 
(unique reflections, after averaging over symmetry-related observations).

HTH,

Kay



On Wed, 16 Apr 2014 17:09:28 +0200, Roberto Battistutta 
<[email protected]> wrote:

>Hi,
>in the Rupp book the following relation is reported (on pag 415):
>Rmerge ≈ 0.8/<I/σ(I)>
>referring to a relation of "the linear merging R-value with the 
>signal-to-noise ratio".
>
>in a 2006 CCP4bb, Manfred Weiss reported:
>Rrim (or Rmeas) = 0.8*sd(i)/I
>
>so, 
>
>First question: is it Rmerge or Rmeas (Rrim) that we are dealing with?
>
>Second question: at the denominator (of the Rupp way to write), it is the 
>aimless Mn(I/sd) (usually indicated as the real signal-to-noise ratio) or the 
>aimless I/sigma (very different from Mn(I/sd) with high redundancy)?
>
>Thank you very much for the clarification.
>
>Best,
>Roberto.
>
>Roberto Battistutta

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