Hi Ed, your example seems to be designed to show that the average of reciprocal values is not the same as the reciprocal of an average value? If that is what you are alluding to, then please not that the (relatively narrow) Wilson distribution of intensities has the effect of making the relation <I/σ(I)> ~ 1/<σ(I)/I> work fairly well in practice.
The relation Rmeas ≈ 0.8/<I/σ(I)> (where I refers to the intensity of unmerged, individual observations) is obviously not an exact one ... rather it depends on how the σ(I) are calculated (the "error model") and some other things. But it should _not_ depend on the multiplicity, and it should hold fairly well at high resolution. Kay On Fri, 18 Apr 2014 10:12:10 -0400, Edward A. Berry <ber...@upstate.edu> wrote: >Roberto Battistutta 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 >> > > >Bernhard Rupp wrote: > > > > 0.8*sd(i)/I = 0.8/(I/sd(i)) > > >--------------------------- > >Yes, but in this context it is worth pointing out that > <I/σ(I)> != 1/<σ(I)/I> > >especially if there is a wide range in values of <I/σ(I)>, >which would be narrower but still significant in the outer shells. > >ave(100, 10, 1) = 37 >ave(0.01, 0.1, 1) = .37 = 1/(2.7) != 1/37 > >So while of course Rupp's equation is correct, if we try to apply it to >average values, >which we have to do to compare with Rmerge, it is no longer correct, so even >at high >multiplicity the two equations quoted in original post seem incompatible. >(Unless I'm badly confused again) >eab
