Conventionally (e.g. in cryo-EM) the SNR is taken as a ratio of averages, either the ratio of the variance of the signal (average of signal squared) to the variance of the noise, i.e. var(signal) / var(noise), or the square root of that, i.e. sd(signal) / sd(noise). See here: https://en.wikipedia.org/wiki/Signal-to-noise_ratio .
Alternatively, it may be defined as the ratio of the mean value of the signal to its standard error, i.e. mean(signal) / sd(noise): https://en.wikipedia.org/wiki/Signal-to-noise_ratio_(imagi ng) <https://en.wikipedia.org/wiki/Signal-to-noise_ratio_(imaging)> , so again a ratio of averages. Whenever you read about SNR you have to check carefully which of the three definitions is in use (and often it's not stated!). I think the confusion of ratio-of-averages vs. average-of-ratios has arisen because in crystallography we're not actually talking about the SNR, rather we're talking about the _average_ SNR, where the average is taken over samples of a population that have _different_ distributions in reciprocal space, whereas in the previous case the samples are taken from a population whose samples are assumed to have the _same_ distribution (and therefore same s.d.). Note that the ratio-of-average and average-of-ratio cases converge if all samples are drawn from the same population with uniform distribution and s.d.. So then in our situation it is indeed correct to say that average SNR = average( I / sd(I) ), i.e. an average of the ratios of averages! When we measure an _individual_ intensity with its s.d., we are already taking averages, but they are averages over time where the standard error is constant. Then, when we take the spatial average SNR over different intensities the sampling distribution and its s.d. naturally varies so we must take the average of ratios. Cheers -- Ian On Fri, 18 Dec 2020 at 20:14, Bernhard Rupp <[email protected]> wrote: > > I don't know the justification; maybe just experience? Surely the higher > the better. I've seen George Sheldrick deriving the value of ~0.8 when > there is _no_ anom signal but I forgot the details, sorry ... > > It is derived from the mean absolute error (cf. p414 in Chapter 8 of BMC, > with help of Ian Tickle), and holds for unmerged data. A reasonable good > indication where to set the cutoff in practice is to look at the site vs > occupancy plot. A distinct drop after a few good sites is usually a good > sign, and that tends to cluster around the ~1.3 ratio. > > > http://www.ruppweb.org/Garland/gallery/Ch10/pages/Biomolecular_Crystallography_Fig_10-30_PART2.htm > > The noise level is actually observable in data without anomalous signal > > > http://www.ruppweb.org/Garland/gallery/Ch10/pages/Biomolecular_Crystallography_Fig_10-29.htm > > Best BR > > > > > > best wishes, > > Kay > > > > >Thanks! > >-- David > > > >####################################################################### > ># > > > >To unsubscribe from the CCP4BB list, click the following link: > >https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1 > > > >This message was issued to members of www.jiscmail.ac.uk/CCP4BB, a > >mailing list hosted by www.jiscmail.ac.uk, terms & conditions are > >available at https://www.jiscmail.ac.uk/policyandsecurity/ > > > > ######################################################################## > > To unsubscribe from the CCP4BB list, click the following link: > https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1 > > This message was issued to members of www.jiscmail.ac.uk/CCP4BB, a > mailing list hosted by www.jiscmail.ac.uk, terms & conditions are > available at https://www.jiscmail.ac.uk/policyandsecurity/ > > ######################################################################## > > To unsubscribe from the CCP4BB list, click the following link: > https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1 > > This message was issued to members of www.jiscmail.ac.uk/CCP4BB, a > mailing list hosted by www.jiscmail.ac.uk, terms & conditions are > available at https://www.jiscmail.ac.uk/policyandsecurity/ > ######################################################################## To unsubscribe from the CCP4BB list, click the following link: https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1 This message was issued to members of www.jiscmail.ac.uk/CCP4BB, a mailing list hosted by www.jiscmail.ac.uk, terms & conditions are available at https://www.jiscmail.ac.uk/policyandsecurity/
