Hi, I'm quite aware of this. Another useful link is: http://en.wikipedia.org/wiki/Pooled_variance This has also been pointed out to me by Robert Schneider (but not on the mailing lists). I am wondering if it is worth it as the number of users who would benefit are quite low. The reason for this is that most users will only have duplicate spectra. Therefore n-1 ends up being 1, as n is the number of replicated spectra, and this collapses down to the currently used variance averaging. In the case where you have collected spectra in triplicate, then implementing this makes sense. But the number of people using relax with triplicate spectra in the last 12 years is probably 1 or 2. So it would be good to implement this, but it's priority is very low. In any case, both averaged variances and pooled variances from a large collection of 2 point sets is horrible statistics, but that's all we've got. Note also that there are two averaging steps. The first is to average the variance for all peaks in the spectrum. The variance for a single peak is the dirty estimate from 2 points. Then if some spectra are only measured once, then the variances for all spectra are averaged. Regards, Edward On 19 June 2013 14:50, Troels E. Linnet <NO-REPLY.INVALID-ADDRESS@xxxxxxx> wrote:
URL: <http://gna.org/support/?3045> Summary: Support for pooled standard deviation for: Peak heights with partially replicated spectra Project: relax Submitted by: tlinnet Submitted on: Wed 19 Jun 2013 12:50:08 PM GMT Category: None Priority: 5 - Normal Severity: 3 - Normal Status: None Privacy: Public Assigned to: None Originator Email: Open/Closed: Open Discussion Lock: Any Operating System: None _______________________________________________________ Details: According to the manual, http://www.nmr-relax.com/manual/spectrum_error_analysis.html, the variance for the replicated datasets are averaged, and used as the variance for single replicated spectrum. This is a very reasonable assumption, but I wonder if a pooled standard deviation should be used instead. If we look in the definition of IUPAC Gold Book: http://goldbook.iupac.org/P04758.html """ Results from various series of measurements can be combined in the following way to give a pooled relative standard deviation $s_{r,p}$: $$ s_{r,p}=\sqrt{\frac{\sum(n_i-1)s_{r,i}^2}{\sum n_i -1}} = \sqrt{\frac{\sum(n_i-1)s_i^2x_i^{-2}}{\sum n_i -1}} $$ """ It is not an easy subject, and the discussion can be "hot": See for example these gals and gils: http://www.physicsforums.com/showthread.php?t=268377 So my question is, is the use of average of variances the right way to estimate the variance for single recorded data point? And should another way be implemented? _______________________________________________________ Reply to this item at: <http://gna.org/support/?3045> _______________________________________________ Message sent via/by Gna! http://gna.org/ _______________________________________________ relax (http://www.nmr-relax.com) This is the relax-devel mailing list relax-devel@xxxxxxx To unsubscribe from this list, get a password reminder, or change your subscription options, visit the list information page at https://mail.gna.org/listinfo/relax-devel