## relax - Support: sr #3045, Support for pooled standard...

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## sr #3045: Support for pooled standard deviation for: Peak heights with partially replicated spectra

 Submitted by: Troels E. Linnet Submitted on: Wed 19 Jun 2013 12:50:08 PM UTC Category: None Priority: 5 - Normal Severity: 3 - Normal Status: Invalid Privacy: Public Assigned to: None Open/Closed: Closed Operating System: None

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Tue 10 Sep 2013 06:45:17 AM UTC, comment #2:

As mentioned in the thread, for the case of replicated spectra the pooled standard deviation is identical to the standard deviation with variance averaging, as all peaks are replicated to the same extent. Therefore closing this sr as invalid.

Edward d Auvergne <bugman>
Fri 02 Aug 2013 08:35:22 AM UTC, comment #1:

Troels E. Linnet <tlinnet>
Wed 19 Jun 2013 12:50:08 PM UTC, original submission:

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?

Troels E. Linnet <tlinnet>

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