On 19 June 2013 15:27, Edward d'Auvergne <
edward@xxxxxxxxxxxxx> wrote:
> Just wait, I got that wrong! First some definitions:
>
> n = number of replicated spectra,
> i = each spin system or peak,
> k = total number of peaks.
>
> The sum at the bottom of would mean that if n-1=1, then the
> denominator would be a large sum. As n-1 would be the same for all i,
> then this becomes the averaged variance divided by k! Therefore as
> you have more and more peaks in the spectrum, the smaller and smaller
> the estimator will be. Taking this to the extreme, as you approach
> infinite peaks in the spectrum, the error approaches zero. That seems
> absurd. Maybe in this case, the unbiased estimator is absurd ;) I
> think I should read that 3rd link you posted.
>
> Regards,
>
> Edward
>
>
>
>
> On 19 June 2013 15:15, Edward d'Auvergne <
edward@xxxxxxxxxxxxx> wrote:
>> 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/
>>>
>>>
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http://www.nmr-relax.com)
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Re: [sr #3045] Support for pooled standard deviation for: Peak heights with partially replicated spectra