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$$ \sigma^2 = \frac{\sum( I_i - I_{av} )}{n -1 } $$
where $\sigma^2$ is the variance, $\sigma$ is the standard deviation, $n$ is the size of the replicated spectra set with i being the corresponding index, $I_i$ is the peak intensity for spectrum $i$ , and $I_{av}$ is the mean over all spectra i .e. the sum of all peak intensities divided by $n$.
$$\sigma_{vol}^2 = \sigma_i^2 * N $$where $\sigma_{''σ<sub>vol}$ </sub>'' is the standard deviation of the volume, $\sigma_{''σ<sub>i}$ </sub>'' is the standard deviation of a single point assumed to be equal to the RMSD of the baseplane noise, <br>and $''N$ '' is the total number of points used in the summation integration method. For a box integration method, this converts to the<br>
$$<math>\sigma_{vol} = \sigma_i * \sqrt{(n*m)}$$</math> where ''n'' and ''m'' are the dimensions of the box.
where $n$ and $m$ {{note|there are the dimensions of the box.<br>Note that a number of programs, for example peakint (http://hugin.ethz.ch/wuthrich/software/xeasy/xeasy_m15.html) does that not use all points within the box.<br> And if the number N can not be determined, this category of error analysis is not possible.}}
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== Intensity Spectrum error analysis ==
[http://www.nmr-relax.com/manual/spectrum_error_analysis.html See the manual]
=== Peak heights with partially replicated spectra ===
When spectra are replicated, the variance for a single spin at a single replicated spectra set is calculated by the formula
<math>\sigma^2 = \frac{\sum( I_i - I_{av} )}{n -1 }</math> where σ<sup>2</sup> is the variance, σ is the standard deviation, ''n'' is the size of the replicated spectra set with ''i'' being the corresponding index, ''I<sub>i</sub>'' is the peak intensity for spectrum ''i'' , and ''I<sub>av</sub>'' is the mean over all spectra i.e. the sum of all peak intensities divided by ''n''. As the value of $''n$ '' in the above equation is '''always very low''' since normally only a couple of spectra are collected per replicated spectra set, '''the variance of all spins''' is '''averaged''' for a '''single replicated spectra set'''. <br>
Although this results in all spins having the same error, the accuracy of the error estimate is significantly improved.
Then the error is simply given by the sum of variances:
<math>
\sigma_{vol}^2 = \sigma_i^2 * N
</math>
Nicholson, Kay, Baldisseri, Arango, Young, Bax, and Torchia (1992) Biochemistry, 31: 5253-5263 equation:
{{note|Also note that for non-point summation methods, for example when line shape fitting is used to determine peak volumes, the equations above cannot be used. <br> Hence again this category of error analysis cannot be used. <br>This is the case for one of the three integration methods used by Sparky (http://www.cgl.ucsf.edu/home/sparky/manual/peaks.html#Integration). <br>And if fancy techniques are used, for example as Cara does to deconvolute overlapping peaks (http://www.cara.ethz.ch/Wiki/Integration), this again makes this error analysis impossible.}}
=== Peak volumes with partially replicated spectra ===
== See also ==
# [http://goldbook.iupac.org/P04758.html IUPAC :pooled standard deviation[RMSD]]
[[Category:Analysistechniques]]