Spectrum error analysis - Revision history

Bugman: removed Category:Analysis; added Category:Analysis techniques using HotCat

2020-10-21T20:45:28Z

removed Category:Analysis; added Category:Analysis techniques using HotCat

Bugman: Fix for the symbols and maths - all $x$ usage has been replaced by $tags or direct HTML conversion.$

2015-11-03T14:33:10Z

Fix for the symbols and maths - all $x$ usage has been replaced by <math> tags or direct HTML conversion.

Bugman: /* Peak volumes with baseplane noise RMSD */ Converted some of the text to use the new {{note}} template.

2015-10-15T19:48:31Z

Peak volumes with baseplane noise RMSD: Converted some of the text to use the new {{note}} template.

Bugman: Forced creation of a TOC - this will improve the formatting on the main page 'Did you know...' section.

2015-10-15T13:37:42Z

Forced creation of a TOC - this will improve the formatting on the main page 'Did you know...' section.

Tlinnet: /* See also */

2013-08-23T09:19:10Z

Tlinnet: /* IUPAC - pooled standard deviation */

2013-08-23T09:18:51Z

IUPAC - pooled standard deviation

Troels Emtekær Linnet: /* IUPAC - pooled standard deviation */

2013-06-19T12:38:42Z

IUPAC - pooled standard deviation

Troels Emtekær Linnet: /* IUPAC - pooled standard deviation */

2013-06-19T12:35:59Z

IUPAC - pooled standard deviation

Troels Emtekær Linnet: /* IUPAC - pooled standard deviation */

2013-06-19T12:32:14Z

IUPAC - pooled standard deviation

Troels Emtekær Linnet: /* See also */

2013-06-19T12:31:56Z

← Older revision		Revision as of 20:45, 21 October 2020
Line 65:		Line 65:
	# [[RMSD]]		# [[RMSD]]

−	[[Category:Analysis]]	+	[[Category:Analysis techniques]]

@@ Line 10: / Line 10: @@
 === 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
-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>
+<math>
 Although this results in all spins having the same error, the accuracy of the error estimate is significantly improved.
@@ Line 31: / Line 35: @@
 Then the error is simply given by the sum of variances:
-$$\sigma_{vol}^2 = \sigma_i^2 * N $$
+where ''σ<sub>vol</sub>'' is the standard deviation of the volume, ''σ<sub>i</sub>'' is the standard deviation of a single point assumed to be equal to the RMSD of the baseplane noise, <br>
-where $\sigma_{vol}$ is the standard deviation of the volume, $\sigma_{i}$ 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>
 Nicholson, Kay, Baldisseri, Arango, Young, Bax, and Torchia (1992) Biochemistry, 31: 5253-5263 equation:
-$$\sigma_{vol} = \sigma_i * \sqrt{(n*m)}$$
+<math>
-where $n$ and $m$ are the dimensions of the box.<br>
+where ''n'' and ''m'' are the dimensions of the box.
 {{note|there are a number of programs, for example peakint (http://hugin.ethz.ch/wuthrich/software/xeasy/xeasy_m15.html) that not use all points within the box.  And if the number N can not be determined, this category of error analysis is not possible.}}

@@ Line 40: / Line 40: @@
 where $n$ and $m$ are the dimensions of the box.<br>
-Also note that non-point summation methods, for example when line shape fitting is used to determine peak volumes, the equations above cannot be used. <br>
+{{note|there are a number of programs, for example peakint (http://hugin.ethz.ch/wuthrich/software/xeasy/xeasy_m15.html) that not use all points within the box.  And if the number N can not be determined, this category of error analysis is not possible.}}
-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>
+{{note|Also for non-point summation methods, for example when line shape fitting is used to determine peak volumes, the equations above cannot be used.  Hence again this category of error analysis cannot be used. 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). 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 ===

← Older revision		Revision as of 13:37, 15 October 2015
Line 1:		Line 1:
		+	__TOC__
		+
	== Intensity Spectrum error analysis ==		== Intensity Spectrum error analysis ==
	[http://www.nmr-relax.com/manual/spectrum_error_analysis.html See the manual]		[http://www.nmr-relax.com/manual/spectrum_error_analysis.html See the manual]

← Older revision		Revision as of 09:19, 23 August 2013
Line 56:		Line 56:

	== See also ==		== See also ==
		+	# [[RMSD]]
		+
	[[Category:Analysis]]		[[Category:Analysis]]

@@ Line 54: / Line 54: @@
 With all spectra replicated and again using any integration methodology, the intensity errors can be calculated as described in the `Peak heights with all spectra replicated' section above.
 == See also ==
 [[Category:Analysis]]

@@ Line 71: / Line 71: @@
 Results from various series of measurements can be combined in the following way to give a pooled relative standard deviation $s_{r,p}$:
 $$
-s_p=\sqrt{\frac{\sum(n_i-1)s_{r,i}^2}{\sum n_i -1}}
+s_{r,p}=\sqrt{\frac{\sum(n_i-1)s_{r,i}^2}{\sum n_i -1}} = \sqrt{\frac{\sum(n_i-1)s_i^2x_i^{-2}}{\sum n_i -1}}
 $$
 == See also ==
 [[Category:Analysis]]

@@ Line 63: / Line 63: @@
 from $k$ series of measurements can be calculated as
 $$
-s_p=sqrt{\frac{(n_1-1)s_1^2+(n_2-1)s_2^2+...+(n_k-1)s_k^2}{n_1+n_2+...+n_k-k}}
+s_p=\sqrt{\frac{(n_1-1)s_1^2+(n_2-1)s_2^2+...+(n_k-1)s_k^2}{n_1+n_2+...+n_k-k}}
 $$
 == See also ==
 [[Category:Analysis]]

Spectrum error analysis - Revision history

Bugman: removed Category:Analysis; added Category:Analysis techniques using HotCat

Bugman: Fix for the symbols and maths - all $x$ usage has been replaced by tags or direct HTML conversion.

Bugman: /* Peak volumes with baseplane noise RMSD */ Converted some of the text to use the new {{note}} template.

Bugman: Forced creation of a TOC - this will improve the formatting on the main page 'Did you know...' section.

Tlinnet: /* See also */

Tlinnet: /* IUPAC - pooled standard deviation */

Troels Emtekær Linnet: /* IUPAC - pooled standard deviation */

Troels Emtekær Linnet: /* IUPAC - pooled standard deviation */

Troels Emtekær Linnet: /* IUPAC - pooled standard deviation */

Troels Emtekær Linnet: /* See also */

Bugman: Fix for the symbols and maths - all $x$ usage has been replaced by $tags or direct HTML conversion.$