Pooled standard deviation - Revision history

Bugman: added Category:Analysis techniques using HotCat

2020-10-21T21:37:12Z

added Category:Analysis techniques using HotCat

Bugman: Fix for the symbols and maths - all $x$ usage has been replaced by $tags or direct HTML conversion.$

2015-11-03T14:35:59Z

Fix for the symbols and maths - all $x$ usage has been replaced by 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

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

2015-10-15T15:00:15Z

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

Tlinnet: Created page with "== IUPAC - pooled standard deviation == [http://goldbook.iupac.org/P04758.html IUPAC :pooled standard deviation] A problem often arises when the combination of several series..."

2013-08-23T09:18:47Z

Created page with "== IUPAC - pooled standard deviation == [http://goldbook.iupac.org/P04758.html IUPAC :pooled standard deviation] A problem often arises when the combination of several series..."

New page

== IUPAC - pooled standard deviation ==
[http://goldbook.iupac.org/P04758.html IUPAC :pooled standard deviation]

A problem often arises when the combination of several series of measurements performed under similar conditions
is desired to achieve an improved estimate of the imprecision of the process. If it can be assumed that all the
series are of the same precision although their means may differ, the pooled standard deviations $s_p$
from $k$ series of measurements can be calculated as
$$
s_p=\sqrt{\frac{(n_1-1)s_1^2+(n_2-1)s_2^2+...+(n_k-1)s_k^2}{n_1+n_2+...+n_k-k}}
$$
The suffices $1, 2, ..., k$ refer to the different series of measurements. In this case it is assumed that there exists a single underlying standard deviation $\sigma$ of which the pooled standard deviation $s_p$ is a better estimate than the individual calculated standard deviations $s_1, s_2, ..., s_k$, For the special case where $k$ sets of duplicate measurements are available, the above equation reduces to
$$
s_p=\sqrt{\frac{\sum(x_{i1}-x_{i2})^2}{2k}}
$$
Results from various series of measurements can be combined in the following way to give a pooled relative standard deviation $s_{r,p}$:
$$
s_{r,p}=\sqrt{\frac{\sum(n_i-1)s_{r,i}^2}{\sum n_i -1}} = \sqrt{\frac{\sum(n_i-1)s_i^2x_i^{-2}}{\sum n_i -1}}
$$

← Older revision		Revision as of 21:37, 21 October 2020
Line 25:		Line 25:
	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}}		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}}
	</math>		</math>
		+
		+	[[Category:Analysis techniques]]

← Older revision		Revision as of 15:00, 15 October 2015
Line 1:		Line 1:
		+	__TOC__
		+
	== IUPAC - pooled standard deviation ==		== IUPAC - pooled standard deviation ==
	[http://goldbook.iupac.org/P04758.html IUPAC :pooled standard deviation]		[http://goldbook.iupac.org/P04758.html IUPAC :pooled standard deviation]

@@ Line 6: / Line 6: @@
 A problem often arises when the combination of several series of measurements performed under similar conditions
 is desired to achieve an improved estimate of the imprecision of the process. If it can be assumed that all the
-series are of the same precision although their means may differ, the pooled standard deviations $s_p$
+series are of the same precision although their means may differ, the pooled standard deviations ''s<sub>p</sub>''
-from $k$ series of measurements can be calculated as
+from ''k'' series of measurements can be calculated as
-$$
 s_p=\sqrt{\frac{(n_1-1)s_1^2+(n_2-1)s_2^2+...+(n_k-1)s_k^2}{n_1+n_2+...+n_k-k}}
-$$
+</math>
-The suffices $1, 2, ..., k$ refer to the different series of measurements. In this case it is assumed that there exists a single underlying standard deviation $\sigma$ of which the pooled standard deviation $s_p$ is a better estimate than the individual calculated standard deviations $s_1, s_2, ..., s_k$, For the special case where $k$ sets of duplicate measurements are available, the above equation reduces to
-$$
 s_p=\sqrt{\frac{\sum(x_{i1}-x_{i2})^2}{2k}}
-$$
+</math>
-Results from various series of measurements can be combined in the following way to give a pooled relative standard deviation $s_{r,p}$:
-$$
+Results from various series of measurements can be combined in the following way to give a pooled relative standard deviation ''s<sub>r,p</sub>'':
 s_{r,p}=\sqrt{\frac{\sum(n_i-1)s_{r,i}^2}{\sum n_i -1}} = \sqrt{\frac{\sum(n_i-1)s_i^2x_i^{-2}}{\sum n_i -1}}
-$$
+</math>

Pooled standard deviation - Revision history

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

Tlinnet: Created page with "== IUPAC - pooled standard deviation == [http://goldbook.iupac.org/P04758.html IUPAC :pooled standard deviation] A problem often arises when the combination of several series..."

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