Correlation analysis - Revision history

Lars-Ake at 09:56, 19 August 2024

2024-08-19T09:56:28Z

← Older revision		Revision as of 11:56, 19 August 2024
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	Calculate the [http://en.wikipedia.org/wiki/Standard_deviation standard deviations] as:		Calculate the [http://en.wikipedia.org/wiki/Standard_deviation standard deviations] as:
	:<math>\sigma x = \~~sqr~~{E (X-Mx)^2}</math> and <math>\sigma y = \~~sqr~~{E (Y-My)^2}</math>		:<math>\sigma x = \sqrt{E (X-Mx)^2}</math> and <math>\sigma y = \sqrt{E (Y-My)^2}</math>

	(The standard deviation is a measure of a "normal" (typical) distance from a point on a curve to the mean value of that curve.)		(The standard deviation is a measure of a "normal" (typical) distance from a point on a curve to the mean value of that curve.)
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	TTest values are calculated according to the formula below, where n is the number of overlapping years and r is the correlation coefficient value.		TTest values are calculated according to the formula below, where n is the number of overlapping years and r is the correlation coefficient value.

	:<math>TTest = r \~~sqr~~{ \frac{(n-2)}{(1 - r^2 )} }</math>		:<math>TTest = r \sqrt{ \frac{(n-2)}{(1 - r^2 )} }</math>

Hoppe: /* Definition of the correlation coefficient */

2012-02-10T11:42:24Z

Definition of the correlation coefficient

← Older revision		Revision as of 13:42, 10 February 2012
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	Define X and Y as paired curve values. There is one X and one Y for each year when the curves lay at a certain position.		Define X and Y as paired curve values. There is one X and one Y for each year when the curves lay at a certain position.
	Define Mx and My as the mean values (or [http://en.wikipedia.org/wiki/Expected_value expected value]) of each curve, i.e:		Define Mx and My as the mean values (or [http://en.wikipedia.org/wiki/Expected_value expected value]) of each curve, i.e:
	:<~~math~~>Mx = E(X)</~~math~~> and <~~math~~>My = E(Y)</~~math~~>		:<tex>Mx = E(X)</tex> and <tex>My = E(Y)</tex>

	Calculate the [http://en.wikipedia.org/wiki/Standard_deviation standard deviations] as:		Calculate the [http://en.wikipedia.org/wiki/Standard_deviation standard deviations] as:

Taxelson at 11:03, 2 June 2010

2010-06-02T11:03:07Z

← Older revision		Revision as of 13:03, 2 June 2010
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	within dendrochronology should best be motivated by practical observations on its efficiency to find correct crossdatings and its efficiency to sort out incorrect matches.<ref name=tattest>[[Torbjörn Axelson]] and [[Lars-Åke Larsson]]: [http://www.cybis.se/forfun/dendro/TTEST/index.htm What is a good TTest value]''</ref>		within dendrochronology should best be motivated by practical observations on its efficiency to find correct crossdatings and its efficiency to sort out incorrect matches.<ref name=tattest>[[Torbjörn Axelson]] and [[Lars-Åke Larsson]]: [http://www.cybis.se/forfun/dendro/TTEST/index.htm What is a good TTest value]''</ref>

	Note: When comparing ring width curves, we do the correlation coefficient mathematics on the [[Normalization\|normalized]] curves! When you document a best value from such a correlation calculus, you should also document the normalization method used, as the requirements on the level of the coefficient to ascertain a dating, differs somewhat with the normalization method used.<ref name=tattest/><ref>There seems to be a custom (especially in Europe?) just to note the t-value. It is in those cases usually the t-value according to [[~~Baille~~/Pilcher normalization]] which is referred to. </ref>		Note: When comparing ring width curves, we do the correlation coefficient mathematics on the [[Normalization\|normalized]] curves! When you document a best value from such a correlation calculus, you should also document the normalization method used, as the requirements on the level of the coefficient to ascertain a dating, differs somewhat with the normalization method used.<ref name=tattest/><ref>There seems to be a custom (especially in Europe?) just to note the t-value. It is in those cases usually the t-value according to [[Baillie/Pilcher normalization]] which is referred to. </ref>

	==Definition of the correlation coefficient==		==Definition of the correlation coefficient==

Taxelson at 11:02, 2 June 2010

2010-06-02T11:02:02Z

← Older revision		Revision as of 13:02, 2 June 2010
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	within dendrochronology should best be motivated by practical observations on its efficiency to find correct crossdatings and its efficiency to sort out incorrect matches.<ref name=tattest>[[Torbjörn Axelson]] and [[Lars-Åke Larsson]]: [http://www.cybis.se/forfun/dendro/TTEST/index.htm What is a good TTest value]''</ref>		within dendrochronology should best be motivated by practical observations on its efficiency to find correct crossdatings and its efficiency to sort out incorrect matches.<ref name=tattest>[[Torbjörn Axelson]] and [[Lars-Åke Larsson]]: [http://www.cybis.se/forfun/dendro/TTEST/index.htm What is a good TTest value]''</ref>

	Note: When comparing ring width curves, we do the correlation coefficient mathematics on the [[Normalization\|normalized]] curves! When you document a best value from such a correlation calculus, you should also document the normalization method used, as the requirements on the level of the coefficient to ascertain a dating, differs somewhat with the normalization method used.<ref name=tattest/><ref>There seems to be a custom (especially in Europe?) just to note the t-value. ~~Than~~ usually the t-value according to [[~~Baillie~~/Pilcher normalization]] is referred to. </ref>		Note: When comparing ring width curves, we do the correlation coefficient mathematics on the [[Normalization\|normalized]] curves! When you document a best value from such a correlation calculus, you should also document the normalization method used, as the requirements on the level of the coefficient to ascertain a dating, differs somewhat with the normalization method used.<ref name=tattest/><ref>There seems to be a custom (especially in Europe?) just to note the t-value. It is in those cases usually the t-value according to [[Baille/Pilcher normalization]] which is referred to. </ref>

	==Definition of the correlation coefficient==		==Definition of the correlation coefficient==

Taxelson at 09:05, 2 June 2010

2010-06-02T09:05:10Z

← Older revision		Revision as of 11:05, 2 June 2010
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	within dendrochronology should best be motivated by practical observations on its efficiency to find correct crossdatings and its efficiency to sort out incorrect matches.<ref name=tattest>[[Torbjörn Axelson]] and [[Lars-Åke Larsson]]: [http://www.cybis.se/forfun/dendro/TTEST/index.htm What is a good TTest value]''</ref>		within dendrochronology should best be motivated by practical observations on its efficiency to find correct crossdatings and its efficiency to sort out incorrect matches.<ref name=tattest>[[Torbjörn Axelson]] and [[Lars-Åke Larsson]]: [http://www.cybis.se/forfun/dendro/TTEST/index.htm What is a good TTest value]''</ref>

	Note: When comparing ring width curves, we do the correlation coefficient mathematics on the [[Normalization\|normalized]] curves! When you document a best value from such a correlation calculus, you should also document the normalization method used, as the requirements on the level of the coefficient to ascertain a dating, differs somewhat with the normalization method used.<ref name=tattest/><ref>There seems to be a custom (especially in Europe?) just to note the t-value. Than usually the t-value according to [[~~Baille~~/Pilcher normalization]] is referred to. </ref>		Note: When comparing ring width curves, we do the correlation coefficient mathematics on the [[Normalization\|normalized]] curves! When you document a best value from such a correlation calculus, you should also document the normalization method used, as the requirements on the level of the coefficient to ascertain a dating, differs somewhat with the normalization method used.<ref name=tattest/><ref>There seems to be a custom (especially in Europe?) just to note the t-value. Than usually the t-value according to [[Baillie/Pilcher normalization]] is referred to. </ref>

	==Definition of the correlation coefficient==		==Definition of the correlation coefficient==

Taxelson: /* The correlation coefficient */

2010-06-02T09:03:06Z

The correlation coefficient

← Older revision		Revision as of 11:03, 2 June 2010
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	It should be noted that the statistical mathematics for the correlation coefficient are defined on the relations between random variables. It should then be noted that		It should be noted that the statistical mathematics for the correlation coefficient are defined on the relations between random variables. It should then be noted that
	ring width values are not random - when a ring is thick, there is a high probability that the next years ring will also be thick. So the use of any correlation coefficient		ring width values are not random - when a ring is thick, there is a high probability that the next years ring will also be thick. So the use of any correlation coefficient
	within dendrochronology should best be motivated by practical observations on its efficiency to find correct crossdatings and its efficiency to sort out incorrect matches		within dendrochronology should best be motivated by practical observations on its efficiency to find correct crossdatings and its efficiency to sort out incorrect matches.<ref name=tattest>[[Torbjörn Axelson]] and [[Lars-Åke Larsson]]: [http://www.cybis.se/forfun/dendro/TTEST/index.htm What is a good TTest value]''</ref>
	~~see~~ <ref name=tattest>[[Torbjörn Axelson]] and [[Lars-Åke Larsson]]: [http://www.cybis.se/forfun/dendro/TTEST/index.htm What is a good TTest value]''</ref>

	Note: When comparing ring width curves, we do the correlation coefficient mathematics on the [[Normalization\|normalized]] curves! When you document a best value from such a correlation calculus, you should also document the normalization method used, as the requirements on the level of the coefficient to ~~acertain~~ a dating, differs somewhat with the normalization method used.<ref name=tattest/>		Note: When comparing ring width curves, we do the correlation coefficient mathematics on the [[Normalization\|normalized]] curves! When you document a best value from such a correlation calculus, you should also document the normalization method used, as the requirements on the level of the coefficient to ascertain a dating, differs somewhat with the normalization method used.<ref name=tattest/><ref>There seems to be a custom (especially in Europe?) just to note the t-value. Than usually the t-value according to [[Baille/Pilcher normalization]] is referred to. </ref>

	==Definition of the correlation coefficient==		==Definition of the correlation coefficient==

Lars-Ake: /* TTest value */

2009-12-31T18:06:31Z

TTest value

← Older revision		Revision as of 20:06, 31 December 2009
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	A TTest value given without the corresponding overlap length, says nothing about the similarity between the curves.		A TTest value given without the corresponding overlap length, says nothing about the similarity between the curves.
	Worst case is to specify two TTest values - when demonstrating similarity - without telling that the values were achieved with different length of the overlap.		Worst case is to specify two TTest values - when demonstrating similarity - without telling that the values were achieved with different length of the overlap.


	When you want to describe the similarity between curves from two different regions, use the correlation coefficient value as a measure and then		When you want to describe the similarity between curves from two different regions, use the correlation coefficient value as a measure and then

Lars-Ake: /* TTest value */

2009-12-31T18:05:20Z

TTest value

← Older revision		Revision as of 20:05, 31 December 2009
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	A high enough TTest value certifies that two ring width curves are properly crossdated when also the overlap between the curves is sufficient.		A high enough TTest value certifies that two ring width curves are properly crossdated when also the overlap between the curves is sufficient.
	A TTest value given without the corresponding overlap length, says nothing about the ~~similiarity~~ between the curves.		A TTest value given without the corresponding overlap length, says nothing about the similarity between the curves.
	Worst case is to specify two TTest values - when demonstrating ~~similiarity~~ - without telling that the values were achieved with different length of the overlap.		Worst case is to specify two TTest values - when demonstrating similarity - without telling that the values were achieved with different length of the overlap.

Lars-Ake: /* TTest value */

2009-12-31T18:02:17Z

TTest value

← Older revision		Revision as of 20:02, 31 December 2009
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	A practical way to find out what is reasonable T-values for a certain [[normalization]] method, is by testing a huge amount of samples of specified length (blocks) towards an unrelated long reference. Such a test has shown that a reasonable minimum level of the T-value is often in the range 5.5-6.5, depending on sample length and normalization method.<ref name=tattest/>		A practical way to find out what is reasonable T-values for a certain [[normalization]] method, is by testing a huge amount of samples of specified length (blocks) towards an unrelated long reference. Such a test has shown that a reasonable minimum level of the T-value is often in the range 5.5-6.5, depending on sample length and normalization method.<ref name=tattest/>


			;Use the correlation coefficient to describe the similarity between curves - never just the TTest value!

			A high enough TTest value certifies that two ring width curves are properly crossdated when also the overlap between the curves is sufficient.
			A TTest value given without the corresponding overlap length, says nothing about the similiarity between the curves.
			Worst case is to specify two TTest values - when demonstrating similiarity - without telling that the values were achieved with different length of the overlap.


			When you want to describe the similarity between curves from two different regions, use the correlation coefficient value as a measure and then
			also specify the normalization method used.

	==Notes==		==Notes==

Lars-Ake: /* TTest value */

2009-07-06T19:56:26Z

TTest value

← Older revision		Revision as of 21:56, 6 July 2009
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	;What is a good TTest-value?		;What is a good TTest-value?
	In general discussions on T-values ~~often~~ values in the range 2.5-3.5 is mentioned as significant, and ~~than~~ the confidence interval is set to ~~for instance~~ 95% or 99%, which may be reasonable in many applications, but not in dendrochronology. A confidence of 95% actually means that you indeed expect one ~~random~~ generated (i.e. false) match every twentieth year of sliding! Or every 100:th year with 99% confidence. ~~But~~ when you slide a sample towards a reference you will normally have hundreds or thousands of scores among which all but one are random. Therefore the confidence level has to be set far above what is common in other contexts.		In general discussions on T-values, values in the range 2.5-3.5 are often mentioned as significant, and then the confidence interval is set to e.g. 95% or 99%, which may be reasonable in many applications, but not in dendrochronology. A confidence of 95% actually means that you indeed expect one randomly generated (i.e. false) match every twentieth year of sliding! Or every 100:th year with 99% confidence. Though when you slide a sample towards a reference you will normally have hundreds or thousands of scores among which all but one are random. Therefore the confidence level has to be set far above what is common in other contexts.

	A practical way to find out what is reasonable T-values for a certain [[normalization]] method, is by testing a huge amount of samples of specified length (blocks) towards an unrelated long reference. Such a test has shown that a reasonable minimum level of the T-value often ~~use to be~~ in the range 5.5-6.5, depending on sample length and normalization method.<ref name=tattest/>		A practical way to find out what is reasonable T-values for a certain [[normalization]] method, is by testing a huge amount of samples of specified length (blocks) towards an unrelated long reference. Such a test has shown that a reasonable minimum level of the T-value is often in the range 5.5-6.5, depending on sample length and normalization method.<ref name=tattest/>

	==Notes==		==Notes==