DeltaCC12 - Revision history

Gassmann at 10:22, 6 September 2018

2018-09-06T10:22:17Z

← Older revision		Revision as of 12:22, 6 September 2018
Line 1:		Line 1:
	ΔCC<sub>1/2</sub> is a quantity that detects datasets/frames which are non-isomorphous. As described in [https://scripts.iucr.org/cgi-bin/paper?zw5005 Assmann and Diederichs (2016)], ΔCC<sub>1/2</sub> is calculated with the σ-τ method. This method is a way to calculate the Pearson correlation coefficient for the special case of two sets of values (intensities) that randomly deviate from their true values. The σ-τ method is not influenced by a random number sequence as shown in [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3457925/ Karplus and Diederichs (2012)]. For the σ-τ method CC<sub>1/2</sub> is calculated for all datasets/frames, which will be called CC<sub>1/2_overall</sub> and CC<sub>1/2</sub> is calculated for all datasets/frames except for one dataset i, which is omitted from calculations and denoted as CC<sub>1/2_i</sub>. The difference of the two quantities is ΔCC<sub>1/2</sub>.		ΔCC<sub>1/2</sub> is a quantity that detects datasets/frames which are non-isomorphous. As described in [https://scripts.iucr.org/cgi-bin/paper?zw5005 Assmann and Diederichs (2016)], ΔCC<sub>1/2</sub> is calculated with the σ-τ method. This method is a way to calculate the Pearson correlation coefficient for the special case of two sets of values (intensities) that randomly deviate from their true values. The σ-τ method is not influenced by a random number sequence as shown in [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3457925/ Karplus and Diederichs (2012)]. For the σ-τ method CC<sub>1/2</sub> is calculated for all datasets/frames, which will be called CC<sub>1/2_overall</sub> and CC<sub>1/2</sub> is calculated for all datasets/frames except for one dataset i, which is omitted from calculations and denoted as CC<sub>1/2_i</sub>. The difference of the two quantities is ΔCC<sub>1/2</sub>.

	: <math>\Delta CC_{1/2}= CC_{1/2 overall}-CC_{1/~~2_i~~} </math>		: <math>\Delta CC_{1/2}= CC_{1/2 overall}-CC_{1/2\_i} </math>

	If ΔCC<sub>1/2</sub> is > 0 (CC<sub>1/2_overall</sub> is bigger than CC<sub>1/2_i</sub>) it means that by omitting dataset i from calculations a lower CC<sub>1/2</sub> results. As we want to maximize CC<sub>1/2</sub> the dataset is kept for calculations, it is improving the whole merged dataset. If Δ CC<sub>1/2</sub> is < 0 (CC<sub>1/2_overall</sub> is smaller than CC<sub>1/2_i</sub>) it means that by omitting dataset i from calculations a higher CC<sub>1/2</sub> results, which is why we want to exclude it from calculations, because it is impairing the whole merged dataset.		If ΔCC<sub>1/2</sub> is > 0 (CC<sub>1/2_overall</sub> is bigger than CC<sub>1/2_i</sub>) it means that by omitting dataset i from calculations a lower CC<sub>1/2</sub> results. As we want to maximize CC<sub>1/2</sub> the dataset is kept for calculations, it is improving the whole merged dataset. If Δ CC<sub>1/2</sub> is < 0 (CC<sub>1/2_overall</sub> is smaller than CC<sub>1/2_i</sub>) it means that by omitting dataset i from calculations a higher CC<sub>1/2</sub> results, which is why we want to exclude it from calculations, because it is impairing the whole merged dataset.

Gassmann at 07:44, 6 September 2018

2018-09-06T07:44:14Z

← Older revision		Revision as of 09:44, 6 September 2018
Line 8:		Line 8:
	== Applications ==		== Applications ==

	The ΔCC<sub>1/2</sub> method is applicable for single frames, SSX data and SFX data. ΔCC<sub>1/2</sub> ~~can be calculated by~~ [[~~XDSCC12~~]].		The ΔCC<sub>1/2</sub> method is applicable for single frames, SSX data and SFX data. The program [[XDSCC12]] calculates ΔCC<sub>1/2</sub> for the isomorphous and anomalous signal for XDS_ASCII.HKL and XSCALE.HKL files. Exact description of calculation and implementation are found at [[CC1/2]].

Gassmann at 07:38, 6 September 2018

2018-09-06T07:38:06Z

← Older revision		Revision as of 09:38, 6 September 2018
Line 1:		Line 1:
	ΔCC<sub>1/2</sub> is a quantity, that detects datasets/frames~~, that~~ are non-isomorphous. As described in [https://scripts.iucr.org/cgi-bin/paper?zw5005 Assmann and Diederichs (2016)], ΔCC<sub>1/2</sub> is calculated with the σ-τ method. This method is a way to calculate the Pearson correlation coefficient for the special case of two sets of values (intensities) that randomly deviate from their true values~~, but~~ is not influenced by a random number sequence as shown in [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3457925/ Karplus and Diederichs (2012)]. For the σ-τ method CC<sub>1/2</sub> is calculated for all datasets/frames, which will be called CC<sub>1/2_overall</sub> and CC<sub>1/2</sub> is calculated for all datasets/frames except for one dataset i, which is omitted from calculations and denoted as CC<sub>1/2_i</sub>. The difference of the two quantities is ΔCC<sub>1/2</sub>.		ΔCC<sub>1/2</sub> is a quantity that detects datasets/frames which are non-isomorphous. As described in [https://scripts.iucr.org/cgi-bin/paper?zw5005 Assmann and Diederichs (2016)], ΔCC<sub>1/2</sub> is calculated with the σ-τ method. This method is a way to calculate the Pearson correlation coefficient for the special case of two sets of values (intensities) that randomly deviate from their true values. The σ-τ method is not influenced by a random number sequence as shown in [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3457925/ Karplus and Diederichs (2012)]. For the σ-τ method CC<sub>1/2</sub> is calculated for all datasets/frames, which will be called CC<sub>1/2_overall</sub> and CC<sub>1/2</sub> is calculated for all datasets/frames except for one dataset i, which is omitted from calculations and denoted as CC<sub>1/2_i</sub>. The difference of the two quantities is ΔCC<sub>1/2</sub>.

	: <math>\Delta CC_{1/2}= CC_{1/2 overall}-CC_{1/~~2 i~~} </math>		: <math>\Delta CC_{1/2}= CC_{1/2 overall}-CC_{1/2_i} </math>

	If ΔCC<sub>1/2_</sub> is > 0 -CC<sub>1/2_overall</sub> is bigger than CC<sub>1/2_i</sub>- that ~~means if~~ omitting dataset i from calculations, a lower CC<sub>1/2</sub> results~~, which is why~~ we want to ~~keep it. Thus~~ it is improving the whole merged dataset. If Δ CC<sub>1/2</sub> is < 0~~, -~~CC<sub>1/2_overall</sub> is smaller than CC<sub>1/2_i</sub> ~~- that~~ means that by omitting dataset i from calculations a higher CC<sub>1/2</sub> results, which is why we want to exclude it from calculations, because it is impairing the whole merged dataset.		If ΔCC<sub>1/2</sub> is > 0 (CC<sub>1/2_overall</sub> is bigger than CC<sub>1/2_i</sub>) it means that by omitting dataset i from calculations a lower CC<sub>1/2</sub> results. As we want to maximize CC<sub>1/2</sub> the dataset is kept for calculations, it is improving the whole merged dataset. If Δ CC<sub>1/2</sub> is < 0 (CC<sub>1/2_overall</sub> is smaller than CC<sub>1/2_i</sub>) it means that by omitting dataset i from calculations a higher CC<sub>1/2</sub> results, which is why we want to exclude it from calculations, because it is impairing the whole merged dataset.


	== Applications ==		== Applications ==

	The ΔCC<sub>1/2</sub> method is applicable for single frames, SSX data and SFX data.		The ΔCC<sub>1/2</sub> method is applicable for single frames, SSX data and SFX data. ΔCC<sub>1/2</sub> can be calculated by [[XDSCC12]].

Gassmann at 14:08, 5 September 2018

2018-09-05T14:08:35Z

← Older revision		Revision as of 16:08, 5 September 2018
Line 6:		Line 6:


	== ~~Program~~ ==		== Applications ==

			The ΔCC<sub>1/2</sub> method is applicable for single frames, SSX data and SFX data.

Gassmann at 14:07, 5 September 2018

2018-09-05T14:07:05Z

@@ Line 1: / Line 1: @@
-ΔCC12 is a quantity, that detects datasets/frames, that are non-isomorphous. As described in [https://scripts.iucr.org/cgi-bin/paper?zw5005 Assmann and Diederichs (2016)], Δcc12 is calculated with the σ-τ method. This method is a way to calculate the Pearson correlation coefficient for the special case of two sets of values (intensities) that randomly deviate from their true values, but is not influenced by a random number sequence as shown in [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3457925/ Karplus and Diederichs (2012)]. For the σ-τ method CC12 is calculated for all datasets/frames, which will be called CC12_overall (?) and CC12 is calculated for all datasets/frames except for one dataset i, which is omitted from calculations and denoted as CC12_i. The difference of the two quantities is Δcc12.
+ΔCC<sub>1/2</sub> is a quantity, that detects datasets/frames, that are non-isomorphous. As described in [https://scripts.iucr.org/cgi-bin/paper?zw5005 Assmann and Diederichs (2016)], ΔCC<sub>1/2</sub> is calculated with the σ-τ method. This method is a way to calculate the Pearson correlation coefficient for the special case of two sets of values (intensities) that randomly deviate from their true values, but is not influenced by a random number sequence as shown in [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3457925/ Karplus and Diederichs (2012)]. For the σ-τ method CC<sub>1/2</sub> is calculated for all datasets/frames, which will be called CC<sub>1/2_overall</sub> and CC<sub>1/2</sub> is calculated for all datasets/frames except for one dataset i, which is omitted from calculations and denoted as CC<sub>1/2_i</sub>. The difference of the two quantities is ΔCC<sub>1/2</sub>.
 : <math>\Delta CC_{1/2}= CC_{1/2 overall}-CC_{1/2 i} </math>
-If ΔCC12 is > 0 -CC12overall is bigger than CC12i- that means if omitting dataset i from calculations, a lower CC12 results, which is why we want to keep it. Thus it is improving the whole merged dataset. If ΔCC12 is < 0, -CC12overall is smaller than CC12i- that means that by omitting dataset i from calculations a higher CC12 results, which is why we want to exclude it from calculations, because it is impairing the whole merged dataset. CC12 is calculated by:
+If ΔCC<sub>1/2_</sub> is > 0 -CC<sub>1/2_overall</sub> is bigger than CC<sub>1/2_i</sub>- that means if omitting dataset i from calculations, a lower CC<sub>1/2</sub> results, which is why we want to keep it. Thus it is improving the whole merged dataset. If Δ CC<sub>1/2</sub> is < 0, -CC<sub>1/2_overall</sub> is smaller than CC<sub>1/2_i</sub> - that means that by omitting dataset i from calculations a higher CC<sub>1/2</sub> results, which is why we want to exclude it from calculations, because it is impairing the whole merged dataset.
 == Program ==

Gassmann at 13:55, 5 September 2018

2018-09-05T13:55:23Z

← Older revision		Revision as of 15:55, 5 September 2018
Line 16:		Line 16:
	<math>\sigma^2_{\epsilon i} = \frac{1}{n-1} \cdot \left ( \sum^n_{j} x^2_{j} - \frac{\left ( \sum^n_{j}x_{j} \right )^2}{ n} \right ) / \frac{n}{2} </math>		<math>\sigma^2_{\epsilon i} = \frac{1}{n-1} \cdot \left ( \sum^n_{j} x^2_{j} - \frac{\left ( \sum^n_{j}x_{j} \right )^2}{ n} \right ) / \frac{n}{2} </math>

	With <math>x_{j} </math> , a single observation j of all observations n of one reflection i. <math>\sigma^2_{\epsilon i} </math> is then divided by the factor <math>\frac{n}{2} </math>, because the variance of the sample mean (the merged observations) is the quantity of interest. ~~As we are considering CC12, the variance <math>\sigma^2_{\epsilon i} </math> is divided~~ by ~~<math>\frac{~~n}{2~~} </math> and not only by '''n'''~~ as ~~described~~ in [https://en.wikipedia.org/wiki/Sample_mean_and_covariance#Variance_of_the_sample_mean ]~~, because we are calculating the random errors of the merged intensities~~ of ~~a half-dataset. The single variance terms~~ are ~~then summed up for~~ all reflections ~~i in a~~ resolution shell ~~and divided by N, the total number of unique reflections.~~		With <math>x_{j} </math> , a single observation j of all observations n of one reflection i. <math>\sigma^2_{\epsilon i} </math> is then divided by the factor <math>\frac{n}{2} </math>, because the variance of the sample mean (the merged observations) is the quantity of interest. The division by n/2 takes care of providing the variance of the mean (merged) intensity of the half-datasets, as defined in [https://en.wikipedia.org/wiki/Sample_mean_and_covariance#Variance_of_the_sample_mean ]. These "variances of means" are averaged over all unique reflections of the resolution shell:


	<math>\sum^N_{i} \sigma^2_{\epsilon i} / N </math>		<math>\sum^N_{i} \sigma^2_{\epsilon i} / N </math>
Line 23:		Line 22:

	----		----



	===''' <math>\sigma^2_{y} </math>'''===		===''' <math>\sigma^2_{y} </math>'''===
Line 32:		Line 29:
	<math>\sigma^2_{y} = \frac{1}{N-1} \cdot \left ( \sum^N_{i} \overline{x}^2 - \frac{\left ( \sum^N_{i} \overline{x} \right )^2}{ N} \right ) </math>		<math>\sigma^2_{y} = \frac{1}{N-1} \cdot \left ( \sum^N_{i} \overline{x}^2 - \frac{\left ( \sum^N_{i} \overline{x} \right )^2}{ N} \right ) </math>

	With <math>\overline{x}</math> , average intensity of all observations from all frames/crystals of one unique reflection i. This is done for all reflections N in a resolution shell.		With <math>\overline{x}= \sum^n_{j} x_{j}</math> , average intensity of all observations from all frames/crystals of one unique reflection i. This is done for all reflections N in a resolution shell.


	== Example ==		== Example ==
	An example is shown for a very simplified data file (unmerged ASCII.HKL). Only two frames/crystals are looked at and the diffraction pattern also consists only of two unique reflections with each three observations for every unique reflection.		An example is shown for a very simplified data file (unmerged ASCII.HKL). Only two frames/crystals are looked at and the diffraction pattern also consists only of two unique reflections with each three observations for every unique reflection.

Gassmann at 13:46, 5 September 2018

2018-09-05T13:46:05Z

← Older revision		Revision as of 15:46, 5 September 2018
Line 10:		Line 10:
	== Implementation ==		== Implementation ==

	===''' <math>\sigma^2_{y} </math>'''===		===''' <math>\sigma^2_{\epsilon} </math>''' - unweighted===

	The ~~unbiased~~ sample ~~variance from all averaged intensities~~ of all unique reflections is ~~calculated~~ by:		The average of all sample variances of the mean across all unique reflections of a resolution shell is obtained by calculating the sample variance of the mean for every unique reflection i by:

	<math>\sigma^2_{y} = \frac{1}{N-1} \cdot \left ( \sum^N_{i} x^~~2_i~~ - \frac{\left ( \sum^N_{i}x_{i} \right )^2}{ N} \right ) </math>		<math>\sigma^2_{\epsilon i} = \frac{1}{n-1} \cdot \left ( \sum^n_{j} x^2_{j} - \frac{\left ( \sum^n_{j}x_{j} \right )^2}{ n} \right ) / \frac{n}{2} </math>

	With <math>x_{i} </math> , ~~average intensity~~ of all observations ~~from all frames/crystals~~ of one ~~unique~~ reflection i. ~~This~~ is ~~done~~ for all reflections N in a resolution shell.		With <math>x_{j} </math> , a single observation j of all observations n of one reflection i. <math>\sigma^2_{\epsilon i} </math> is then divided by the factor <math>\frac{n}{2} </math>, because the variance of the sample mean (the merged observations) is the quantity of interest. As we are considering CC12, the variance <math>\sigma^2_{\epsilon i} </math> is divided by <math>\frac{n}{2} </math> and not only by '''n''' as described in [https://en.wikipedia.org/wiki/Sample_mean_and_covariance#Variance_of_the_sample_mean ], because we are calculating the random errors of the merged intensities of a half-dataset. The single variance terms are then summed up for all reflections i in a resolution shell and divided by N, the total number of unique reflections.


	~~----~~		<math>\sum^N_{i} \sigma^2_{\epsilon i} / N </math>

	~~===''' <math>\sigma^2_{\epsilon} </math>''' - unweighted===~~

	~~The average of all sample variances of the mean across all unique reflections of a resolution shell is obtained by calculating the sample variance of the mean for every unique reflection i by:~~		----

	~~<math>\sigma^2_{\epsilon i} = \frac{1}{n-1} \cdot \left ( \sum^n_{j} x^2_{j} - \frac{\left ( \sum^n_{j}x_{j} \right )^2}{ n} \right ) / \frac{n}{2} </math>~~

	With <math>x_{j} </math> , a single observation j of all observations n of one reflection i. <math>\sigma^2_{\epsilon i} </math> is then divided by the factor <math>\frac{n}{2} </math>, because the variance of the sample mean (the merged observations) is the quantity of interest. As we are considering CC12, the variance <math>\sigma^2_{\epsilon i} </math> is divided by <math>\frac{n}{2} </math> and not only by '''n''' as described in [https://en.wikipedia.org/wiki/Sample_mean_and_covariance#Variance_of_the_sample_mean ], because we are calculating the random errors of the merged intensities of a half-dataset. The single variance terms are then summed up for all reflections i in a resolution shell and divided by N, the total number of unique reflections.

			===''' <math>\sigma^2_{y} </math>'''===

	~~<math>\sum^N_{i} \sigma^2_{\epsilon i} / N </math>~~		The unbiased sample variance from all averaged intensities of all unique reflections is calculated by:

			<math>\sigma^2_{y} = \frac{1}{N-1} \cdot \left ( \sum^N_{i} \overline{x}^2 - \frac{\left ( \sum^N_{i} \overline{x} \right )^2}{ N} \right ) </math>

			With <math>\overline{x}</math> , average intensity of all observations from all frames/crystals of one unique reflection i. This is done for all reflections N in a resolution shell.
	== Example ==		== Example ==
	An example is shown for a very simplified data file (unmerged ASCII.HKL). Only two frames/crystals are looked at and the diffraction pattern also consists only of two unique reflections with each three observations for every unique reflection.		An example is shown for a very simplified data file (unmerged ASCII.HKL). Only two frames/crystals are looked at and the diffraction pattern also consists only of two unique reflections with each three observations for every unique reflection.

Gassmann at 13:28, 5 September 2018

2018-09-05T13:28:12Z

← Older revision		Revision as of 15:28, 5 September 2018
Line 38:		Line 38:
	<pre>		<pre>
	First reflection with 6 observations:		First reflection with 6 observations:
	2 0 0 9.156E+02 3.686E+00 ~~1532.7 1573.4~~ ~~0.4 0.04149~~ 1		h k l int σ(int) #datset
	0 2 0 5.584E+02 3.093E+00 ~~1532.7 1516.6~~ ~~0.7 0.04129~~ 1		2 0 0 9.156E+02 3.686E+00 1
	0 0 2 6.301E+02 2.405E+01 ~~1570.7 1562.9 0.9~~ ~~0.02624~~ 1		0 2 0 5.584E+02 3.093E+00 1
	2 0 0 9.256E+02 3.686E+00 ~~1532.7 1573.4~~ ~~1.4 0.04149~~ 2		0 0 2 6.301E+02 2.405E+01 1
	0 2 0 2.584E+02 3.093E+00 ~~1532.7 1516.6~~ ~~1.7 0.04129~~ 2		2 0 0 9.256E+02 3.686E+00 2
	0 0 2 7.301E+02 2.405E+01 ~~1570.7 1562.9~~ ~~1.9 0.02624~~ 2		0 2 0 2.584E+02 3.093E+00 2
			0 0 2 7.301E+02 2.405E+01 2
	</pre>		</pre>
	<math>x_{i} </math> , the average intensity of all observations from all frames/crystals of this reflection = 669.6999		<math>x_{i} </math> , the average intensity of all observations from all frames/crystals of this reflection = 669.6999
Line 52:		Line 53:
	<pre>		<pre>
	Second reflection with 6 observations:		Second reflection with 6 observations:
	1 1 2 2.395E+01 8.932E+01 ~~1558.2 1508.9 0.4~~ ~~0.05239~~ 1		h k l int σ(int) #datset
	1 2 1 9.065E+01 7.407E+00 ~~1539.1 1507.3 0.2~~ ~~0.05473~~ 1		1 1 2 2.395E+01 8.932E+01 1
	2 1 1 5.981E+01 9.125E+00 ~~1538.8 1507.4 0.9~~ ~~0.05470~~ 1		1 2 1 9.065E+01 7.407E+00 1
	1 1 2 3.395E+01 8.932E+01 ~~1558.2 1508.9 1.4~~ ~~0.05239~~ 2		2 1 1 5.981E+01 9.125E+00 1
	1 2 1 9.065E+01 7.407E+00 ~~1539.1 1507.3 1.2~~ ~~0.05473~~ 2		1 1 2 3.395E+01 8.932E+01 2
	2 1 1 1.608E+01 2.215E+01 ~~1519.8 1516.6 1.3~~ ~~0.04126~~ 2		1 2 1 9.065E+01 7.407E+00 2
			2 1 1 1.608E+01 2.215E+01 2
	</pre>		</pre>
	<math>x_{i} </math> , the average intensity of all observations from all frames/crystals of this reflection = 52.5150		<math>x_{i} </math> , the average intensity of all observations from all frames/crystals of this reflection = 52.5150

Gassmann at 13:24, 5 September 2018

2018-09-05T13:24:59Z

← Older revision		Revision as of 15:24, 5 September 2018
Line 25:		Line 25:
	The average of all sample variances of the mean across all unique reflections of a resolution shell is obtained by calculating the sample variance of the mean for every unique reflection i by:		The average of all sample variances of the mean across all unique reflections of a resolution shell is obtained by calculating the sample variance of the mean for every unique reflection i by:

	<math>\sigma^2_{\epsilon i} = \frac{1}{n-1} \cdot \left ( \sum^n_{j} x^2_{j} - \frac{\left ( \sum^n_{j}x_{j} \right )^2}{ n} \right ) ~~\backslash~~ \frac{n}{2} </math>		<math>\sigma^2_{\epsilon i} = \frac{1}{n-1} \cdot \left ( \sum^n_{j} x^2_{j} - \frac{\left ( \sum^n_{j}x_{j} \right )^2}{ n} \right ) / \frac{n}{2} </math>

	With <math>x_{j} </math> , a single observation j of all observations n of one reflection i. <math>\sigma^2_{\epsilon i} </math> is then divided by the factor <math>\frac{n}{2} </math>, because the variance of the sample mean (the merged observations) is the quantity of interest. As we are considering CC12, the variance <math>\sigma^2_{\epsilon i} </math> is divided by <math>\frac{n}{2} </math> and not only by '''n''' as described in [https://en.wikipedia.org/wiki/Sample_mean_and_covariance#Variance_of_the_sample_mean ], because we are calculating the random errors of the merged intensities of a half-dataset. The single variance terms are then summed up for all reflections i in a resolution shell and divided by N, the total number of unique reflections.		With <math>x_{j} </math> , a single observation j of all observations n of one reflection i. <math>\sigma^2_{\epsilon i} </math> is then divided by the factor <math>\frac{n}{2} </math>, because the variance of the sample mean (the merged observations) is the quantity of interest. As we are considering CC12, the variance <math>\sigma^2_{\epsilon i} </math> is divided by <math>\frac{n}{2} </math> and not only by '''n''' as described in [https://en.wikipedia.org/wiki/Sample_mean_and_covariance#Variance_of_the_sample_mean ], because we are calculating the random errors of the merged intensities of a half-dataset. The single variance terms are then summed up for all reflections i in a resolution shell and divided by N, the total number of unique reflections.


	<math>\sum^N_{i} \sigma^2_{\epsilon i} ~~\backslash~~ N </math>		<math>\sum^N_{i} \sigma^2_{\epsilon i} / N </math>


	~~----~~

	~~===''' <math>\sigma^2_{\epsilon} </math>''' -weighted===~~

	~~to be edited~~

	== Example ==		== Example ==
Line 74:		Line 68:
	<math>\sigma^2_{y} </math>, the variance of all the averaged intensities = 190458.6533		<math>\sigma^2_{y} </math>, the variance of all the averaged intensities = 190458.6533

			As a result of these calculations CC12 =



	== Program ==		== Program ==

Gassmann at 13:09, 5 September 2018

2018-09-05T13:09:13Z

← Older revision		Revision as of 15:09, 5 September 2018
Line 68:		Line 68:

	<math>\sigma^2_{\epsilon i} </math>, the unbiased sample variance of the mean of all observations of this unique reflection i = 363.3267 (1089.9803/(n/2))		<math>\sigma^2_{\epsilon i} </math>, the unbiased sample variance of the mean of all observations of this unique reflection i = 363.3267 (1089.9803/(n/2))


			<math>\sigma^2_{\epsilon} </math> , the average of all the <math>\sigma^2_{\epsilon i} </math> = 10605.7733

			<math>\sigma^2_{y} </math>, the variance of all the averaged intensities = 190458.6533