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DeltaCC12: Difference between revisions
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== Implementation == | == Implementation == | ||
===''' <math>\sigma^2_{y} </math>'''=== | ===''' <math>\sigma^2_{y} </math>'''=== | ||
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<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_{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> | ||
With <math>x_{i} </math> , average intensity of a unique reflection i. This is done for all reflections n in a resolution shell. | 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. | ||
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===''' <math>\sigma^2_{\epsilon} </math>'''=== | |||
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 by: | |||
<math>\sigma^2_{\epsilon} = \frac{1}{n-1} \cdot \left ( \sum^n_{i} x^2_i - \frac{\left ( \sum^n_{i}x_{i} \right )^2}{ n} \right ) \backslash \frac{n}{2} </math> | |||
With <math>x_{i} </math> , a single observation i of all observations n one reflection. <math>\sigma^2_{\epsilon} </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 This is done for all reflections n in a resolution shell. | |||