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CC1/2: Difference between revisions
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→\sigma^2_{y}
(→\sigma^2_{\epsilon}: change nomenclature from sigma to s) |
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Let N be the number of reflections in a resolution shell. With <math>\overline{x}_{i}= \sum^n_{j} x_{j,i}</math> , the unbiased sample variance from all averaged intensities of all unique reflections is calculated by: | Let N be the number of reflections in a resolution shell. With <math>\overline{x}_{i}= \sum^n_{j} x_{j,i}</math> , the unbiased sample variance from all averaged intensities of all unique reflections is calculated by: | ||
<math> | <math>s^2_{y} = \frac{1}{N-1} \cdot \left (\sum^N_{i} \overline{x}_{i}^2 - \frac{\left ( \sum^N_{i} \overline{x}_{i} \right )^2}{ N} \right ) </math> | ||
---- | ---- | ||
If the standard deviations <math>\sigma_{int\_j,i} </math> for the single observations are considered as weights, <math> | If the standard deviations <math>\sigma_{int\_j,i} </math> for the single observations are considered as weights w<sub>I</sub>, <math>s^2_{y}</math> is obtained from | ||
<math>\overline{x}_{i_w} = \frac{\sum^n_{j} w_{j,i} x_{j,i}} {\sum^n_{j}w_{j,i}}</math>: | <math>\overline{x}_{i_w} = \frac{\sum^n_{j} w_{j,i} x_{j,i}} {\sum^n_{j}w_{j,i}}</math>: | ||
<math> | <math>s^2_{y_w} = \frac{1}{N-1} \cdot \left (\sum^N_{i} \overline{x}_{i_w}^2 - \frac{\left ( \sum^N_{i} \overline{x}_{i_w} \right )^2}{ N} \right ) </math> | ||
== Example == | == Example == | ||