CC1/2: Difference between revisions

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If the standard deviations <math>\sigma_{int} </math> for the single observations are considered as weights for the CC<sub>1/2</sub> calculation, with <math>\sum^{n_{i}}_{j}w_{i}=\sum^{n_{i}}_{j}\frac{1}{\sigma_{int}^2} </math> the unbiased '''weighted''' sample variance of the mean for every unique reflection i is obtained by:  
If the standard deviations <math>\sigma_{int} </math> for the single observations are considered as weights for the CC<sub>1/2</sub> calculation, with <math>\sum^{n_{i}}_{j}w_{i}=\sum^{n_{i}}_{j}\frac{1}{\sigma_{int}^2} </math> the unbiased '''weighted''' sample variance of the mean for every unique reflection i is obtained by:  


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


These " weighted variances of means" are averaged over all unique reflections of the resolution shell:
These " weighted variances of means" are averaged over all unique reflections of the resolution shell:
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