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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\_j,i} </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\_j,i}^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}} -\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> | <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> | ||