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CC1/2: Difference between revisions
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weighted version of sigma-y formula
(→Example: fix )) |
(weighted version of sigma-y formula) |
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<math>\sigma^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> | <math>\sigma^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> | ||
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If the standard deviations <math>\sigma_{int\_j,i} </math> for the single observations are considered as weights, <math>\sigma^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>\sigma^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> | |||
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== why CC<sub>1/2</sub> can be negative == | == why CC<sub>1/2</sub> can be negative == | ||
If the numerator of the formula becomes negative, CC<sub>1/2</sub> is negative. This happens if the variance of the average intensities across the unique reflections of a resolution shell is low, but the individual measurements of each unique reflection vary strongly. This is discussed in §4.1 of [https://cms.uni-konstanz.de/index.php?eID=tx_nawsecuredl&u=0&g=0&t=1475179096&hash=5cf64234a23a794a1894c5408384c57208d7b602&file=fileadmin/biologie/ag-strucbio/pdfs/Assman2016_JApplCryst.pdf Assmann, G., Brehm, W. and Diederichs, K. (2016) Identification of rogue datasets in serial crystallography (2016) J. Appl. Cryst. 49, 1021-1028.] | |||