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DeltaCC12: Difference between revisions
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===''' <math>\sigma^2_{\epsilon} </math>'''=== | ===''' <math>\sigma^2_{\epsilon} </math>''' - unweighted=== | ||
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 i by: | 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 i by: | ||
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<math>\sigma^2_{\epsilon i} = \frac{1}{n-1} \cdot \left ( \sum^n_{j} x^2_{j} - \frac{\left ( \sum^n_{j}x_{j} \right )^2}{ n} \right ) \backslash \frac{n}{2} </math> | <math>\sigma^2_{\epsilon i} = \frac{1}{n-1} \cdot \left ( \sum^n_{j} x^2_{j} - \frac{\left ( \sum^n_{j}x_{j} \right )^2}{ n} \right ) \backslash \frac{n}{2} </math> | ||
With <math>x_{j} </math> , a single observation j of all observations n of one reflection i. <math>\sigma^2_{\epsilon i} </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 CC12, the variance <math>\sigma^2_{\epsilon i} </math> is divided by <math>\frac{n}{2} </math> and not by n as described in [https://en.wikipedia.org/wiki/Sample_mean_and_covariance#Variance_of_the_sample_mean ]. This is done for all reflections n in a resolution shell. | With <math>x_{j} </math> , a single observation j of all observations n of one reflection i. <math>\sigma^2_{\epsilon i} </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 CC12, the variance <math>\sigma^2_{\epsilon i} </math> is divided by <math>\frac{n}{2} </math> and not by '''n''' as described in [https://en.wikipedia.org/wiki/Sample_mean_and_covariance#Variance_of_the_sample_mean ]. This is done for all reflections n in a resolution shell. | ||
===''' <math>\sigma^2_{\epsilon} </math>''' -weighted=== | |||
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