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CC1/2: Difference between revisions
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With <math>x_{j,i} </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 (intensities of the merged observations) is the quantity of interest. The division by n/2 takes care of providing the variance of the mean (merged) intensity of the half-datasets, as defined in [https://en.wikipedia.org/wiki/Sample_mean_and_covariance#Variance_of_the_sample_mean ]. These "variances of means" are averaged over all unique reflections of the resolution shell: | With <math>x_{j,i} </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 (intensities of the merged observations) is the quantity of interest. The division by n/2 takes care of providing the variance of the mean (merged) intensity of the half-datasets, as defined in [https://en.wikipedia.org/wiki/Sample_mean_and_covariance#Variance_of_the_sample_mean ]. These "variances of means" are averaged over all unique reflections of the resolution shell: | ||
<math>\sum^N_{i} \sigma^2_{\epsilon i} / N </math> | <math>\sigma^2_{\epsilon}=\sum^N_{i} \sigma^2_{\epsilon i} / N </math> | ||