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CC1/2: Difference between revisions
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→Method
(weighted version of sigma-y formula) |
(→Method) |
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<math>\sigma^2_{\epsilon_w}=\sum^N_{i} \sigma^2_{\epsilon i\_w} / N </math> | <math>\sigma^2_{\epsilon_w}=\sum^N_{i} \sigma^2_{\epsilon i\_w} / N </math> | ||
It should be noted that it is not straightforward to define the correct way to calculate a weighted variance (and the weighted variance of the mean). The formula <math>s^2_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 )</math> is also found at [https://www.itl.nist.gov/div898/software/dataplot/refman2/ch2/weightsd.pdf] | |||
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<math>\overline{x}_{i_w} = \frac{\sum^n_{j} w_{j,i} x_{j,i}} {\sum^n_{j}w_{j,i}}</math>: | <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> | <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> | ||
== Example == | == Example == | ||