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 Jun 19, 2006, 11:56:04 AM (17 years ago)
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trunk/doc/Statistics.tex
r494 r586 49 49 50 50 The first group is when some of the measurements are known to be more 51 precise than others. The more precise a measurem tns isthe larger51 precise than others. The more precise a measurement is, the larger 52 52 weight it is given. The simplest case is when the weight are given 53 53 before the measurements and they can be treated as deterministic. It … … 70 70 can be treated as independent of the observable. 71 71 72 Since there are various origin for a weight occuring in a statistical73 analysis, there are various way to treat the weights and in general72 Since there are various origins for a weight occuring in a statistical 73 analysis, there are various ways to treat the weights and in general 74 74 the analysis should be tailored to treat the weights correctly. We 75 75 have not chosen one situation for our implementations, so see specific … … 83 83 \end{itemize} 84 84 An important case is when weights are binary (either 1 or 0). Then we 85 get same result using the weighted version as using the data with85 get the same result using the weighted version as using the data with 86 86 weight not equal to zero and the nonweighted version. Hence, using 87 87 binary weights and the weighted version missing values can be treated … … 182 182 the variance is estimated as $\sigma_x^2=\frac{\sum 183 183 w_xw_y(xm_x)^2}{\sum w_xw_y}$. As in the nonweighted case we define 184 the correlation to be the ratio between the covariance and geom trical185 aver gae of the variances184 the correlation to be the ratio between the covariance and geometrical 185 average of the variances 186 186 187 187 $\frac{\sum w_xw_y(xm_x)(ym_y)}{\sqrt{\sum w_xw_y(xm_x)^2\sum
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