Standard deviation

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Standard deviation
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Category: Standard deviation
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Standard deviation

To aggregate two standard deviation with equal weight one should also use the correlation coefficient between the two random variables. When, e.g., aggregating standard deviation for left and right brain volumes the standard deviation for the total brain volume will be:[1]

<math>\sigma_T = \sqrt{\sigma_L^2 + \sigma^2_R + 2\sigma_L\sigma_R\rho_{LR}}</math>

For human brain volume studies the unknown <math>\rho_{LR}</math> have been set to 0.78 based on an independent study.[2] If <math>\sigma_L = \sigma_R = 1, \rho_{LR}=0.78</math>

<math>\sigma_T = \sqrt{1+1+2 \times 0.78} \approx 1.89</math>

[edit] References

  1. Progressive lateral ventricular enlargement in schizophrenia: a meta-analysis of longitudinal MRI studies. See also Brain volume abnormalities in major depressive disorder: a meta-analysis of magnetic resonance imaging studies.
  2. Canonical correlation analysis of sub-cortical brain structures using non-rigid registration
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