Chunk #13 — Findings — Improvements in PLINK 1.9 — Bit population count

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Second-generation PLINK: rising to the challenge of larger and richer datasets.

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The correlation coefficient of interest can then be expressed as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\begin{array}{@{}rcl@{}} r & = & \frac{|I_{x,y}|^{-1}\sum_{i\in I_{x,y}}\left(v_{i} - \overline{v}\right)\left(w_{i} - \overline{w}\right)}{\sqrt{\left(\overline{v^{2}} - \overline{v}^{2}\right)\left(\overline{w^{2}} - \overline{w}^{2}\right)}} \\ & = & \frac{|I_{x,y}|^{-1}\sum_{i=1}^{n}v_{i}w_{i} - \overline{v}\cdot \overline{w}}{\sqrt{\left(\overline{v^{2}} - \overline{v}^{2}\right)\left(\overline{w^{2}} - \overline{w}^{2}\right)}} \end{array} $$ \end{document}r=|Ix,y|−1∑i∈Ix,yvi−v¯wi−w¯v2¯−v¯2w2¯−w¯2=|Ix,y|−1∑i=1nviwi−v¯·w¯v2¯−v¯2w2¯−w¯2