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As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059  '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as
 
As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059  '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as
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<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>
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<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.
     
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