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Pearson Correlation Coefficient

Suppose that we have 2 samples/columns, X and Y. N features from feature1 to featureN. The test statistics is computed as :

denominator1: ${{\sum X^2 - \frac{{\sum X}{\sum X}}{N}}} $

denominator2: ${{\sum Y^2 - \frac{{\sum Y}{\sum Y}}{N}}} $

r = $\frac{\sum{XY}-\frac{\sum {X}\sum{Y}}{N}}\sqrt{{denominator1*denominator2}}$

Spearman Rank-Order Correlation

Suppose that we have 2 samples/columns, the test statistics is computed as :

Spearman-corr = $\frac{\sum{(X_i-\bar X)(Y_i-\bar Y)}}{\sqrt{\sum{(X_i-\bar X)^2}\sum{(Y_i-\bar Y)^2}}}$

where X_i is the rank of the ith X value, Y_i is the rank of the ith Y value, $\bar X$ is the mean of the $X_i$ values, and $\bar Y$ is the mean of the $Y_i$ values.

Real Example

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Topic revision: r5 - 09 May 2005, JoanZhang
 

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