Formula for Pearson correlation - 2

The Pearson correlation is denoted with r and calculated as follows:

\[r = \frac{covariance\:of\:x\:and\:y}{variability\:of\:x\:and\:y\:seperately}\]


\[r = \frac{\sum{(x-\bar{x})(y-\bar{y})}}{\sqrt{\sum{(x-\bar{x})^2} \sum{(y-\bar{y})^2}}}\]

which is the same as:

\[r = \frac{N \sum{xy}-(\sum{x})(\sum{y})}{\sqrt{[N\sum{x^2}-(\sum{x})^2] [N\sum{y^2}-(\sum{y})^2]}}\]

  • N: number of pairs of scores
  • x: x scores
  • y: y scores
  • : mean of x scores
  • ȳ: mean of y scores
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