Pearson's Product Moment Correlation

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The correlation between two variables, x and y, with weighted means of \bar{x} and \bar{y} respectively, is:

r = \frac{\sum ^n _{i=1}w_i(x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum ^n _{i=1}w_i(x_i - \bar{x})^2} \sqrt{\sum ^n _{i=1}w_i(y_i - \bar{y})^2}}

where:

w_i is the Calibrated Weight for the ith of n observations
p \approx \Pr(t_{\sum^n_{i=1}w_i-2} \ge r\sqrt{\frac{\sum^n_{i=1}w_i-2}{1 - r^2}})

See also

Correlations - Comparing Two Numeric Variables