Pearson's Product Moment Correlation

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

$r=\frac{\sum _{i=1}^n{w}_i(x_i-\overline{x})(y_i-\overline{y})}{\sqrt{\sum _{i=1}^n{w}_i(x_i-\overline{x}{)}^2}\sqrt{\sum _{i=1}^n{w}_i(y_i-\overline{y}{)}^2}}$

where:

$w_i$ is the Calibrated Weight for the $i$th of $n$ observations

$p\approx \mathrm{Pr}(t_{\sum _{i=1}^n{w}_i-2}\ge r\sqrt{\frac{\sum _{i=1}^n{w}_i-2}{1-r^2}})$

See also

Correlations - Comparing Two Numeric Variables