math

### correlation

t-statistic for correlation, $r$ $t = r \sqrt{\frac{n-2}{1-r^2}}$

The reverse equation is $r = \frac{t}{\sqrt{t^2 + n-2}}$

Derivation of the reverse equation: \begin{align*} & t = r \sqrt{\frac{n-2}{1-r^2}} & \\ & \frac{t^2}{r^2} = \frac{n-2}{1-r^2} & \\ & \frac{t^2}{n-2} = \frac{r^2}{1-r^2} & \\ & \frac{t^2}{t^2 + n-2} = r^2 & \\ & r = \sqrt{\frac{t^2}{t^2 + n-2}} & \end{align*}