Z-test for non-zero correlation

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Are two variables significantly correlated with a population correlation $\rho$ different from zero ?

$\displaystyle H_0:\rho$	$\displaystyle =$	0	(6.4)
$\displaystyle H_1: \rho$	$\displaystyle \neq$	$\displaystyle 0 \nonumber$

Two-sided test using a t statistic with Student's t sampling distribution

$\displaystyle T$

$\displaystyle =$

$\displaystyle \frac{r\sqrt{n-2}}{\sqrt{1-r^2}}\sim t_{n-2}$

David Stephenson 2005-09-30