If the true correlation between X and Y within the general population is
rho=0, and if the size of the sample,
N, on which an observed value of
r is based is equal to or greater than 6, then the quantity
 t =
 r sqrt[(1—r^{2})/(N—2)]

is distributed approximately as
t with
df=
N—2. Application of this formula to any particular observed sample value of
r will accordingly test the null hypothesis that the observed value comes from a population in which
rho=0.
To assess the significance of any particular instance of
r,
enter the values of
N[
>6] and
r into the designated cells below, then click the 'Calculate' button.
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©Richard Lowry 2001
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