Significance of a Correlation Coefficient

The logic and computational details of correlation are
described in Chapter 3 of Concepts and Applications.
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—r2)/(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.
N =
r =
   
t
df
Probability
directional 
non-directional 

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