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| From Boniface(1995) a Pearson correlation, r, from N pairs of observations can be tested using a t distribution on N-2 degrees of freedom and a test statistic equal to | From Boniface (1995) a Pearson correlation, r, from N pairs of observations can be tested using a t distribution on N-2 degrees of freedom and a test statistic equal to |
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| Equivalently the square of ths test statistic may be compared to a F distribution having 1, N-2 degrees of freedom. | Equivalently the square of this test statistic may be compared to a F distribution having 1, N-2 degrees of freedom. |
How many degrees of freedom do I use to test the magnitude of a Pearson correlation?
From Boniface (1995) a Pearson correlation, r, from N pairs of observations can be tested using a t distribution on N-2 degrees of freedom and a test statistic equal to
$$r sqrt{\frac{N-2}{1-r^text{2}}}$$.
Equivalently the square of this test statistic may be compared to a F distribution having 1, N-2 degrees of freedom.
Reference
Boniface DR (1995) Experiment design and statistical methods for behavioural and social research. Chapman and Hall:London.