A note on estimating a correlation using multiple scores from a set of subjects

In general 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.

The above, however, assumes that the observations are independent. If this is not the case, for example combining more than one score on the same subject, then it is suggested that a subject summary score measure such as a mean score is used so that variation is only between subject. See the articles by Martin Bland given [attachment:bmjmb1.pdf here] and [attachment:bmjmb2.pdf here] for further details.

Reference

Boniface DR (1995) Experiment design and statistical methods for behavioural and social research. Chapman and Hall:London.