# Re: Minimum number of cases for a correlation?

• From: "Ray Koopman" <koopman@xxxxxx>
• Date: 28 May 2006 23:13:18 -0700

Greg Heath wrote:
John Uebersax wrote:
Is an N of 12 just too small for a correlation?

In answering this I think one also needs to take into consideration the
likely magnitude of the correlation coefficient. For example, if, in a
given set of data, N = 12 and r = 1.0, then the N is probably large
enough to show association.

One suggestion might be to construct, say, the 90% confidence interval
of the correlation coefficient. That will adequately convey the
uncertainty in estimation due to the small N.

How is this obtained when rho ~= 0?

I know that when rho = 0,

1. t = r*sqrt((n-2)/(1-r^2)) is t(n-2) for a binormal distribution in x
and y.
2. z = invtanh(r) --> N{0,1/(n-3)} as n --> inf.

Can these be generalized for rho ~= 0?

For samples from a bivariate normal population,
arctanh(r) --> N{arctanh(rho),1/(n-3)} as n --> inf.
This leads to the approximate confidence interval
tanh[arctanh(r) +/- z/sqrt(n-3)],
where z is a critical value from the standard normal distribution
(e.g., 1.96 for a 95% CI).

.