Peter H. Schonemann
On non-null tests of intraclass correlations
Chinese Journal of Psychology, 1991, 33, 3-10.
It is shown that the non-null distribution of a simple transform of the 2-variable intraclass correlation is central F. Hence, in principle, standard F tables could be used to test hypothesis about intraclass correlations.
In a simulation, Fisher's normal approximation was compared with the exact test for three different intraclass correlation estimates. Overall, the results were very close, confirming that Fisher's z-transform is an excellent approximation even when the sample size is small.