I wish to compare two intra-class correlations: males vs. females. Each
group has a sample of 13 persons, with 3 measurements on each person. The
-loneway- program provides the following estimates:
male: ICC=.90, s.e.= .046 95%CI: .809, .990
female: ICC=.69, s.e.= .120 95%CI: .459, .929
The manual states that the confidence intervals are computed as:
(rho-1.96*se , rho+1.96*se).
This indicates to me that the confidence intervals are computed under the
assumption that rho is normally distributed. If this is valid, it would
seem appropriate to extend the assumption to provide for a simple method to
test the difference between the two ICCs:
e.g., z = (icc1 - icc2)/sqrt(se^2 + se^2). (Or more conservatively, to use
the t-distribution, rather than z).
Does this make sense?
It does (asymptotically for large sample numbers) if the 2 ICCs are
statistically independent. If one ICC is for males and the other is for
females, then this will be the case.
