What test should I use to statistically compare two intraclass correlation coefficients (ICC)?

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I need to compare two generalizability (G) coefficients for data that are from two separate populations. G coefficients are a type of intraclass correlation coefficient (ICC). The literature on statistically comparing G coefficients is sparse by all accounts, so I thought that the best I might do was find out the recommendation for statistically comparing ICCs.

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A simple and reliable method is to look not only at point estimates of ICCs, but also at their confidence intervals. You can check whether there is an overlap between the CIs of a given ICC and the point estimate of another ICC. If an overlapping is present, you can't reject the hypothesis that the two ICCs are not different.