# Re: st: comparing two ICCs

 From Roger Newson To statalist@hsphsun2.harvard.edu Subject Re: st: comparing two ICCs Date Tue, 18 Jun 2002 20:57:52 +0100

```At 15:22 18/06/02 -0400, Paul Visintainer wrote:
```
```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.

However, with large ICCs such as these, the use of CIs of the form estimate +/- 2*SE might be questionable, unless the sample number is really huge, because the sampling distribution of sample ICCs and their differences tends to be skewed if the corresponding population ICCs and/or their differences are far from zero. It might be a better idea to use the bootstrap, with percentile-based confidence limits. See -[R] bstrap- or -help bstrap-.

Another, less orthodox alternative might be to use intraclass Kendall's correlation coefficients, and calculating CIs for their differences, using my own -somersd- package together with -joinby-. See -ssc describe somersd- and -help joinby-.

I hope this helps.

Roger

--
Roger Newson
Lecturer in Medical Statistics
Department of Public Health Sciences
King's College London
5th Floor, Capital House
42 Weston Street
London SE1 3QD
United Kingdom

Tel: 020 7848 6648 International +44 20 7848 6648
Fax: 020 7848 6620 International +44 20 7848 6620
or 020 7848 6605 International +44 20 7848 6605
Email: roger.newson@kcl.ac.uk

Opinions expressed are those of the author, not the institution.

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