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We are measuring two waves from a biological signal. As an example consider the ECG $P$ wave and $T$ wave. From a single trace, the amplitude of both of these waves is measured. We want to compare the inter-session reliability of the two waves; doing a second measurement a week later. So in this example we have $P_1$, $P_2$, $T_1$ and $T_2$. We expect, and have found, correlations between ($P_1$, $P_2$) ($P_1$, $T_1$) and all of the combinations. $ICC_{2,1}$ for the $P$ wave ($P_1$, $P_2$) was $0.8$ and for the $T$ wave was $0.6$. Confidence intervals for each ICC can be computed by bootstrap but how can we compare the test-retest reliabilities of the two waves?

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    $\begingroup$ Do $P_1$, $P_2$, $T_1$ and $T_2$ all refer to vectors of exchangeable values (exchangeable within a vector)? Or is there, for example, some sensible a priori pairing between the values in $P_1$ and $T_1$, so that the ordering of the values in each vector is not arbitrary? $\endgroup$ – Jake Westfall Nov 17 '13 at 22:35
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Lu L, Shara NM. Reliability analysis: calculate and compare intra-class correlation coefficients (ICC) in SAS. Northeast SAS Users Group; 2007. illustrate a method to compare 2 independent ICCs In a similar fashion ou could calculate bootstrapped ICCs differences of paired observations and use a one sample t test. This can easily be implemented in R using the boot and ICC packages Also try reading this.

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