For a systematic survey of ICC (A,1), we can find that the ICC population can be written for absolute consent (36) Note that, contrary to correlation, the issue of linear versus non-linear association does not occur in the evaluation of the agreement. This is because a good agreement requires an approximate linear relationship between the results. For example, in the case of two advisors, good agreement requires that yi1 and yi2 be close, such as yi1 – yi2 in case of perfect agreement. ICC distributions (C,1) are insensitive to the presence of distortion; they remain the same, regardless of the strength of the bias. Using Eq (13), we find for the three ICC distributions (C,1) 2C – 102/(102 – 52) – 0.8. They coincide with ICC distribution (1) (zero-bias) and ICC distribution (A,1) when distortions are very low. This indicates that the confidence limits of 2C (the ICC consistency population of Model 2) will be the same as the confidence limits of 1 (Model 1 ICC population, i.e. in the absence of bias). Thus, Figure 8 can be used to graphically deduct not only the confidence limits corresponding to an ICC (1) calculated from an experimental matrix compatible with Model 1, but also the confidence limits corresponding to an ICC value (C,1) calculated from a matrix compatible with Model 2.
This finding is consistent with the confidence formulas provided by McGraw and Wong , provided the number of subjects is not too small. We are now turning to the consistency version of the intraclassical correlation coefficient of the population defined with Model 3 in the same way as for Model 2, i.e. as (27) reminder that size 2 – 2 , Eq (27) is identical to the ICC population, called McGraw and Wong`s « Case 3A » . In fact, Eq (27) is identical to Eq (13), and with Eq (25), there is again the ICC formula (C,1) of Eq (14), also in agreement with McGraw and Wong . This result is also achieved by Bartko , with the additional assumption that the notion of interaction is negligible.