“In simple terms the ICC is the ratio of true score variance (between-subjects variance) to true score variance plus error. If the true score variance is sufficiently large, reliability will always appear high and vice versa.”
“The Bland and Altman methods are independent of the true variability in the observations.”
“In the meantime the following points should be noted. Bland and Altman 95% limits of agreement indicate a range of error, but this must be interpreted with reference to the range of measurement values obtained. Therefore, Bland and Altman tests should be complemented by raw data and/or ranges. If using the ICC, the between-subjects variation should be a meaningful index of reliability, i.e. the variation between subjects in the selected sample must reflect the true population of interest.”
“Conclusions: The ICC and Bland and Altman tests are appropriate for analysis of reliability studies of similar design to that described, but neither test alone provides sufficient information and it is recommended that both are used.”
Source: Rankin, G., & Stokes, M. (1998). Reliability of assessment tools in rehabilitation: An illustration of appropriate statistical analyses. Clinical Rehabilitation, 12(3), 187–199. https://doi.org/10.1191/026921598672178340