This paper, authored by J. Martin Bland and Douglas G. Altman, discusses the analysis of agreement between two methods of measurement when multiple observations are available for each individual. The authors address the limitations of the traditional limits of agreement (LoA) method, which assumes independent observations, and propose methods to handle clustered observations, whether the underlying quantity is changing or constant. For the "non-constant" case where the true value varies, the authors estimate the mean difference and standard deviation of differences using one-way analysis of variance. They calculate two different variances: one for repeated differences within subjects and another for differences between averages across subjects. The estimated variance for individual differences is derived from these components, and the 95% limits of agreement are then calculated. For the "constant" case where the true value does not change, the authors assume that the variability is composed of three components: variability across individuals, heterogeneity of individual averages, and variability of repeated measurements. They derive the estimated standard deviation for individual differences and calculate the 95% limits of agreement accordingly. The paper emphasizes the importance of considering the data structure to avoid producing overly narrow limits of agreement, which could lead to incorrect conclusions about the agreement between methods. The authors provide numerical examples to illustrate their methods and highlight the advantages of using replicate observations to compare the repeatability of measurement methods.This paper, authored by J. Martin Bland and Douglas G. Altman, discusses the analysis of agreement between two methods of measurement when multiple observations are available for each individual. The authors address the limitations of the traditional limits of agreement (LoA) method, which assumes independent observations, and propose methods to handle clustered observations, whether the underlying quantity is changing or constant. For the "non-constant" case where the true value varies, the authors estimate the mean difference and standard deviation of differences using one-way analysis of variance. They calculate two different variances: one for repeated differences within subjects and another for differences between averages across subjects. The estimated variance for individual differences is derived from these components, and the 95% limits of agreement are then calculated. For the "constant" case where the true value does not change, the authors assume that the variability is composed of three components: variability across individuals, heterogeneity of individual averages, and variability of repeated measurements. They derive the estimated standard deviation for individual differences and calculate the 95% limits of agreement accordingly. The paper emphasizes the importance of considering the data structure to avoid producing overly narrow limits of agreement, which could lead to incorrect conclusions about the agreement between methods. The authors provide numerical examples to illustrate their methods and highlight the advantages of using replicate observations to compare the repeatability of measurement methods.