Consider a study on n topics and assume that each subject is evaluated by a different group of two judges. Once again, do yik to designate the assessment of the subject of Ith by Judge Kth (1≤i≤n, 1≤k≤2). Let the values of the average and variance of yik and 12 Cov (yi1, yi2) covariance between yi1 and yi2. The CCC is defined as: Example 6. Consider example 5 again. The average and variance of yi1 and the correlation (example) between yi1 and yi2 are given by: μ⌢1-3, μ⌢2-8, σ⌢12-2.5, σ⌢22-2.5 and σ⌢12-1. The result (11) is that p⌢ccc-2⌢12⌢12-σ⌢22(μ⌢1-μ⌢2) 2-0.053 . We can also obtain p⌢CCC using the decomposition result which, in our case, gives p⌢-1, C⌢b-0.0533 and p⌢CCC⌢⌢b – 0.0533. The agreement, also called reproducibility, is a term closely related to correlation, but fundamentally different from them.
Like the correlation, the agreement also assesses the relationship between the results of interest, but as the name suggests, the emphasis is on the degree of agreement in opinions between two or more individuals or in the outcomes between two or more assessments of variables of interest. An example of agreement in psychological research is the consensus among several clinicians on psychiatric diagnoses in a group of patients. In biomedical sciences, the agreement can also measure the reproducibility (i.e. reliability) of a laboratory result, if repeated in the same center or if it is performed in several centers under the same conditions. It is not wise to talk about the concordance (reproducibility) between variables that measure different constructions; Thus, when measuring the association between different variables – such as weight and height – one can judge the correlation, but not the concordance. For continuous results, intraclass correlation (CCI) is a popular measure of compliance. Like the Pearson correlation, CCI is an estimate of the extent of the relationship between variables (in this case between multiple evaluations of the same variable). However, the ICC also takes into account the bias of counsel, the element that distinguishes the match from the correlation; in other words, good agreement (reproducibility) requires not only a good correlation, but also a small bias of bias. We discussed the concepts of concordance and correlation and described the different measures that can be used to assess the relationships between variables of interest. We focused on continuous measurements and methods of results. Different methods should be used for non-continuous results.
For example, for categorical results, another version of Kendalls Tau, known as Kendalls Tau b, can be used to assess correlation, and Kappa can be used to evaluate chords.  Consider a sample of subjects and a continuous bivariat result (ui, vi) of each subject in the sample (1≤i≤n). The Pearson correlation is the most popular statistic for measuring the association between the two variables ui and vi: In this example, the pearson correlation is p⌢-0.531, while spearmans n⌢ 1. Thus, only Spearman-Rho captures the perfect non-linear relationship between ui and vi. As ui and vi are linearly related, the pearson correlation can be applied, giving p⌢-1, indicating a perfect correlation. However, the data clearly do not indicate a perfect consistency; In fact, the two judges do not agree. Like the Pearson and Spearman correlations, the Kendalls sample⌢ in (8) assesses the following population parameters: that pCCC-1 (-1) if and only if p-1 (-1), 1 -2 and 12-22.  So, pCCC-1 (-1) if and only if and only if and only if yi1 -(10) yi2 (yi1-yi2), i.e.
if there is a perfect agreement (disagreement). The Bias Cb correction factor (0≤Cb≤1) in (12) assesses the level of bias, with the smaller cb indicating greater distortion. Therefore, unlike CCI, poor match may be due to low correlation (small p) or large distortion (small cb).