# What Is The Difference Between Correlation And Agreement

Example 6. Consider Example 5 again. The mean (sample) and variance of yi1 as well as the correlation (sample) 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. Thus, it follows from (11) that p⌢ccc=2σ⌢12σ⌢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=p⌢C⌢b = 0.0533. In this example, the Pearson correlation is p⌢=0.531, while the Spearman correlation is ρ⌢=1. Thus, only the Spearman Rho captures the perfect nonlinear relationship between ui and vi. Any two pairs of bivariate results (ui, vi) and (uj, vj) that satisfy (5) or (6) are considered concordant or discordant; That is, ui and vi are either larger or both smaller than uj and vj. Thus, the perfect positive (negative) correlation of Spearmans Rho corresponds to the perfect concordance (discothetance); i.e. concordant (discordant) pairs (ui, vi) and (uj, vj) for all 1≤i<j≤n. The wrong association between ui and vi, as indicated by the product-moment correlation, contradicts the perfect conceptual correlation between the two variables.

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