Since the overall probability of the concordance is Σi πii, the probability of a concordance under the zero hypothesis is equal to Σi+π+i. Also note that Σi πii = 0 does not mean a match and that Σi πii = 1 indicates a perfect match. Kappa statistics are defined in such a way that a larger value implies greater concordance, in addition: Wilding GE, Consiglio JD, Shan G. Precise approaches to test hypotheses based on the Kappa coefficient in the class. Stat Med. 2014;33 (17): 2998-3012. doi.org/10.1002/sim.6135. As noted above, correlation is not synonymous with concordance. Correlation refers to the existence of a relationship between two different variables, while concordance refers to the concordance between two measures of a variable.
Two groups of highly correlated observations may have a mismatch; However, if the two groups of values are identical, they will certainly be highly correlated. For example, in the example of hemoglobin, the correlation coefficient between the values of the two methods is high, although the concordance is poor [Figure 2]; (r = 0.98). The other way to look at it is that, although the individual points are not close enough to the dotted line (the smallest square line;[ 2] which indicates a good correlation), these are quite far from the black line crossed which represents the line of the perfect correspondence (Figure 2: the black line crossed). If a good match is made, points are expected to fall on or near this line (the black line) crossed. .
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