Think of two ophthalmologists who measure the pressure of the ophthalmometer with a tonometer. Each patient therefore has two measures – one of each observer. CCI provides an estimate of the overall agreement between these values. It is akin to a “variance analysis” in that it considers the differences in intermediate pairs expressed as a percentage of the overall variance of the observations (i.e. the overall variability in the “2n” observations, which would be the sum of the differences between pairs and sub-pairs). CCI can take a value of 0 to 1, 0 not agreeing and 1 indicating a perfect match. As mentioned above, correlation is not synonymous with agreement. The correlation refers to the existence of a relationship between two different variables, while the agreement considers the agreement between two measures of a variable. Two sets of observations, strongly correlated, may have a poor agreement; However, if the two sets of values agree, they will certainly be strongly correlated. For example, in the hemoglobin example, the correlation coefficient between the values of the two methods is high, although the agreement is poor [Figure 2]; (r – 0.98). The other way of looking at it is that, although the different points are not close enough to the dotted line (least square line; , indicating a good correlation), these are quite far from the running black line that represents the perfect chord line (Figure 2: the black line running). If there is a good agreement, the dots should fall on or near this line (of the current black line).
If two instruments or techniques are used to measure the same variable on a continuous scale, Bland Altman plots can be used to estimate match. This diagram is a diagram of the difference between the two measurements (axis Y) with the average of the two measurements (X axis). It therefore offers a graphic representation of distortion (average difference between the two observers or techniques) with approval limits of 95%. These are indicated by the formula: the statistical methods used to assess compliance vary depending on the nature of the variables examined and the number of observers between whom an agreement is sought. These are summarized in Table 2 and explained below. It is important to note that in each of the three situations in Table 1, the passport percentages are the same for both examiners, and if the two examiners are compared to a typical 2-×-2 test for mated data (McNemar test), there would be no difference between their performance; On the other hand, the agreement between the observers is very different in these three situations.