Actually, calculation and display of Pearson's correlation in such a situation is purely anecdotal because if relationship between two methods of clinical measurement is not deterministic (i.e. points do not stand along the line Y=1), this implies that there is a difference between the both methods, and analysis of « disagreement » is only accessible through representation of Bland & Altman.
In other words, if Pearson's correlation measures strength of a linear relationship between 2 quantitative variables (in our example 2 methods of clinical measurement), but not agreement between the both series of measurements. Then it is possible to calculate, on a same data set, a high Pearson's correlation coefficient and a low agreement.
Bland & Altman solved the following problem: as equality between 2 methods of clinical measurement is not verified, how is it possible to evaluate agreement between them? You want to know by how much the new method is likely to differ from the old: if this is not enough to cause problems in clinical interpretation you can replace the old method by the new or use the two interchangeably.
First step consists in visual analysis of plot of the difference between the methods (ordinate) against their mean (abscissa). If points' repartition is uniform (i.e. gap between couples of points is independent of their mean) then, we can calculate the bias of measures between both methods (cf. next step). On the other hand, if differences are related to means, it is recommended to practice a log transformation of data in order to "reduce" this link.
Second step consists in calculate numeric parameters to evaluate agreement between the both methods :
- you can summarise the lack of agreement by calculating the bias, estimated by the mean d and standard deviation Sd of gaps between couples of points ;
- limits of agreement (95%) are calculated with d +/- 1.96 Sd
95% of differences will lie between these limits d + 1.96 Sd et d - 1.96 Sd
Conditions of use (automatically checked with StatEL) : differences between both methods are distributiion-free.