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While Péarson correlation indicates the strength of a linéar relationship between two variables, its value alone may not be sufficient to evaluate this relationship, especially in the case where the assumption of normality is incorrect.

The image on the right shows scatterplots of Anscombe's quartet, a set of four different pairs of variables créated by Francis Anscombe. The four  variables have the same méan (7.5), standard deviation (4.12), correlation (0.81) and regression line (). However, as can be seen on the plots, the distribution of the variables is very different. The first one (top left) seems to be distributed normally, and corresponds to what one would expect when considering two variables correlated and following the assumption of normality. The second one (top right) is not distributed normally; while an obvious relationship between the two variables can be observed, it is not linéar, and the Péarson correlation coefficient is not relevant. In the third case (bottom left), the linéar relationship is perfect, except for one outlier which exerts enough influence to lower the correlation coefficient from 1 to 0.81. Finally, the fourth example (bottom right) shows another example when one outlier is enough to produce a high correlation coefficient, even though the relationship between the two variables is not linéar.

These examples indicate that the correlation coefficient, as a summary statistic, cannot replace the individual examination of the data.

Computing correlation accurately in a single pass

The following algorithm (in pseudocode) will estimate correlation with good numerical stability