A Tukey sum-difference plot allows users to study more effectively the deviations of data points from the 45-degree line y = x.

A scatterplot with the line y = x drawn inside
is frequently used to compare 2 variables.
It is the *vertical* deviation
from a point to the line y = x that matters here,
not the shortest distance from a point to the line y = x.
It is hard to compare the vertical deviations of the points from the line
because the non-zero slope of the line y = x affects our visual
perception.

Fig. A: A traditional way to compare 2 numerical variables |

A Tukey sum-difference plot is the result of rotating the point cloud in a scatterplot 45-degree clockwise followed by an expansion of the vertical scale. It allows users to study more effectively the deviations of the points from the line y = x.

It is much easier to compare the 2 red points in the Tukey sum-difference plot in Fig. B.

Fig. B: A Tukey sum-difference plot |