The Tukey Mean-Difference Plot:
The Tukey mean-difference plot is a scatter graph produced not for (x,y) values themselves, but for modified coordinates (X,Y)
Such a plot is useful, for example, to analyze data with strong correlation between x and y – when the (x,y) dots on the plot are close to the diagonal x=y. In this case, the value of the transformed variable X is about the same as x and y; and the variable Y shows the difference between x and y.
The Tukey mean-difference plot is meaningful for two similar variables – that is, when both x and y are of the same physical dimension and expressed in the same units – e.g mass in pounds (or kilograms, …), length in foots (or meters, …). Otherwise, it makes no sense to sum up or subtract values of the variables x and y.