# The Tukey Mean-Difference Plot

#### Statistical Glossary

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)

 X = (x+y) 2 ,
 Y = y–x.

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.

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