Effect of Linear Transformations on Pearson's r



Linear transformations have no effect on Pearson's correlation coefficient. Thus, the correlation between height and weight is the same regardless of whether height is measured in inches, feet, centimeters or even miles. This is a very desirable property since, with the exception of ratio scales, choices among measurement scales that are linear transformations of each other are arbitrary. For instance, scores on the Scholastic Aptitude Test (SAT) range from 200-800. It was an arbitrary decision to set 200 to 800 as the range. The test would not be any different if 100 points were subtracted from each score and then each score were multiplied by 3. Scores on the SAT would then range from 300-2100. The Pearson's correlation between SAT and some other variable (such as college grade point average) would not be affected by this linear transformation.