Units-free variables

Since we want to describe the strength of a relationship in a way that is not affected by linear scaling of the two variables, we first describe how to find a units-free version of a variable whose values are unaffected by scaling of the original variable.

From its z-score, you can tell whether any value is high (with z over +2) or low (with z under -2) in relation to the other individuals.

Class marks in exams

Since the z-scores for each exam are relative to that exam's mean and st devn, they correct the raw marks for the different levels of difficulty of the different exams.

The table below shows all z-scores together.