Why is r preferred to covariance as a measure of association?
r is preferred to covariance as a measure of association because it is a pure number with no unit. This means units of measurement are not part of r, making it easier to interpret and compare across different datasets. For instance, r between height in feet and weight in kilograms could be 0.7.
Another advantage is that the value of r lies between minus one and plus one (-1 r 1). This fixed range helps in understanding the strength and direction of the relationship. A value close to +1 or -1 indicates strong linear relationship, while a value close to zero indicates weak relation. Covariance, on the other hand, can take any value depending on the scale of variables, making interpretation difficult.
Explanation
The textbook clearly states that 'r has no unit. It is a pure number.' This is the primary advantage over covariance. Additionally, the context mentions that 'The value of the correlation coefficient lies between minus one and plus one, -1 r 1' and that 'If r is outside this range it indicates error in calculation.' This bounded nature of r makes it superior for interpreting the degree of association. Covariance lacks these standardized properties, making r the preferred measure.