A researcher finds that the correlation between variable A

. A researcher finds that the correlation between variable A and variable B is r =+.20. She also finds that the correlation between variable C and variable B is r = -.40. Which relationship is scientifically more useful and by how much?

Solution

First note the statement that because the Pearson correlation coefficient only measures linear relationships, variables that have curvilinear relationships are not well described by r, and the observed correlation will be close to zero.

The value of the correlation coefficient ranges from r= –1.00 to r = +1.00. The direction of the linear relationship is indicated by the sign of the correlation coefficient. Positive values of r (such as r = .54 or r = .67) indicate that the relationship is positive linear (i.e., the pattern of the dots on the scatter plot runs from the lower left to the upper right), whereas negative values ofr (such as r = –.30 or r = –.72) indicate negative linear relationships (i.e., the dots run from the upper left to the lower right).

The strength of the linear relationship is indexed by the distance of the correlation coefficient from zero (its absolute value). For instance, r = –.54 is a stronger relationship than r = .30, and r = .72 is a stronger relationship than r = –.57.

from the given data, we can say that C and B is more useful as it has more validity. (it\'s absurd to ask by how much it is useful but even if you want to mention compare the modulus value and not with sign.)