A researcher finds that the correlation between variable A and variable B is
r= 5 1.20. She also finds that the correlation between variable C and variable B is
r= 5 2.40. Which relationship is scientifically more useful and by how much?
A correlation coefficient cannot exceed ± 1. From your data, neither would be useful.
To determine which relationship is scientifically more useful, we need to examine the magnitude of the correlation coefficients. The correlation coefficient, denoted by "r," measures the strength and direction of the linear relationship between two variables.
In this case, the researcher found that the correlation between variable A and variable B is r = 1.20, and the correlation between variable C and variable B is r = 2.40.
The magnitude of a correlation coefficient ranges from 0 to 1. The closer the absolute value of the correlation coefficient is to 1, the stronger the relationship. Therefore, the relationship with the larger absolute value of the correlation coefficient is considered more useful in a scientific context.
Comparing the magnitudes, we see that the correlation coefficient between variable C and variable B (r = 2.40) has a larger absolute value than the correlation coefficient between variable A and variable B (r = 1.20). Thus, the relationship between variable C and variable B is scientifically more useful.
The difference in magnitude between these two correlation coefficients is given by:
|2.40| - |1.20| = 2.40 - 1.20 = 1.20
Therefore, the relationship between variable C and variable B is 1.20 units more useful than the relationship between variable A and variable B.