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?
Assuming the sample size is the same, r^2 accounts for the amount of variability explained by r.
r^2 = .04
r^2 = .16
To determine which relationship is scientifically more useful, we need to consider the strength and direction of the correlations.
The correlation coefficient, denoted as r, measures the strength and direction of the relationship between two variables. It ranges from -1 to +1, with -1 indicating a perfect negative relationship, +1 indicating a perfect positive relationship, and 0 indicating no relationship.
In this case, the researcher has found that:
1. The correlation between variable A and variable B is r = +.20. This means that there is a positive but weak relationship between variable A and variable B. The positive sign indicates that as variable A increases, variable B also tends to increase, but the relationship is not very strong.
2. The correlation between variable C and variable B is r = -.40. This means that there is a negative and moderate relationship between variable C and variable B. The negative sign indicates that as variable C increases, variable B tends to decrease, and the magnitude of -0.40 suggests a stronger relationship compared to +0.20.
Therefore, scientifically speaking, the relationship between variable C and variable B is more useful or meaningful because it has a stronger correlation (absolute value of -0.40 vs. +0.20). However, it is important to note that the concept of "usefulness" may vary depending on the specific research context and goals.