The correlation between two variables in a study was extremely low, and much lower than expected (r = 0.01). Which of the following statements could be feasible explanations for the small observed relationship between X and Y?
A) in reality, there is in fact negligible systematic variation of X and Y
B) the relationship between X and Y is curvilinear
C) the range of response options on X was too narrow
D) A and B
E) B and C
F) all of the above

Question

Quizplus · Accepted Answer

It is possible that all of the above factors contributed to the small observed relationship between X and Y. If there is negligible systematic variation of X and Y, then it makes sense that the correlation coefficient would be close to zero. If the relationship between X and Y is curvilinear, then a linear correlation coefficient may not accurately reflect the relationship. Finally, if the range of response options on X was too narrow, then it may have been difficult to detect variation in Y based on X.

The Correlation Between Two Variables in a Study Was Extremely