Which of the following is (are) not the possible value(s) of Pearson’s correlations?
Choose all that apply
a) 1.6
b) 1.0
c) -0.99
d) 0.0
e) -1.0
The correct answer and explanation is:
The correct answer is a) 1.6.
Explanation:
Pearson’s correlation coefficient, often denoted as r, is a measure of the linear relationship between two variables. The value of r can range between -1.0 and +1.0. This scale indicates how strongly two variables are related to each other and the direction of their relationship. Here’s a breakdown of the possible values:
- 1.0: This indicates a perfect positive linear relationship. As one variable increases, the other increases in exact proportion.
- -1.0: This indicates a perfect negative linear relationship. As one variable increases, the other decreases in exact proportion.
- 0.0: This indicates no linear relationship between the two variables. Changes in one variable do not predict any change in the other.
- -0.99: This represents a very strong negative linear relationship, where most of the data points lie on a straight line but with a slight negative slope.
- 1.6: This is not a valid value for Pearson’s correlation. Pearson’s r cannot exceed the range of -1.0 to +1.0. Any value outside this range indicates an error in the calculation or interpretation.
In conclusion, while the other values (1.0, -0.99, 0.0, and -1.0) are all within the valid range for Pearson’s correlation, 1.6 is not a possible value. A value of 1.6 suggests a miscalculation, as Pearson’s correlation is bounded within the [-1.0, 1.0] range.