Which of the following correlations is the strongest?
a. 0.52
b. -0.25
c. -0.88
d. 0.78
The correct answer and explanation is:
The strongest correlation in the list is c. -0.88.
In statistics, the strength of a correlation is determined by the absolute value of the correlation coefficient, which ranges from -1 to +1. A value closer to -1 or +1 indicates a stronger relationship between the two variables, while a value closer to 0 indicates a weaker relationship. The sign (positive or negative) indicates the direction of the relationship, where:
- Positive values (e.g., 0.52, 0.78) indicate that as one variable increases, the other also increases.
- Negative values (e.g., -0.25, -0.88) indicate that as one variable increases, the other decreases.
In the case of -0.88, the absolute value (0.88) is the largest among the options provided, meaning this correlation represents the strongest relationship. The negative sign indicates a negative or inverse relationship, meaning as one variable increases, the other decreases.
Here’s a breakdown of the other choices:
- 0.52 indicates a moderate positive correlation, but it is weaker than -0.88 because its absolute value is smaller.
- -0.25 represents a weak negative correlation, and its absolute value is much smaller than 0.88.
- 0.78 indicates a strong positive correlation but is still not as strong as -0.88 because the absolute value of -0.88 is greater than 0.78.
In summary, correlation strength is all about the absolute value of the coefficient, and -0.88 stands out as the strongest because it is closest to the extreme values of -1 or +1.