Final answer:
Covariance measures the direction and strength of the linear relationship between two variables, while the correlation coefficient, denoted as r, quantifies this relationship's strength and direction, ranging from -1 to +1. Covariance indicates the direction of the linear relationship, and a significant correlation coefficient suggests a true relationship rather than chance.
Step-by-step explanation:
Covariance is a statistical measure that determines the degree to which two variables change together. However, it's not accurate to say that covariance tells us how much the scores of two variables differ from each other. Instead, covariance provides a measure of the strength and direction of the linear relationship between two variables. When the covariance is positive, it indicates that the two variables tend to increase or decrease together. A negative covariance indicates that as one variable increases, the other tends to decrease, and vice versa.
The correlation coefficient, often represented by the letter r, is closely related to covariance and ranges from -1 to +1. It indicates the strength and direction of a linear relationship between variables. A correlation coefficient close to 1 signifies a strong positive relationship, while a value close to -1 indicates a strong negative relationship. If r is close to zero, it suggests a weak or no linear relationship. The correlation coefficient does not imply causation, even if the relationship is strong.
For a positive correlation, as one variable increases so does the other, and for a negative correlation the opposite is true. The value of the correlation coefficient is influenced by the number of observations in the data sample. Furthermore, when we say that a correlation coefficient is statistically significant, it means that it is likely different from zero and represents a true relationship and not just a random chance.