The linear relationship between two variables
Sample Solution
1. Understanding Correlation
Correlation is a statistical measure that describes the relationship between two variables. This relationship can be positive, negative, or have no correlation.
- Positive Correlation (+): As one variable increases, the other variable also increases. For example, there's a positive correlation between height and weight. Taller individuals tend to weigh more.
- Negative Correlation (-): As one variable increases, the other variable decreases. For instance, there's a negative correlation between hours of sleep and stress levels. More sleep is generally associated with lower stress.
- No Correlation (0): There is no relationship between the two variables. For instance, there is likely no correlation between shoe size and IQ.
Example of a Spurious Correlation:
Sometimes, two variables may appear to be correlated, but their relationship is purely coincidental and has no underlying causal link. This is known as a spurious correlation.
For example, there might be a correlation between the number of ice cream sales and drowning incidents. Both tend to increase during the summer months, but one doesn't cause the other. The underlying factor is likely the warmer weather, which leads to more people swimming and also increases ice cream consumption.
Full Answer Section
2. Empirical Study and Correlation Analysis
Note: To provide a specific example, I'd need access to recent research databases. However, I can illustrate the process and potential findings using a hypothetical study.
Hypothetical Study:
Let's assume a study investigates the relationship between hours of studying and exam scores. The researchers might use Pearson correlation analysis to measure the linear relationship between these two continuous variables.
APA-Style Reporting and Interpretation:
- Correlation coefficient (r): The researchers find a strong positive correlation between hours of studying and exam scores, r(100) = .85, p < .01.
- Interpretation: This indicates that students who study more hours tend to have higher exam scores. The strong positive correlation suggests a substantial linear relationship between these two variables. However, it's important to note that correlation doesn't imply causation. Further research would be needed to determine if increased studying directly causes higher exam scores.