Overview
This lecture explains how to interpret the correlation coefficient (r) in scatter plots, focusing on distinguishing correlation from causation and stressing the importance of context when describing associations.
Identifying Linear Trends and Correlation
- A linear trend in data allows the use of the correlation coefficient (r).
- Correlation coefficient (r) is used only for linear associations.
Interpreting the Correlation Coefficient (r)
- The sign of r (positive or negative) indicates the direction of the association.
- The magnitude of r tells how strong the association is: closer to 1 or -1 means stronger association.
- An r value of 0.777 is positive and close to 1, indicating a strong, positive association.
Contextualizing the Correlation
- When describing r, always mention the specific variables involved.
- For example: There is a positive and strong association between years of education and salary (in thousands of dollars per year).
- Always include both variables when interpreting the correlation in context.
Correlation Does Not Imply Causation
- Use the phrase "tend to" when describing relationships (e.g., more education tends to lead to higher salaries).
- "Tend to" reflects that correlation does not guarantee causation.
- Having more education does not automatically result in a higher salary; exceptions exist.
Key Terms & Definitions
- Correlation coefficient (r) — a measure of the strength and direction of a linear relationship between two variables.
- Linear trend — a relationship where data points approximate a straight line.
- Causation — a relationship where one variable directly causes changes in another.
- Association — a relationship or link between two variables, not necessarily causal.
Action Items / Next Steps
- Practice interpreting correlation coefficients with context using scatter plot examples.
- Remember to include both variables and use "tend to" in your interpretations.