M09.02.12 Correlation
Correlation is a statistical measure (denoted by rrr, ranging from -1.0 to +1.0) that indicates the extent to which two variables are linearly related. However, correlation does not imply causation; it only shows an association, not the cause of the relationship.
Types of Correlation
- Pearson Correlation: Compares two interval-level variables (e.g., height and weight).
- Spearman Correlation: Compares two ordinal-level variables (e.g., ranks in a race).
Interpreting Correlation Coefficients
The value of the correlation coefficient, rrr, shows:
- Positive Correlation (0 < r ≤ 1.0): Variables move in the same direction. For instance, higher MCAT scores are often associated with higher medical school grades.
- Negative Correlation (-1.0 ≤ r < 0): One variable increases while the other decreases. For example, there is often a negative correlation between age and quickness of reflexes.
- Zero Correlation (r = 0): Indicates no linear relationship between variables, such as height and success in medical school.
The strength of correlation increases as rrr approaches -1.0 or +1.0. Values closer to zero indicate weaker relationships.
Scatterplots and Correlation Visualization
Scatterplots are commonly used to visualize correlations, with data points approximating a line:
- Positive Slope: Shows a positive correlation.
- Negative Slope: Shows a negative correlation.
- No Slope: Indicates zero correlation.
Types of Correlations in Scatterplots
| Correlation Type | Example |
|---|---|
| Strong Positive Correlation | Data points close and trend upwards |
| Weak Positive Correlation | Data points loosely trend upwards |
| Strong Negative Correlation | Data points close and trend downwards |
| Weak Negative Correlation | Data points loosely trend downwards |
| Zero Correlation (r = 0) | No apparent pattern |
Points to Remember
- Correlation does not imply causation.
- Correlation values:
- Interval data: Use correlation tests (e.g., Pearson correlation).
- Nominal data: Use chi-square tests.
- Combination of nominal and interval data: Use t-tests.
- Exam Tips:
- You won’t need to compute statistical tests but be prepared to interpret scatterplots.
- Recognize scatterplot slopes and understand which scatterplot shows a stronger correlation.
Bibliography
- Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
- Gravetter, F., & Wallnau, L. (2016). Statistics for the Behavioral Sciences. Cengage Learning.