Pearson's r measures the strength and direction of a straight-line relationship between two numeric variables. It ranges from −1 to +1.
Why it matters
Researchers constantly ask whether two measurements move together — study hours and scores, BMI and blood pressure.
Key ideas
- r near +1: both rise together
- r near −1: one rises as the other falls
- r near 0: no straight-line relationship
- r² = share of variation the two variables share
- Always plot the data first
- Correlation is not causation
Real-life research example
Hours of study and exam score for 8 students: more hours tend to go with higher scores, so r is positive and strong.
When to use
- Both variables numeric and the scatter looks roughly straight
- No extreme outliers
When NOT to use
- Curved relationships → plot first, consider transformation
- Ranks, strong skew or outliers → Spearman
- Don't claim one variable causes the other
Mini example
Hours: 1, 2, 3, 4, 5, 6, 7, 8 Score: 52, 55, 61, 60, 68, 72, 75, 80 Paste the two lists into the calculator.
Quick takeaway
r tells you how tightly points hug a line — not why. Plot, then compute, then interpret carefully.
Try it yourself
Run the example, then change the last score to 20. How does r change? What does this say about outliers?
Model answer
One outlier can weaken r dramatically. That is why you plot the data before trusting a correlation coefficient.