Pearson's Product-Moment Correlation Coefficient Calculator
A statistical measure that quantifies the strength and direction of the linear relationship between two continuous interval or ratio variables.
Formula first
Overview
Pearson's r produces a value between -1 and +1, where +1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 indicates no linear correlation. In geographical research, it is essential for testing hypotheses about how two variables, such as distance from a CBD and property prices, covary across a landscape. The coefficient assumes that the data is normally distributed and that the relationship is strictly linear.
Symbols
Variables
r = Correlation Coefficient, n = Sample size, x = Variable 1 data points, y = Variable 2 data points
Apply it well
When To Use
When to use: Use when analyzing two sets of interval or ratio data to determine if a linear trend exists between them.
Why it matters: It allows geographers to move beyond visual inspection of scatter graphs to provide a statistically significant confirmation of relationships between environmental or social variables.
Avoid these traps
Common Mistakes
- Forgetting to square the sum (Σx)² versus summing the squares Σx².
- Applying the test to non-linear relationships (e.g., exponential growth patterns).
- Ignoring the impact of extreme outliers which can heavily bias the result.
One free problem
Practice Problem
Given a small sample where n=5, Σx=15, Σy=20, Σxy=70, Σx²=55, and Σy²=90, calculate Pearson's r.
Solve for:
Hint: Calculate the numerator first, then the denominator parts separately.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Pearson, K. (1896). Mathematical Contributions to the Theory of Evolution.
- Burt, J. E., Barber, G. M., & Rigby, D. L. (2009). Elementary Statistics for Geographers.
- AQA/Edexcel A-Level Geography Specification - Quantitative Skills: Statistical Analysis