Pearson Product-Moment Correlation Coefficient Calculator
Measures the linear correlation between two variables, ranging from -1 to +1, where S terms represent sums of products and squares.
Formula first
Overview
The Pearson Product-Moment Correlation Coefficient, often written as r, measures the strength and direction of a linear relationship between two continuous variables. It standardises covariance by the product of the standard deviations, so the result is dimensionless and always falls between -1 and +1. This makes it a core statistic for analysing association in data, psychology, economics, and other quantitative fields.
Symbols
Variables
r = Correlation Coefficient, Sxy = Sum of Products, Sxx = Sum of Squares for X, Syy = Sum of Squares for Y
Apply it well
When To Use
When to use: Use this formula when you need to measure the linear relationship between two continuous variables or when summary statistics have already been calculated and you need a correlation coefficient.
Why it matters: It is one of the most widely used measures in statistics and data analysis because it helps quantify how strongly two variables move together. It also underpins regression analysis and many higher-level statistical methods.
Avoid these traps
Common Mistakes
- Treating correlation as causation.
- Using it for a clearly non-linear relationship.
- Confusing the S-values with raw sums.
One free problem
Practice Problem
A data set has Sxx = 20, Syy = 45, and Sxy = 25. Calculate the Pearson Product-Moment Correlation Coefficient.
Solve for:
Hint: Substitute the values into r = Sxy / sqrt(Sxx * Syy).
The full worked solution stays in the interactive walkthrough.
References
Sources
- A-Level Statistics and Data Analysis Textbooks (e.g., Edexcel, AQA, OCR specifications)
- GeeksforGeeks: Pearson Correlation Coefficient
- Psychology Town: Pearson's Correlation Coefficient: A Comprehensive Guide