Pearson Correlation Coefficient Calculator
This Pearson correlation coefficient calculator provides full details of the correlation calculation, including sums, means, and the step-by-step computation of r, r², and significance testing.
Further Information
The Pearson correlation coefficient (r) is a measure of the linear correlation between two variables. It ranges from -1 (perfect negative correlation) through 0 (no correlation) to +1 (perfect positive correlation).
Requirements
- Two continuous variables measured on interval or ratio scales
- Linear relationship between variables
- Normally distributed variables (approximately)
- No significant outliers
- At least 3 pairs of observations
Null Hypothesis
H₀: ρ = 0, where ρ (rho) is the population correlation coefficient.
The null hypothesis states that there is no linear relationship between the two variables in the population. A significant result suggests that the observed correlation is unlikely to be due to chance.
Equation
r = [nΣXY - (ΣX)(ΣY)] / √[nΣX² - (ΣX)²][nΣY² - (ΣY)²]
Where n is the sample size, ΣXY is the sum of the products, ΣX and ΣY are the sums of each variable, and ΣX² and ΣY² are the sums of squares.
Interpretation
- r = +1: Perfect positive linear relationship
- r = 0: No linear relationship
- r = -1: Perfect negative linear relationship
- |r| > 0.7: Strong correlation
- |r| = 0.3-0.7: Moderate correlation
- |r| < 0.3: Weak correlation
