How To Calculate Pearson’S Correlation Coefficient By Hand

Introduction & Importance

Pearson’s correlation coefficient, named after its creator Sir Francis Galton, is a statistical measure that expresses the extent to which two variables are linearly related. It’s crucial in data analysis as it helps understand the relationship between two variables…

How to Use This Calculator

1. Enter the data points for both data sets in the respective input fields.
2. Click the “Calculate” button.
3. View the results below the calculator.

Formula & Methodology

The formula for Pearson’s correlation coefficient (r) is:

r = Σ[(xᵢ – x̄)(yᵢ – ȳ)] / √[Σ(xᵢ – x̄)² * Σ(yᵢ – ȳ)²]

Where:

• xᵢ and yᵢ are the individual data points.
• x̄ and ȳ are the means of the respective data sets.

Real-World Examples

Data & Statistics

Example Data Set 1

Data Point	Value
1	5
2	7
3	8

Example Data Set 2

Data Point	Value
1	10
2	14
3	13

Expert Tips

• Pearson’s r ranges from -1 to 1. A value of 0 indicates no correlation.
• Positive values indicate a direct relationship, negative values indicate an inverse relationship.
• Consider the context and significance level when interpreting the results.

Interactive FAQ

What does Pearson’s r measure?

Pearson’s r measures the strength and direction of a linear relationship between two variables.

How can I interpret the results?

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Learn more about Pearson’s correlation coefficient

Khan Academy’s guide on Pearson’s r