Calculate Pearson Correlation Coefficient By Hand

The Pearson correlation coefficient is a statistical measure that calculates the linear correlation between two variables. It’s crucial for understanding the relationship between two sets of data. Our calculator helps you compute this coefficient by hand effortlessly.

1. Enter the data for the first set in the ‘Enter Data Set 1’ field, separated by commas.
2. Enter the data for the second set in the ‘Enter Data Set 2’ field, separated by commas.
3. Click the ‘Calculate’ button to find the Pearson correlation coefficient.

The formula for the Pearson 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 two data sets.

Comparison of Pearson Correlation Coefficients

Data Set 1	Data Set 2	Pearson Correlation Coefficient
1,2,3,4,5	2,3,4,5,6	0.9746315789473684
1,1,1,1,1	2,2,2,2,2	1

• Always ensure your data sets have the same number of values.
• Pearson correlation coefficient only measures linear relationships. For non-linear relationships, consider other correlation measures.

What does a Pearson correlation coefficient of 1 mean?

A Pearson correlation coefficient of 1 means there’s a perfect positive linear relationship between the two data sets.

For more information, see these authoritative sources:

• Statistics How To
• Khan Academy