Correlation Coefficient Calculator

Calculate Pearson’s and Spearman’s correlation with scatter plot visualization

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About Correlation Coefficient

1. What is a correlation coefficient?

A correlation coefficient is a statistical measure that describes the strength and direction of a relationship between two variables. The most commonly used correlation coefficients are Pearson’s r and Spearman’s ρ.

2. What is Pearson's correlation coefficient (r)?

Pearson's r measures the linear relationship between two continuous variables. The coefficient value ranges from -1 to 1:

  • +1 indicates a perfect positive linear correlation
  • 0 indicates no linear correlation
  • -1 indicates a perfect negative linear correlation
3. What is Spearman's rank correlation coefficient (ρ)?

Spearman's ρ measures the strength and direction of the monotonic relationship between two ranked variables. It's particularly useful when:

  • Data is not normally distributed
  • There are outliers that might skew Pearson's results
  • You're dealing with ordinal or ranked data
4. Does this calculator show step-by-step calculations?

This tool not only gives final correlation values but also displays a step-by-step breakdown of each calculation. It's ideal for:

  • Students learning statistics
  • Teachers demonstrating concepts
  • Analysts verifying their computations

The steps show how the values are derived — enhancing understanding and transparency.

How to Use

  • Enter two sets of numeric values (X and Y) of equal length.
  • Separate values with commas or spaces.
  • Alternatively, upload a CSV file with two columns of numbers.
  • Results and scatter plot update automatically.
  • Use the Download CSV button to save data and results.
  • A step-by-step breakdown of the correlation calculations is displayed below the results, showing intermediate values and formulas used.

Frequently Asked Questions

1. What is the difference between Pearson and Spearman correlation?

Pearson measures the strength of a linear relationship between two continuous variables, while Spearman measures the strength of a monotonic relationship using the ranks of values. Pearson is sensitive to outliers; Spearman is more robust for non-linear or ordinal data.

2. When should I use Spearman instead of Pearson?

Use Spearman correlation when your data is not normally distributed, contains outliers, or involves ordinal/ranked variables. It's also preferred when the relationship is monotonic but not necessarily linear.

3. What does a correlation coefficient of 0 mean?

A correlation of 0 means there is no linear relationship between the variables. However, a non-linear relationship may still exist.

4. Is correlation the same as causation?

No. Correlation only shows that two variables are related in some way — it does not imply that one causes the other. For causation, further statistical analysis or controlled experiments are required.

5. What is the range of correlation coefficients?

Both Pearson's and Spearman's correlation coefficients range from -1 to +1. A value of +1 means a perfect positive correlation, -1 means perfect negative, and 0 means no correlation.