Correlation Coefficient Calculator

Calculate Pearson and Spearman correlation coefficients to evaluate the relationship between two variables.

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About Correlation Coefficient Calculator

The Correlation Coefficient Calculator computes the Pearson correlation coefficient and the Spearman rank correlation coefficient to evaluate the strength and direction of the relationship between two variables.

What is the Pearson Correlation Coefficient?

The Pearson correlation coefficient (\( r \)) measures the linear relationship between two continuous variables. It ranges from -1 to 1, where:

\( r = 1 \): Perfect positive linear correlation.
\( r = -1 \): Perfect negative linear correlation.
\( r = 0 \): No linear correlation.

The Pearson correlation coefficient is calculated using the following formula:

\( r = \frac{\sum (X_i - \bar{X})(Y_i - \bar{Y})}{\sqrt{\sum (X_i - \bar{X})^2 \sum (Y_i - \bar{Y})^2}} \)

Where:
\( X_i, Y_i \) = Individual data points for variables X and Y
\( \bar{X}, \bar{Y} \) = Means of variables X and Y

What is the Spearman Rank Correlation Coefficient?

The Spearman rank correlation coefficient (\( \rho \)) measures the monotonic relationship between two variables using ranked data. It is suitable for both continuous and ordinal variables.

The Spearman correlation coefficient is calculated using the following formula:

\( \rho = 1 - \frac{6 \sum d_i^2}{n(n^2 - 1)} \)

Where:
\( d_i \) = Difference between the ranks of corresponding values of X and Y
\( n \) = Number of observations

Interpretation of Correlation Coefficients

Values close to 1 or -1 indicate a strong correlation.
Values close to 0 indicate a weak correlation.
The sign indicates the direction of the relationship (positive or negative).

Use Cases of Correlation Analysis

Correlation analysis is widely used in various fields:

Finance: Assessing the relationship between stock prices and economic indicators.
Medicine: Studying the association between dosage levels and patient recovery times.
Psychology: Exploring the relationship between stress levels and sleep quality.
Marketing: Analyzing the correlation between advertising spend and sales revenue.