Correlation Coefficient Calculator

Calculate Pearson and Spearman correlation coefficients to measure the strength and direction of relationships between variables.

Data Input

Correlation Type

X Values

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Y Values

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The formula for Pearson's correlation coefficient is:

r = \frac{\sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=1}^{n} (x_i - \bar{x})^2 \sum_{i=1}^{n} (y_i - \bar{y})^2}}

Where:

Spearman's correlation assesses monotonic relationships by ranking the data and applying Pearson's formula to the ranks:

\rho = \frac{\sum_{i=1}^{n} (R(x_i) - \bar{R(x)})(R(y_i) - \bar{R(y)})}{\sqrt{\sum_{i=1}^{n} (R(x_i) - \bar{R(x)})^2 \sum_{i=1}^{n} (R(y_i) - \bar{R(y)})^2}}

Where:

Convert raw scores to standardized z-scores.

Conduct t-tests to compare means.

Perform chi-square tests for independence or goodness of fit.

Calculate and interpret odds ratios.