# Spearman Correlation Calculator

Instructions: You can use this Spearman Correlation Calculator tool to compute Spearman’s Correlation Coefficient for two variables X and Y. All you have to do is type your X and Y data, either in comma or space separated format (For example: “2, 3, 4, 5”, or “3 4 5 6 7”).

X data (comma separated)
Y data (comma separated)

More about the Spearman correlation coefficient:

The correlation coefficient calculated above corresponds to Spearman’s correlation coefficient. The requirements for computing it is that the two variables X and Y are measured at least at the interval level (which means that it does not work with nominal or ordinal variables).

The formula for Pearson’s correlation coefficient is:

$r_S =\frac{n \sum_{i=1}^n Rank(x_i) Rank(y_i) – \left(\sum_{i=1}^n Rank(x_i) \right) \left(\sum_{i=1}^n Rank(y_i) \right) }{\sqrt{n \sum_{i=1}^n Rank(x_i)^2 – \left( \sum_{i=1}^n Rank(x_i) \right)^2} \sqrt{n \sum_{i=1}^n Rank(y_i)^2 – \left( \sum_{i=1}^n Rank(y_i) \right)^2} }$

or equivalently

$r = \frac{\sum_{i=1}^n Rank(x_i) Rank(y_i) – \frac{1}{n}\left(\sum_{i=1}^n Rank(x_i) \right) \left(\sum_{i=1}^n Rank(y_i) \right) }{\sqrt{\sum_{i=1}^n Rank(x_i)^2 – \frac{1}{n}\left( \sum_{i=1}^n Rank(x_i) \right)^2} \sqrt{\sum_{i=1}^n Rank(y_i)^2 – \frac{1}{n}\left( \sum_{i=1}^n Rank(y_i) \right)^2}} = \frac{SS_{\tilde X \tilde Y}}{\sqrt{SS_{\tilde X \tilde X}\cdot SS_{\tilde Y \tilde Y} }}$