Definition:Spearman's Rank Correlation Coefficient

Definition

Let $X$ and $Y$ be two rankings assigned to the same set of entities.

The Spearman's rank correlation coefficient is the Pearson correlation coefficient between $X$ and $Y$.

Examples

Examination Results

Let $S$ be a class of students.

Let $\sequence {x_i}$ and $\sequence {y_i}$ be rankings of $S$ based on the examination results in French and Mathematics respectively.

Spearman's rank correlation coefficient may be appropriate to determine the correlation between $\sequence {x_i}$ and $\sequence {y_i}$.

Also see

• Results about Spearman's rank correlation coefficient can be found here.

Source of Name

This entry was named for Charles Edward Spearman.

Historical Note

Spearman's rank correlation coefficient was devised by Charles Edward Spearman in $1904$.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): correlation coefficient: 2.
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Spearman's rank correlation coefficient
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): correlation coefficient: 2.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Spearman's rank correlation coefficient
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): rank correlation coefficient