Spearman's Rank Correlation Coefficient

Basics of Spearman’s Rank Correlation Coefficient

• Spearman’s rank correlation coefficient is a statistical measure of the strength and direction of the monotonic relationship between two ranked variables.
• It’s a non-parametric test which is used when data isn’t normally distributed or when there are outliers that could distort the correlation measure.

Calculation of Spearman’s Rank

• The Spearman’s Rank involves ranking the data from smallest to largest, while keeping track of the original order.
• Each value is given a rank. If two or more values are equal, they are given an average rank.

Computation of Spearman’s Coefficient

• The formula for Spearman’s coefficient (denoted by rho or rs) is based on the differences in ranks of paired observations (di) and the number of observations (n).
• The Spearman’s rank correlation coefficient is calculated as rs = 1 - (6 Σdi²) / [n(n² - 1)].

Interpreting Spearman’s Coefficient

• The correlation coefficient can range from -1 to +1, where +1 shows a perfect positive rank correlation, and -1 shows a perfect negative rank correlation.
• A value near zero implies weak or no correlation.

Applications of Spearman’s Rank

• It’s often used in the social sciences, business, and physics to introduce correlation from ordinal data.
• Spearman’s Rank Correlation Coefficient can also be used when the assumption of linear relationship or constant variance is violated.

Remember, the rank correlation coefficient is robust to outliers, and hence, Spearman’s rank correlation test is often preferred over Pearson’s correlation test while dealing with ordinal data or outliers in the data.