Skip to content

Spearman Correlation Coefficient (\(Rs\) or \(\rho\)) [Not Normal] [2 Continuous]

Description

The Spearman Correlation Coefficient, denoted as Rs (\(\rho\)), is a non-parametric measure of statistical dependence between two variables. It assesses how well the relationship between the variables can be described by a monotonic function. Unlike Pearson's correlation, which measures linear relationships, Spearman's correlation evaluates the rank-order relationship.

Spearman's correlation coefficient ranges from -1 to 1:

  • 1 indicates a perfect positive monotonic relationship
  • -1 indicates a perfect negative monotonic relationship
  • 0 indicates no monotonic relationship

Formula

\[ \rho = 1 - \frac{6 \sum d_i^2}{n(n^2 - 1)} \]
  • \(\rho\) = Spearman's rank correlation coefficient
  • \(d_i\) = difference between the two ranks of each observation
  • \(n\) = number of observations

To compute it:

  1. Convert the raw scores to ranks.
  2. Find the difference between the ranks for each pair of data points.
  3. Apply the formula.