Spearman Average Ranks and Permutations
See how average ranks and exact permutations handle tied ordinal data.
Free theory articleSee how average ranks and exact permutations handle tied ordinal data.
Concept & interpretation
Spearman's rank correlation coefficient (rho) is a non-parametric measure of statistical dependence between two variables. It assesses how well the relationship between two variables can be described using a monotonic function.
Experiment
Explore the impact of ties on the Spearman correlation coefficient using the interactive module.
- Open the module and locate the control labeled "Data". Change its value to "Monotone". Observe that the "Spearman rho" is 1.0 and the "No-tie shortcut" also yields 1.0 because there are no ties.
- Change the "Data" control to "Joint ties". Notice that the "Ties present" result changes to "Yes" and the "No-tie shortcut" becomes "Unavailable", demonstrating that the shortcut formula 1 - 6 sum(d²)/(n(n²-1)) cannot be used when ties are present.
- Set the "Sample size" control to 3. Observe how the "Exact two-sided p" value and the graph update to reflect the smaller sample size and the reduced number of permutations.