Spearman's Rank Correlation Calculator (Rho) with Steps
Calculate Spearman's Rho for non-parametric data. Shows step-by-step ranking, d-squared calculation, and significance (p-value) for statistics students.
Variable X Values
Variable Y Values
| X | Y | Rank X | Rank Y | d | d2 |
|---|
About
Spearman's Rank Correlation Coefficient (ρ) is a non-parametric measure of rank correlation. Unlike Pearson's correlation, which assumes a linear relationship and normal distribution, Spearman's assesses how well the relationship between two variables can be described using a monotonic function. This makes it ideal for ordinal data or continuous data with significant outliers.
This tool does the heavy lifting of ranking the raw data - a tedious source of error in manual calculation. It handles tied ranks using the average rank method and determines statistical significance against standard critical values for p = 0.05 and p = 0.01.
Formulas
For data with no tied ranks, Spearman's ρ is calculated as:
Where di is the difference between ranks:
Reference Data
| Correlation (ρ) | Interpretation | Visual Pattern |
|---|---|---|
| +1.0 | Perfect Positive | Ranks increase together perfectly. |
| +0.7 to +0.9 | Very Strong | Clear upward trend in ranks. |
| +0.4 to +0.6 | Moderate | Loose association. |
| 0 | No Correlation | Random distribution. |
| -1.0 | Perfect Negative | One rank rises, the other falls perfectly. |