Spearman Correlation
Spearman's rank correlation coefficient (ρ) measures the strength and direction of monotonic relationships between two paired variables. Unlike Pearson's correlation, it does not require the relationship to be linear, making it suitable for ordinal data and non-linear monotonic relationships.
"Spearman's rank correlation coefficient (ρ) measures the strength and direction of monotonic relationships between paired data. Unlike Pearson's correlation, it does not require the relationship to be linear, making it suitable for ordinal data and non-linear relationships."
Step 1 — Choose your input method
| Method | When to use |
|---|---|
| Manual | Type or paste your two columns of values |
| Excel | Upload an .xlsx / .xls / .csv file and pick the two columns to correlate |
Step 2 — Provide your data
In Manual mode you see two text areas (variable X and variable Y) and two label fields. A Use Random Generated Data button creates correlated example values.
In Excel mode you upload your file, pick the sheet and columns. Column names become variable labels automatically.
Step 3 — Calculate
Click Calculate Correlation.
Step 4 — Read the results
| Field | What it shows |
|---|---|
| Spearman's rho (ρ) | Coefficient from −1 to +1 |
| p-value | Significance (NEJM-formatted) |
| Sample Size (n) | Number of observations used |
| Critical Value (α = 0.05) | The critical |
| Interpretation | Plain-language summary of strength, direction, and significance |
Step 5 — Rank-difference table
A full Rank Calculation Table shows:
| Column | What it shows |
|---|---|
| X Rank | Rank of the X value (ties averaged) |
| Y Rank | Rank of the Y value (ties averaged) |
| d = X Rank − Y Rank | Difference between ranks |
| d² | Squared difference |
A Total row shows Σ d².
Step 6 — Visualisation and discussion
A ScatterPlot is rendered below the results.
A UniversalChatBot follows for discussion.
Statistical methods used
Test statistic — Spearman's ρ
| Component | Formula |
|---|---|
| Rank differences | dᵢ = rank(xᵢ) − rank(yᵢ) |
| Spearman's ρ | 1 − (6 × Σ dᵢ²) / (n × (n² − 1)) |
| t-statistic | t = ρ × √((n − 2) / (1 − ρ²)) |
| p-value | Two-tailed, from t-distribution with df = n − 2 |
Hypothesis statement
- H₀: ρ_s = 0 (no monotonic association)
- H₁: ρ_s ≠ 0 (two-tailed)
- Significance level: α = 0.05
Effect size — Spearman's ρ interpretation
| |ρ| | Strength |
|---|---|
| < 0.30 | Weak |
| 0.30 – 0.50 | Moderate |
| 0.50 – 0.70 | Strong |
| ≥ 0.70 | Very strong |
Tie handling: Average ranking — observations with the same value receive the average of the ranks they would otherwise occupy.