Spearman Rank Correlation Statistical test
What is Spearman Correlation?
Spearman Rank Correlation (often denoted as rho or rho) is a non-parametric measure of rank correlation that assesses how well the relationship between two variables can be described using a monotonic function. Unlike Pearson correlation, which measures linear relationships, Spearman correlation evaluates monotonic relationships-relationships where variables tend to change together, but not necessarily at a constant rate.
Key Characteristics
- Non-parametric: Does not assume your data follows a normal distribution
- Rank-based: Uses the rank of values rather than raw values
- Monotonic: Measures both linear and non-linear monotonic relationships
- Robust: Less sensitive to outliers than Pearson correlation
How It Works
The Spearman correlation coefficient is calculated by:
- Rank Conversion: Convert each variable's values to ranks (1st, 2nd, 3rd, etc.)
- Difference Calculation: Calculate the difference between ranks for each pair
- Coefficient Calculation: Apply the Spearman formula to determine correlation strength
The coefficient ranges from -1 to +1:
- +1: Perfect positive monotonic relationship (as one variable increases, the other always increases)
- 0: No monotonic relationship
- -1: Perfect negative monotonic relationship (as one variable increases, the other always decreases)
Interpreting Spearman Correlation Values
| Coefficient Range | Interpretation | Strength |
|---|---|---|
| 0.9 to 1.0 | Very strong positive correlation | Very strong |
| 0.7 to 0.9 | Strong positive correlation | Strong |
| 0.5 to 0.7 | Moderate positive correlation | Moderate |
| 0.3 to 0.5 | Weak positive correlation | Weak |
| 0.0 to 0.3 | Negligible correlation | Very weak |
| -0.3 to 0.0 | Negligible correlation | Very weak |
| -0.5 to -0.3 | Weak negative correlation | Weak |
| -0.7 to -0.5 | Moderate negative correlation | Moderate |
| -0.9 to -0.7 | Strong negative correlation | Strong |
| -1.0 to -0.9 | Very strong negative correlation | Very strong |
When to Use Spearman Correlation
Use Spearman correlation when:
- Data is ordinal: Your variables are ranked (e.g., disease stages, survey responses)
- Non-normal distribution: Your data doesn't follow a normal distribution
- Outliers present: Your data contains extreme values that would distort Pearson correlation
- Non-linear but monotonic: The relationship is not linear but consistently increases or decreases
- Small sample size: You have limited data points
Spearman vs. Pearson Correlation
| Aspect | Spearman | Pearson |
|---|---|---|
| Relationship Type | Monotonic (any consistent pattern) | Linear (straight-line) |
| Data Distribution | No distribution assumptions | Assumes normal distribution |
| Outlier Sensitivity | Robust to outliers | Sensitive to outliers |
| Data Type | Ordinal, interval, or ratio | Interval or ratio only |
| Calculation | Uses ranks | Uses actual values |
Applications in CMMI-DCC
In the CMMI Data Coordinating Center, Spearman correlation is used for:
- Clinical Marker Analysis: Identifying relationships between blood markers and health outcomes
- Microbiome Studies: Correlating bacterial abundance with metabolite levels
- Questionnaire Analysis: Analyzing relationships between survey responses and clinical measures
- Non-linear Patterns: Detecting relationships that aren't straight-line patterns
- Robust Analysis: Providing correlation measures that aren't distorted by outlier values
Example Interpretation
If you calculate a Spearman correlation of 0.75 between a metabolite and a health score:
- Direction: Positive relationship (higher metabolite levels associated with higher health scores)
- Strength: Strong correlation
- Type: Monotonic relationship (as metabolite increases, health score tends to increase)
- P-Value: Check statistical significance (typically p < 0.05 indicates significance)
Statistical Significance
The P-Value tells you whether the observed correlation is statistically significant:
- p < 0.05: Correlation is statistically significant (not due to random chance)
- p >= 0.05: Correlation is not statistically significant (could be due to random chance)
Always interpret both the correlation coefficient AND the p-value together.
Related Terms
- P-Value: Determines statistical significance of the correlation
- Correlation Analysis: The broader process of evaluating variable relationships
- Monotonic Relationship: A relationship that consistently increases or decreases