Correlation Analysis Process
What is Correlation Analysis?
Correlation Analysis is a statistical method used to evaluate the strength and direction of the relationship between two or more variables. It quantifies how closely changes in one variable are associated with changes in another variable.
Key Concepts
Correlation Coefficient
The correlation coefficient (r or rho) is a numerical measure ranging from -1 to +1 that indicates the strength and direction of the relationship:
| Coefficient | Direction | Strength | Interpretation |
|---|---|---|---|
| +1.0 | Positive | Perfect | As one variable increases, the other always increases proportionally |
| +0.7 to +0.9 | Positive | Strong | As one variable increases, the other tends to increase strongly |
| +0.4 to +0.6 | Positive | Moderate | As one variable increases, the other tends to increase moderately |
| +0.1 to +0.3 | Positive | Weak | As one variable increases, the other tends to increase slightly |
| 0.0 | None | None | No relationship between variables |
| -0.1 to -0.3 | Negative | Weak | As one variable increases, the other tends to decrease slightly |
| -0.4 to -0.6 | Negative | Moderate | As one variable increases, the other tends to decrease moderately |
| -0.7 to -0.9 | Negative | Strong | As one variable increases, the other tends to decrease strongly |
| -1.0 | Negative | Perfect | As one variable increases, the other always decreases proportionally |
Types of Correlation
Positive Correlation
Variables move in the same direction:
- As one increases, the other increases
- As one decreases, the other decreases
Examples in Biomedical Research:
- Age and blood pressure (generally)
- BMI and body fat percentage
- Exercise duration and cardiovascular fitness
Negative Correlation
Variables move in opposite directions:
- As one increases, the other decreases
- As one decreases, the other increases
Examples in Biomedical Research:
- Physical activity and resting heart rate
- Medication dosage and symptom severity
- Age and bone density (in older adults)
No Correlation
No relationship between variables:
- Changes in one variable don't predict changes in the other
- Correlation coefficient near 0
Common Correlation Methods
Pearson Correlation (r)
- Measures: Linear relationships
- Data Type: Continuous (interval or ratio)
- Assumptions: Normal distribution, linear relationship, homoscedasticity
- Use When: You have continuous, normally distributed data with linear relationships
Spearman Rank Correlation (rho)
- Measures: Monotonic relationships (any consistent pattern)
- Data Type: Ordinal, interval, or ratio
- Assumptions: None (non-parametric)
- Use When: You have ranked data, non-normal distributions, outliers, or non-linear monotonic relationships
Kendall's Tau ()
- Measures: Ordinal association
- Data Type: Ordinal or ranked
- Assumptions: None (non-parametric)
- Use When: You have small sample sizes or many tied ranks
Correlation vs. Causation
WARNING: Critical Concept: Correlation does NOT imply causation
Why?
- Third Variable Problem: An unmeasured variable may cause both correlated variables
- Directionality: Correlation doesn't indicate which variable influences the other
- Spurious Correlation: Coincidental relationships occur by chance
Classic Example:
- Ice cream sales and drowning deaths are positively correlated
- Does ice cream cause drowning? No
- Third variable: Temperature (summer = more ice cream + more swimming)
To Prove Causation, You Need:
- Temporal precedence (cause precedes effect)
- Experimental design with random assignment
- Ruling out alternative explanations
- Dose-response relationship
- Biological plausibility
Steps in Correlation Analysis
1. Data Preparation
- Check data types: Ensure variables are continuous or ordinal
- Handle missing values: Remove or impute missing data
- Identify outliers: Decide how to handle extreme values
- Check assumptions: Verify distribution and relationship type
2. Visual Exploration
- Scatter plot: Visualize the relationship
- Check linearity: Determine if relationship is linear
- Identify clusters: Look for subgroups in data
- Detect outliers: Spot unusual observations
3. Choose Correlation Method
- Pearson: For linear relationships with normal distributions
- Spearman: For monotonic relationships or non-normal data
- Kendall's Tau: For small samples or ordinal data
4. Calculate Correlation Coefficient
- Compute correlation coefficient (r, rho, or )
- Obtain numerical measure of strength and direction
5. Assess Statistical Significance
- Calculate p-value
- Determine if correlation is statistically significant (typically p < 0.05)
- Report confidence intervals if available
6. Interpret Results
- Strength: Weak, moderate, or strong based on coefficient magnitude
- Direction: Positive or negative relationship
- Significance: Statistically significant or not
- Practical Importance: Consider effect size and context
Applications in CMMI-DCC
Clinical Data Analysis
- CBC Correlations: Relationships between different blood cell types
- Vital Signs: Correlation between heart rate, blood pressure, and respiratory rate
- Longitudinal Changes: How clinical markers change together over time
Omics Data Integration
- Metabolite Associations: Identify correlated metabolites
- Protein Networks: Find proteins with similar expression patterns
- Multi-Omics Integration: Correlate metabolomics with proteomics data
Microbiome Research
- Bacterial Abundance: Correlations between different bacterial taxa
- Microbiome-Host: Correlate microbial features with clinical markers
- Diet-Microbiome: Analyze relationships between diet and microbiome composition
Questionnaire Analysis
- Item Correlations: Relationships between survey questions
- Health Behaviors: Correlate lifestyle factors with health outcomes
- Quality of Life: Analyze relationships between different health domains
Best Practices
DO:
[YES] Visualize data first: Always create scatter plots
[YES] Check assumptions: Verify data meets test requirements
[YES] Report effect size: Include correlation coefficient
[YES] Report p-values: Indicate statistical significance
[YES] Consider context: Interpret biological/practical significance
[YES] Handle outliers appropriately: Decide based on data and context
[YES] Use appropriate method: Choose Pearson vs. Spearman based on data characteristics
DON'T:
[NO] Assume causation: Correlation causation
[NO] Ignore outliers: Can distort correlation coefficients
[NO] Rely on p-values alone: Also consider effect size and confidence intervals
[NO] Over-interpret weak correlations: Small correlations may not be meaningful
[NO] Forget to check assumptions: Violating assumptions can invalidate results
[NO] Analyze non-linear data with Pearson: Use Spearman for non-linear monotonic relationships
Interpreting Correlation Strength
Context Matters:
- Social Sciences (many variables): r = 0.3 might be meaningful
- Physical Sciences (controlled conditions): r = 0.8 might be expected
- Biomarker Discovery: r = 0.5 could indicate a useful diagnostic marker
- Highly controlled experiments: Expect stronger correlations
Rule of Thumb Interpretation:
| |r| Range | Interpretation |
|----------|----------------|
| 0.00 - 0.19 | Very weak to negligible |
| 0.20 - 0.39 | Weak |
| 0.40 - 0.59 | Moderate |
| 0.60 - 0.79 | Strong |
| 0.80 - 1.0 | Very strong |
Limitations
- Only measures linear/monotonic relationships: Can miss complex non-linear patterns
- Sensitive to outliers: Extreme values can distort correlation
- Doesn't capture non-monotonic relationships: Can't detect U-shaped or other complex patterns
- Assumes independence: Data points should be independent
- Sample size dependence: Small samples may produce unreliable estimates
Advanced Topics
Partial Correlation
Correlation between two variables while controlling for the effect of one or more other variables.
Correlation Matrix
Table showing correlations between all pairs of variables in a dataset.
Multiple Testing Correction
When testing many correlations, adjust p-values to control false discovery rate (e.g., Bonferroni correction).
Related Terms
- Spearman Correlation: Non-parametric correlation method used in CMMI-DCC
- P-Value: Determines statistical significance of correlation
- Statistical Analysis: Broader field of analyzing data