Home
Back
Sample Correlation Coefficient Formula:
| From: | To: |
The sample correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It ranges from -1 (perfect negative correlation) to +1 (perfect positive correlation), with 0 indicating no linear correlation.
The calculator uses the formula:
Where:
Explanation: The correlation coefficient standardizes the covariance by dividing by the product of the standard deviations, making it dimensionless and comparable across different datasets.
Details: Correlation analysis is fundamental in statistics for identifying relationships between variables, though it does not imply causation. It's widely used in research, data analysis, and predictive modeling.
Tips: Enter comma-separated values for both X and Y variables. Ensure both lists have the same number of values (minimum 2). Values can be integers or decimals.
Q1: What does the correlation coefficient value mean?
A: Values close to ±1 indicate strong linear relationship, values near 0 indicate weak or no linear relationship. Positive values mean both variables increase together, negative means one increases as the other decreases.
Q2: What's the difference between correlation and causation?
A: Correlation measures association, but doesn't prove that one variable causes changes in the other. Other factors or coincidence may be involved.
Q3: What sample size is needed for reliable correlation?
A: Generally, larger samples provide more reliable estimates. Minimum 30 observations is often recommended for statistical significance testing.
Q4: Can correlation detect non-linear relationships?
A: No, Pearson's r only measures linear relationships. Non-linear relationships may show low correlation despite strong association.
Q5: When is correlation considered statistically significant?
A: Significance depends on both the correlation value and sample size. Larger samples can detect smaller correlations as significant.