1. What is Pearson Correlation Coefficient?

The Pearson Product-Moment Correlation Coefficient (PMCC or r) measures the linear correlation between two variables X and Y. It ranges from -1 to +1, where +1 is total positive linear correlation, 0 is no linear correlation, and -1 is total negative linear correlation.

2. How Does the Calculator Work?

The calculator uses the Pearson correlation formula:

Where:

• \( x_i, y_i \) — Individual data points
• \( \bar{x}, \bar{y} \) — Means of X and Y variables
• \( r \) — Correlation coefficient (unitless, range: -1 to +1)

Explanation: The formula calculates how much the variables change together (covariance) divided by the product of their standard deviations.

3. Interpretation of PMCC Values

Guidelines:

• 0.00 to ±0.30: Negligible correlation
• ±0.30 to ±0.50: Weak correlation
• ±0.50 to ±0.70: Moderate correlation
• ±0.70 to ±0.90: Strong correlation
• ±0.90 to ±1.00: Very strong correlation

4. Using the Calculator

Tips: Enter comma-separated values for both X and Y variables. Both lists must have the same number of values. At least 2 data points are required.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between correlation and causation?
A: Correlation measures association, but doesn't imply causation. Other factors may influence the relationship.

Q2: Can PMCC detect non-linear relationships?
A: No, PMCC only measures linear relationships. For non-linear relationships, consider other correlation measures.

Q3: How many data points are needed for reliable PMCC?
A: Generally, at least 30 pairs provide stable estimates, but the calculator works with as few as 2.

Q4: What if my data has outliers?
A: PMCC is sensitive to outliers. Consider examining scatterplots or using robust correlation measures.

Q5: Can I use PMCC for ordinal data?
A: For ordinal data, Spearman's rank correlation is more appropriate.