1. What is Pearson Correlation Coefficient?

The Pearson correlation coefficient (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
• \( \Sigma \) — Summation across all data points

Explanation: The numerator measures covariance between X and Y, while the denominator normalizes this value by the product of standard deviations.

3. Interpretation of Correlation Values

Guidelines:

• 0.8 to 1.0: Very strong correlation
• 0.6 to 0.8: Strong correlation
• 0.4 to 0.6: Moderate correlation
• 0.2 to 0.4: Weak correlation
• 0.0 to 0.2: Very weak or no correlation
• Negative values indicate inverse relationships

4. Using the Calculator

Tips: Enter comma-separated values for both X and Y variables. Both lists must have the same number of values. Values should be numerical (decimals allowed).

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: What are the assumptions for Pearson correlation?
A: Assumes linear relationship, continuous variables, normally distributed, and homoscedasticity.

Q3: When should I use Spearman instead of Pearson?
A: Use Spearman for ordinal data or when relationship is monotonic but not linear.

Q4: How many data points do I need?
A: Generally, at least 30 pairs for reliable results, though more is better.

Q5: Can outliers affect the correlation?
A: Yes, Pearson correlation is sensitive to outliers. Consider examining scatterplots.