1. What is the Sample Correlation Coefficient?

The sample correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1, where -1 indicates perfect negative correlation, +1 indicates perfect positive correlation, and 0 indicates no linear correlation.

2. How Does the Calculator Work?

The calculator uses the Pearson correlation coefficient formula:

Where:

• \( x_i \) — Individual x data point
• \( \bar{x} \) — Mean of x values
• \( y_i \) — Individual y data point
• \( \bar{y} \) — Mean of y values
• \( n \) — Sample size
• \( s_x \) — Standard deviation of x values
• \( s_y \) — Standard deviation of y values

Explanation: The numerator calculates the covariance between x and y, while the denominator normalizes this by the product of their standard deviations.

3. Interpretation of Correlation Coefficient

Details:

• 0.00-0.19: Very weak correlation
• 0.20-0.39: Weak correlation
• 0.40-0.59: Moderate correlation
• 0.60-0.79: Strong correlation
• 0.80-1.00: Very strong correlation

Negative values indicate inverse relationships.

4. Using the Calculator

Tips: Enter comma-separated values for both x and y variables. Ensure both lists have the same number of values. The calculator automatically filters non-numeric entries.

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 both variables.

Q2: What are the assumptions for Pearson's r?
A: Assumes linear relationship, continuous variables, normally distributed data, and homoscedasticity.

Q3: When should I use Spearman's correlation instead?
A: Use Spearman's for ordinal data or when the relationship is monotonic but not linear.

Q4: How many data points do I need?
A: At least 5-10 pairs for meaningful results, though more is better for reliability.

Q5: Can correlation be used for prediction?
A: While it measures association, regression analysis is needed for prediction.