1. What is Spearman Correlation?

The Spearman correlation coefficient (r_s) is a non-parametric measure of rank correlation between two variables. It assesses how well the relationship between two variables can be described using a monotonic function.

2. How Does the Calculator Work?

The calculator uses the Spearman rank correlation formula:

Where:

• \( d_i \) — Difference between ranks of corresponding variables
• \( n \) — Number of observations

Explanation: The formula converts raw scores to ranks and calculates Pearson correlation on the ranked data. It's particularly useful when data doesn't meet Pearson correlation assumptions.

3. Interpretation of Results

Details: The coefficient ranges from -1 to 1, where 1 indicates perfect positive monotonic correlation, -1 perfect negative monotonic correlation, and 0 no 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 (minimum 2). The calculator automatically handles tied ranks.

5. Frequently Asked Questions (FAQ)

Q1: When should I use Spearman instead of Pearson?
A: Use Spearman when data is ordinal or when the relationship is monotonic but not necessarily linear. Also when data violates Pearson's normality assumption.

Q2: How does Spearman handle tied ranks?
A: The calculator uses average ranks for tied values, which is the standard approach for handling ties in Spearman correlation.

Q3: What's the minimum sample size needed?
A: Technically you need at least 2 pairs, but for meaningful results, at least 5-10 pairs are recommended.

Q4: Can Spearman correlation detect non-monotonic relationships?
A: No, Spearman only detects monotonic relationships. For complex non-monotonic relationships, other methods may be needed.

Q5: How is significance determined for Spearman correlation?
A: Statistical significance can be assessed via hypothesis testing, though this calculator focuses only on the coefficient calculation.