Spearman's Correlation Calculator

Spearman's Correlation Formula:

\[ \rho = 1 - \frac{6 \times \sum d_i^2}{n(n^2 - 1)} \]

Spearman's Correlation Coefficient (ρ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Spearman's Correlation?

Spearman's correlation coefficient (ρ) is a non-parametric measure of rank correlation that assesses how well the relationship between two variables can be described using a monotonic function. It measures the strength and direction of association between ranked variables.

2. How Does the Calculator Work?

The calculator uses the Spearman's correlation formula:

\[ \rho = 1 - \frac{6 \times \sum d_i^2}{n(n^2 - 1)} \]

Where:

\( d_i \) — Difference between ranks of each observation
\( n \) — Number of observations (sample size)
\( \sum d_i^2 \) — Sum of squared rank differences

Explanation: The coefficient ranges from -1 to +1, where +1 indicates perfect positive correlation, -1 indicates perfect negative correlation, and 0 indicates no correlation.

3. Importance of Spearman's Correlation

Details: Spearman's correlation is particularly useful when data doesn't meet the assumptions of Pearson's correlation (normality, linearity). It's robust to outliers and works well with ordinal data or non-linear relationships.

4. Using the Calculator

Tips: Enter the rank differences (d_i values) separated by commas or spaces. The calculator will compute the Spearman's correlation coefficient. Ensure you have at least 2 observations for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: When should I use Spearman's correlation instead of Pearson's?
A: Use Spearman's when your data is ordinal, not normally distributed, or when the relationship is monotonic but not necessarily linear.

Q2: What does a Spearman correlation of 0.8 mean?
A: A correlation of 0.8 indicates a strong positive monotonic relationship between the variables - as one variable increases, the other tends to increase as well.

Q3: How do I interpret negative Spearman correlation values?
A: Negative values indicate an inverse relationship - as one variable increases, the other tends to decrease.

Q4: What are the assumptions for Spearman's correlation?
A: The main assumptions are that variables are at least ordinal and that the relationship is monotonic. No assumption of normality is required.

Q5: How is Spearman's correlation different from Kendall's tau?
A: Both are rank-based correlations, but they use different computational approaches. Spearman's is more sensitive to errors in ranking and generally has higher power, while Kendall's tau is more robust and easier to interpret probabilistically.