Spearman's Rank Correlation Calculator
This calculator is designed for statisticians and researchers who need to compute Spearman's rank correlation coefficient to measure the strength and direction of association between two ranked variables.
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Spearman's Rank Correlation:
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Data Source and Methodology
All calculations are based on the established statistical method for Spearman's rank correlation, as detailed in this Wikipedia article. All calculations strictly adhere to these formulas and data.
The Formula Explained
\[ r_s = 1 - \frac{6 \sum d_i^2}{n(n^2 - 1)} \]
Glossary of Terms
- Data Set X: The first set of ranked data values.
- Data Set Y: The second set of ranked data values.
- Spearman's Rank Correlation: A measure of rank correlation that evaluates the relationship between two variables.
How It Works: A Step-by-Step Example
Consider data sets X: [1, 2, 3] and Y: [3, 2, 1]. The rank differences are calculated, squared, and summed. The formula then calculates the correlation coefficient using the given ranks.
Frequently Asked Questions (FAQ)
- What is Spearman's Rank Correlation? It is a statistical measure of the strength and direction of a relationship between two ranked variables.
- How is it different from Pearson's correlation? Spearman's correlation assesses monotonic relationships, while Pearson's assesses linear relationships.
- Can it be used for non-parametric data? Yes, it is suitable for non-parametric data.
- What are the assumptions of Spearman's correlation? It assumes that the data is ordinal or continuous and ranked.
- What do the results indicate? A value close to 1 or -1 indicates a strong correlation, while a value close to 0 indicates little to no correlation.