The Spearman Correlation Calculator simplifies the process of calculating the Spearman correlation coefficient, which assesses the strength and direction of association between two ranked variables. This tool is invaluable in scenarios where data does not meet the assumptions necessary for Pearson correlation, particularly when dealing with ordinal variables or non-normally distributed data.
Formula of Spearman Correlation Calculator
The Spearman correlation coefficient is a robust non-parametric measure that provides insights into the monotonic relationship between two variables. Here’s how it’s calculated:
Rank the Data:
Assign ranks to the values in both datasets. For any tied values, assign the average rank.
Calculate the Differences:
Compute the difference (di) between the ranks of corresponding values from the two datasets.
Square the Differences:
Square each of the differences to obtain di squared.
Sum of Squared Differences:
Calculate the sum of all squared differences (sum of di squared).
Apply the Formula:
rho = 1 – (6 * sum of di squared) / (n * (n squared – 1))
where n is the number of pairs of ranks.
Table of Commonly Searched Terms
| Term | Description |
|---|---|
| Spearman correlation | A measure of rank correlation between two variables |
| Non-parametric statistics | Statistical methods not based on parameterized distributions |
| Rank correlation | Correlation between ranks of values in datasets |
| Tied ranks | Average ranks assigned to tied values in data |
Example
Let’s calculate the Spearman correlation coefficient for the following data:
| Data Set X | Rank X | Data Set Y | Rank Y |
|---|---|---|---|
| 10 | 3 | 30 | 2 |
| 20 | 2 | 40 | 1 |
| 30 | 1 | 50 | 3 |
- Rank the Data:
- Data Set X ranks: 1, 2, 3
- Data Set Y ranks: 2, 1, 3
- Calculate the Differences:
- Differences (d_i): (3-2), (2-1), (1-3) = 1, 1, -2
- Square the Differences:
- Squared differences (d_i squared): 1, 1, 4
- Sum of Squared Differences:
- Sum of d_i squared: 1 + 1 + 4 = 6
- Apply the Formula:
- rho = 1 – (6 * 6) / (3 * (3 squared – 1))
- rho = 1 – (36 / (3 * 8))
- rho = 1 – (36 / 24)
- rho = 1 – 1.5 = -0.5
The Spearman correlation coefficient for this data is -0.5, indicating a moderate negative correlation between the two ranked variables.
Most Common FAQs
Spearman correlation is used for ranked data and does not assume a linear relationship, making it suitable for ordinal data and non-linear relationships.
Yes, the Spearman correlation coefficient can be utilize to test hypotheses about the association between variables, especially in non-parametric statistical analysis.