Enter the difference between the ranks of corresponding variables and the number of observations into the calculator to determine the Spearman Rank Correlation. This calculator can also evaluate any of the variables given the others are known.

Spearman Rank Correlation Formula

The following formula is used to calculate the Spearman Rank Correlation. 

ρ = 1 - (6 * Σd^2) / (n * (n^2 - 1))

Variables:

  • ρ is the Spearman Rank Correlation
  • d is the difference between the ranks of corresponding variables
  • Σd^2 is the sum of the squares of the rank differences n is the number of observations

To calculate the Spearman Rank Correlation, first find the difference between the ranks of each pair of corresponding variables. Square each of these differences and sum them up. Multiply this sum by 6. Then, multiply the number of observations by the difference between the square of the number of observations and 1. Subtract the first result from 1 and divide by the second result.

What is a Spearman Rank Correlation?

Spearman Rank Correlation, also known as Spearman’s rho, is a non-parametric measure of statistical dependence between two variables. It assesses how well the relationship between two variables can be described using a monotonic function. In simpler terms, it measures the strength and direction of the association between two ranked variables. It is often used when the assumptions of Pearson’s correlation coefficient are not met, such as when data is not normally distributed or when there are outliers.

How to Calculate Spearman Rank Correlation?

The following steps outline how to calculate the Spearman Rank Correlation.

  1. First, determine the difference between the ranks of corresponding variables (d).
  2. Next, calculate the sum of the squares of the rank differences (Σd^2).
  3. Next, determine the number of observations (n).
  4. Next, calculate the numerator of the formula: 6 * Σd^2.
  5. Next, calculate the denominator of the formula: n * (n^2 – 1).
  6. Finally, calculate the Spearman Rank Correlation using the formula: ρ = 1 – (numerator) / (denominator).
  7. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

d = 2, 4, 1, 3, 5

n = 5

Calculate the Spearman Rank Correlation.