Spearman Correlation Testing in R Programming

Last Updated : 28 Jul, 2025

Spearman Correlation Testing in R programming is a statistical method used to evaluate the strength and direction of a monotonic relationship between two ranked variables. Unlike Pearson correlation, it does not assume normal distribution or linearity, making it ideal for ordinal data and non-linear associations.

Spearman’s correlation, often denoted as Spearman’s rho (\rho), measures the strength and direction of the monotonic relationship between two ranked variables. It ranges from -1 to +1:

  • +1: A perfect positive monotonic relationship.
  • 0: No monotonic relationship.
  • -1: A perfect negative monotonic relationship.

Formula:

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

Where:

  • \rho is the Spearman Correlation coefficient
  • d_i is the difference between the ranks of corresponding variables.
  • n is the number of observations.

Implementation of Spearman Correlation Testing in R

We calculate the Spearman correlation using two methods in R programming language.

1. Calculating Spearman Correlation Using cor() Function

We calculate the Spearman correlation coefficient between two numeric vectors using cor() to get only the correlation coefficient.

  • cor: Calculates the correlation coefficient between two numeric vectors.
  • method: Specifies the type of correlation method (here, it is "spearman").
  • cat: Used to concatenate and print the final correlation value.
R 
x = c(15, 18, 21, 15, 21)
y = c(25, 25, 27, 27, 27)
result = cor(x, y, method = "spearman")
cat("Spearman correlation coefficient is:", result)

Output:

Spearman correlation coefficient is: 0.4564355

2. Calculating Spearman Correlation Using cor.test() Function

We compute the Spearman correlation coefficient using cor.test() to get both the coefficient and p-value for hypothesis testing.

  • cor.test: Performs a test of association or correlation between two numeric vectors.
  • method: Specifies the type of correlation method (here, it is "spearman").
R 
x = c(15, 18, 21, 15, 21)
y = c(25, 25, 27, 27, 27)
result = cor.test(x, y, method = "spearman")
print(result)

Output:

spearman_correlation
Output
  • S is the value of the test statistic (S = 10.871)
  • p-value is the significance level of the test statistic (p-value = 0.4397).
  • alternative hypothesis is a character string describing the alternative hypothesis (true rho is not equal to 0).
  • sample estimates is the correlation coefficient. For Spearman correlation coefficient it’s named as rho (Cor.coeff = 0.4564).
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