Spearman Correlation Testing in R Programming

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.

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").

x = c(15, 18, 21, 15, 21)
y = c(25, 25, 27, 27, 27)
result = cor.test(x, y, method = "spearman")
print(result)

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).