Spearman Rank Correlation Analysis using Agri Analyze

The blog is about Spearman Rank Correlation theory, when to use, calculation along with formulas, testing its significance, solved example and step by step guide for Agri Analyze (Reading time 10 mins)

Correlation is a statistical measure that quantifies the strength and direction of the relationship between two variables. For example, it can be used to assess whether there is a connection between the heights of fathers and their sons.

There are two primary types of correlation analysis:

Parametric Correlation: This method, often using Pearson's correlation coefficient (r), measures the linear relationship between numerical variables. It assumes a specific distribution of the data.
Non-Parametric Correlation: Employing techniques like Kendall's tau or Spearman's rho, these methods analyze the relationship between variables based on their ranks rather than their actual values. They are suitable for categorical data or ordinal (rank) data and do not require assumptions about data distribution.

One of the key assumptions in correlation analysis is that both variables being studied are normally distributed. If at least one of the variables follows a normal distribution, linear correlation can still be used. However, if neither variable is normally distributed, the linear correlation method is not appropriate. In such situations, rank correlation should be utilized instead.

There are two distinct methods for computing rank correlation: Spearman's rank correlation and Kendall's tau. Both methods can be applied to the same dataset. Numerically, Spearman's rank correlation typically yields higher values than Kendall's tau. However, both methods generally produce nearly identical inferences, so there is no compelling reason to favor one over the other. Spearman's rank correlation is more widely used due to its computational simplicity.

Spearman's rank correlation is sometimes called . In order to avoid confusion with the population correlation coefficient , the notation , is used to represent Spearman's correlation coefficient. Spearman's rank correlation procedure starts with ranking of the measurements of the variable X and Y separately. The differences between the ranks of each of n pairs are then found out. They are denoted by d. The Spearman's rank correlation is then computed by using the formula:

Testing the Significance of the Correlation Coefficient: A Step-by-Step Guide

To test the significance of the correlation coefficient, typically perform a hypothesis test to determine whether the observed correlation is statistically significant. The steps for testing the significance of the correlation coefficient r are as follows:

Solved example of Spearman Rank Correlation

Problem statement: There are two variables X and Y each having 5 observations. Compute the Spearman rank correlation and also test its significance using t test. The data is shared below:

X: 10, 20, 30, 40, 50 and Y: 20, 25, 15, 35, 30