Correlation Tests: Kendall’s

Correlation is a statistical method used to assess a possible association between two numeric variables, X and Y. There are several statistical coefficients that we can use to quantify correlation depending on the underlying relation of the data:

• Pearson’s
• Spearman’s
• Kendall’s

To calculate Kendall’s correlation coefficient between two numeric variables, X and Y, in R, you can use the cor() function with the method = "kendall" argument. Here’s an example code:

# Create two numeric variables, X and Y
X <- c(5, 10, 15, 20, 25)
Y <- c(15, 25, 35, 45, 55)

# Calculate Kendall's correlation coefficient between X and Y
correlation <- cor(X, Y, method = "kendall")

# Print the correlation coefficient
print(correlation)

In this example, we have created two numeric variables, X and Y, with five values each. We then use the cor() function to calculate Kendall’s correlation coefficient between X and Y, using the method = "kendall" argument to specify the type of correlation coefficient we want to calculate. Finally, we print the correlation coefficient using the print() function.

The print(correlation) output will be a single value, which represents the Kendall’s correlation coefficient between the two variables. The value ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation.

The interpretation of Kendall’s correlation coefficient is similar to that of the other two correlation coefficients. Here’s a breakdown of how to interpret different values:

• If the correlation coefficient is close to 1, it indicates a strong positive correlation between the two variables, meaning that when one variable increases, the other variable tends to increase.
• If the correlation coefficient is close to -1, it indicates a strong negative correlation between the two variables, meaning that when one variable increases, the other variable tends to decrease.
• If the correlation coefficient is close to 0, it indicates no or weak correlation between the two variables, meaning that there is no clear relationship between them.

Kendall’s correlation coefficient is also a non-parametric measure of correlation, meaning it does not assume any particular distribution for the data. It is a measure of the strength and direction of the monotonic relationship between the two variables, which means it measures how well the relationship can be described using a monotonic function (i.e., a function that either always increases or always decreases). Kendall’s correlation coefficient is similar to Spearman’s rank correlation coefficient in this respect, but is a bit more computationally efficient.