Spearman’s correlation coefficient is a non-parametric measure of the correlation between two variables. It is useful in analysing the correlation between variables where the relationship is monotonic but not necessarily linear.

A monotonic relationship exists when one variable increases, the other always increases, or when one variable increases, the other always decreases. Visualised as a chart of x against y, the slope of the relationship must be either always positive or always negative, but must never switch between the two.

Example in R

Let’s create some example data:

set.seed(150)
data <- data.frame(x = rnorm(100, mean = 50, sd = 10),
random = sample(c(100:500), 100, replace = TRUE))
data$y <- (data$x^5/1000000) + (data$random)
plot(data$x, data$y)

If we want to calculate the Spearman’ correlation of x and y in data, we can use the following code:

This is slightly lower than the Spearman’s correlation because the Pearson correlation coefficient measures the linear relationship between variables. Thus the Spearman’s coefficient is the appropriate statistic for non-linear relationships.

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