Pearson vs Spearman correlation: which one, and when (in R)

Pearson measures linear association; Spearman measures monotonic association on ranks. A clear R example shows exactly when they disagree — and which to trust.

Both quantify how two variables move together, but they answer subtly different questions. Choosing wrong can hide a strong relationship or overstate a fragile one. (Want a quick number and scatter plot? Use our correlation calculator.)

The difference in one sentence

• Pearson measures the strength of a linear relationship, using the raw values.
• Spearman measures the strength of a monotonic relationship, using the ranks — so it captures “as X goes up, Y goes up” even when the shape is curved, and it shrugs off outliers.

Where they disagree

Take a strong but curved (exponential) relationship:

library(ggplot2)
set.seed(3)
x <- 1:60
y <- exp(x / 18) + rnorm(60, 0, 2)

pear <- cor(x, y)                      # Pearson
spear <- cor(x, y, method = "spearman") # Spearman

ggplot(data.frame(x, y), aes(x, y)) +
  geom_point(colour = "#17a2b8", alpha = 0.7) +
  labs(title = sprintf("Pearson r = %.2f   vs   Spearman rho = %.2f", pear, spear),
       x = "X", y = "Y") +
  theme_minimal(base_family = "sans") +
  theme(plot.title = element_text(face = "bold", colour = "#1b2a4a"))

Figure 1

The relationship is essentially perfect and increasing, so Spearman is near 1. Pearson is lower because the relationship isn’t a straight line — it’s penalised for the curvature.

Getting the test

cor.test(x, y, method = "spearman")

    Spearman's rank correlation rho

data:  x and y
S = 2214, p-value < 2.2e-16
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho 
0.9384829 

cor.test() gives the coefficient, the test statistic and a p-value for either method.

How to choose

• Pearson when the relationship looks linear and the data are roughly normal without wild outliers.
• Spearman when the relationship is monotonic but curved, the data are ordinal, or outliers/skew are present.

Always plot first — a coefficient without a scatter plot hides curvature and outliers. And whichever you use: correlation is not causation.

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