Same correlation, wildly different data: always plot first

Anscombe’s quartet in tidy form — four datasets with identical summary statistics and completely different stories. A 50-year-old lesson that still gets ignored.

A correlation coefficient in a report feels like a fact. But r is a summary, and summaries hide things. The classic demonstration is Anscombe’s quartet (1973) — four small datasets constructed to share nearly identical means, variances, correlations and regression lines. It ships with base R.

Identical numbers…

library(tidyverse)

quartet <- map_dfr(1:4, function(i) {
  tibble(
    set = paste("Dataset", c("I", "II", "III", "IV")[i]),
    x   = anscombe[[paste0("x", i)]],
    y   = anscombe[[paste0("y", i)]]
  )
})

quartet |>
  group_by(set) |>
  summarise(
    mean_x = mean(x), mean_y = mean(y),
    r      = cor(x, y),
    slope  = coef(lm(y ~ x))[2]
  ) |>
  mutate(across(where(is.numeric), ~ round(.x, 2)))

# A tibble: 4 × 5
  set         mean_x mean_y     r slope
  <chr>        <dbl>  <dbl> <dbl> <dbl>
1 Dataset I        9    7.5  0.82   0.5
2 Dataset II       9    7.5  0.82   0.5
3 Dataset III      9    7.5  0.82   0.5
4 Dataset IV       9    7.5  0.82   0.5

Four datasets, and to two decimal places the same mean, the same r = 0.82, the same regression slope.

…completely different stories

ggplot(quartet, aes(x, y)) +
  geom_smooth(method = "lm", se = FALSE,
              colour = "#2f6fed", linewidth = 0.9, formula = y ~ x) +
  geom_point(colour = "#1b2a4a", size = 2.4, alpha = 0.85) +
  facet_wrap(~set) +
  labs(
    title = "Anscombe's quartet: one correlation, four realities",
    subtitle = "Every panel has r ≈ 0.82 and the same fitted line",
    x = NULL, y = NULL
  ) +
  theme_minimal() +
  theme(plot.title = element_text(face = "bold", colour = "#1b2a4a"),
        strip.text = element_text(face = "bold", colour = "#1b2a4a"))

Figure 1

Only Dataset I is what a reader imagines when they see “r = .82”: a linear relationship with noise. Dataset II is a curve — a linear model is simply the wrong shape. Dataset III is a perfect line plus one outlier dragging the fit. Dataset IV has no relationship at all; a single extreme point manufactures the entire correlation.

What this means in practice

Before any correlation or regression lands in one of our reports, the workflow is fixed:

1. Plot the raw data — a scatter plot per pair, faceted if there are groups.
2. Check influence — one point should never own the result (Cook’s distance, or just delete-and-refit).
3. Match the method to the shape — a monotone curve may call for Spearman’s rank correlation; a genuine curve calls for a different model, not a caveat.

The numbers are the end of the analysis. The picture is the beginning.