Four questions
| Question | What to describe |
|---|---|
| Form | Linear, curved, segmented, clustered, or no clear pattern |
| Direction | Upward, downward, or changing across the range |
| Strength | How tightly points follow the described form |
| Exceptions | Outliers, leverage points, gaps, ceiling/floor effects |
A strong curve can have weak Pearson correlation. A single remote point can create an apparently strong line. Use correlation interpretation only after the plotted form is understood.
Common traps
Overplotting can hide thousands of cases behind a few marks; transparency, jitter, or density displays help. Aggregated points can show a relationship that differs from the individual-level pattern. Restricted range can weaken a real association. Mixed groups can create or erase a pooled trend.
Anscombe’s quartet famously shows datasets with nearly identical summary statistics but very different scatter plots.2 The lesson is not decorative: the picture can reveal structure the coefficient cannot.
Compare with histograms for each variable’s distribution and box plots for grouped spread.
A defensible reporting sentence
“The plot showed a moderate upward curved relationship, two clusters, and one high-leverage observation. Because the form was nonlinear, a single Pearson r was not treated as a complete summary.”