Audit the Scatterplot Behind a Correlation

Plot the observations that actually enter the analysis

Use the same paired records and transformations used for the reported correlation. Label both axes with variable names and units, and record the complete-pair count. If either measurement is missing, document that exclusion instead of plotting one population and calculating the coefficient on another.

The NIST scatterplot guidance describes inspecting linear and nonlinear relationships, changing variation, and unusual observations. A scatterplot is an analytical check, not merely a decorative companion to a correlation table.

Look for shape before assigning a label

Ask whether the relationship is approximately straight, curved, or separated into groups. Check whether the vertical spread changes across the horizontal axis. Identify areas with few observations and avoid implying that the pattern extends beyond the measured range.

Consider a fictional example with x values −2, −1, 0, 1, 2 and corresponding y values 4, 1, 0, 1, 4. Pearson correlation is zero by symmetry, but the plotted points follow an exact curved relationship. “No linear association” and “no relationship” are therefore different statements. The example is deliberately constructed for teaching, not a real research finding.

Investigate influence and grouping

A single distant observation can substantially alter a correlation. Check its source record, units, measurement process, and eligibility before deciding what to do. Do not remove it merely because the coefficient becomes more impressive without it. Preserve corrections and show justified sensitivity analyses when influential valid observations matter.

If the sample includes different sites or populations, inspect those groups as well as the combined plot. A pooled association can reflect differences between groups rather than the same within-group relationship. Choose grouping variables based on the design and scientific question, not an unrestricted search for a preferred pattern.

Check the observational unit

Several visits from one participant create correlated pairs. An ordinary correlation treating every row as independent can misrepresent uncertainty and may mix within-person and between-person relationships. State whether the analysis concerns people, visits, specimens, or another unit, and use a method appropriate to that structure.

Use the correlation audit worksheet to record these checks. For an appropriate independent-pair Pearson analysis, the Fisher interval guide explains one approximate interval calculation. Its formula cannot replace the design review.

Finish by retaining the plot, coefficient method, transformations, sample definition, and decisions about unusual records. Where points overlap heavily, use a suitable display that reveals density without changing the underlying values. Keep interpretation tied to what the plot supports: correlation is not proof of causation, agreement, or predictive performance in a new population. The audit should reveal what a single summary number leaves out.

Source checked on 2 November 2026; fictional zero correlation independently recalculated.