Describe › Standalone plots

Q-Q normal plot

A Q-Q plot draws empirical quantiles against standard-normal quantiles with a mean ± SD reference line, so points hugging the line indicate normality.

What is Q-Q normal plot?

A Q-Q plot is the most useful single visualisation for normality assessment. Empirical quantiles (sorted observations) go on the y-axis, theoretical normal quantiles (z) on the x-axis. If the data are normal the points fall on a straight line passing through the mean with slope SD.

The shape of the departure tells you exactly what's wrong. S-shape ⇒ heavy tails (Cauchy, t-distribution). Inverted S ⇒ light tails. Convex curve ⇒ right skew. Concave curve ⇒ left skew. A normality p-value can tell you something is off, but only the Q-Q plot tells you what.

When should I use Q-Q normal plot?

  • After (or instead of) a numerical normality test, to understand the shape of any departure.
  • Regression / ANOVA diagnostics on the residuals — strictly the residuals are what need to be normal, not the raw outcome.

What data does it need?

One numeric column.

What does it report?

Scatter of (theoretical z, observed value) + reference line.

How do I interpret the result?

Slight wiggles at the extremes are normal even for normal data because the order statistics there are noisy — focus on the body of the plot.

If only a handful of points at the extremes lift off the line and the centre is straight, the issue is outliers, not the distribution shape. Re-check with the box plot + ROUT.

See also