Read the pattern, not a correlation score
| Pattern | Likely reading | Check |
|---|---|---|
| Points roughly follow a line | Distribution broadly matches the reference shape | Look for tail departures hidden by the center. |
| Ends bend away in opposite directions | Heavier tails than the reference | Inspect extreme observations and model sensitivity. |
| Ends bend inward | Lighter tails | Confirm with histogram and substantive bounds. |
| One-sided curve | Skewness | Tail direction and possible transformation/model choice. |
| A few remote points | Isolated extremes or data issues | Verify records; do not delete from the plot alone. |
| Horizontal steps | Ties or discrete/rounded data | A continuous normal reference may be inappropriate. |
The axes can be reversed by software, which reverses some visual descriptions. Read axis labels before memorizing “up means right skew.”
How the plot is constructed
The data are sorted. Each order position is paired with a probability and then with the corresponding quantile from the reference distribution. If the sample differs only in location and scale, the points lie approximately on a line; the intercept and slope absorb those two differences. Wilk and Gnanadesikan developed probability plotting as a family of graphical methods for comparing ordered observations with theoretical distributions.3
R’s qqnorm creates a normal QQ plot and qqline adds a robust line through selected quartiles.2 That line is a software construction, not a statistical acceptance threshold.
Plot the quantity whose assumption matters
Regression and ANOVA assumptions usually concern model errors, so inspect residuals rather than requiring the raw outcome to be normal. A mixture of groups can make pooled raw data nonnormal even when the conditional error model is reasonable.
Use residual plots for mean structure, variance, leverage, and influence. Skewness and kurtosis describe aspects of shape numerically, while normality tests provide a formal p-value whose sensitivity changes with sample size.
Why a QQ plot can beat a binary normality test
At large n, a normality test can detect a tiny departure with little practical effect. At small n, it may miss a consequential tail pattern. A QQ plot shows where the mismatch lies: center, one tail, both tails, or isolated points. It does not remove the need for uncertainty or design-aware judgment, but it answers more than “reject/do not reject.”
A defensible reporting sentence
“The residual QQ plot followed the reference line through the center but departed in both tails, indicating heavier-than-normal tail behavior. We assessed the sensitivity of intervals and influential observations rather than declaring normality from a single p-value.”