qqplot() — Q-Q plot

Checks whether data follows a normal bell curve.

qqnorm(x); qqline(x)

Key idea

• A Q-Q plot compares your data's quantiles (equal-sized ranking cut-offs) against those of a normal bell curve.
• Dots lying close to the straight diagonal line suggest the data is roughly normal (bell-shaped).
• A curved or S-shaped pattern signals skew (a lopsided shape) or heavy tails instead of normality.
• Dots dipping below the line at the left end and rising above it at the right point to heavier tails — more extreme values than a normal curve.
• It is a quick visual check before using tests that assume the data is normal. (e.g. n = 40 points)

Definition

$$\left({\Phi }^{-1}\left(\frac{i-0.5}{n}\right),x_{(i)}\right)\text{should fall on a line}$$

$x_{(i)}$

the i-th smallest data value

$i$

its rank, 1 to n

$n$

how many points

${\Phi }^{-1}$

the matching normal quantile

In plain words

Line up the dots, and if they follow the straight line, your data is bell-shaped (normal).

Where you'd use it

• Before running a t-test on 40 exam scores, a qqplot checks the normality the test assumes; if the dots hug the straight line, you can trust the test, but a strong curve warns the data is not bell-shaped.
• After fitting a regression, plot its leftover errors on a Q-Q plot — dots near the line mean the errors are normal, supporting your model’s assumptions.
• A Q-Q plot of measurements whose dots fall below the line at the left end and climb above it at the right reveals heavy tails (more extreme values than a normal curve would have), while a curve bending away on one side only signals skew.

Frequently asked questions

What does a Q-Q plot check?

Whether data follows a distribution (often normal). Points on the line = good fit; S-shapes flag skew or heavy tails.