Uncertainty and models

Quantile-quantile plot (QQ plot)

Compares quantiles from two distributions to assess differences in location, scale and shape.

Plot
Model diagnostics
Distribution

What it answers

Do two distributions have matching quantiles?

Shape: Quantile pairs and reference line
What it shows: Location shifts, scale differences and tail departures.

Example

The question

Are our delivery times close to a normal distribution?

Sample quantiles against normal quantiles (QQ plot, illustrative)

Points follow the straight line through the middle, so the bulk looks normal. The top two points sit well above it: the upper tail is heavier than normal.

Illustrative data. It belongs to no company.

When to use it

Use it when

Checking distributional assumptions or comparing samples.

Avoid it when

Unexplained quantile conventions or a need to compare frequencies directly.

How to read it

Compare paired quantiles with the reference line; inspect slope and curvature.

Note

Can compare a sample with a model or another sample.

The data you need

Layout: Long table
Fields: Value: number
One row is: One raw numeric observation. What is the grain?
Rules: Choose a theoretical comparison distribution or supply a second sample. Quantile alignment must be defined.
Optional: Precomputed alternative: QuantileA,QuantileB with paired quantiles in matching order.
Preparation: Choose a comparison distribution or sample and match quantile levels using a stated convention.
Units: Each axis uses its distribution's quantile units, unless one is a standard theoretical scale.

A long table: one row per observation, few columns. New data adds rows.

Worked example

SampleA1,2,3 and SampleB2,4,6. Paired order quantiles lie on Y=2X, showing a scale difference.

Value
10
12
12
18
23

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