Stratified sampling

Stratified sampling divides the population into non-overlapping subgroups (strata) by a relevant characteristic, then draws a random sample within each. Precision improves when the stratifying variable is related to the outcome of interest.

ByHoang TruongUpdated July 2, 2026

FrameworkSampling design

See it move

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A population of 1,000 customers splits into three spend tiers: 600 low-spend, 300 medium-spend and 100 high-spend. Stratified sampling draws separately within each tier, in proportion to its size, so the small high-spend group is never swamped by chance the way a single random draw from the whole 1,000 might swamp it.

Where it fits

TopicFoundations: Data, Populations & SamplingCoreSubjectData Analysis & StatisticsCore

The formula

LaTeX

n_h = n \cdot \frac{N_h}{N}

Variables

$n_{h}$: Sample size allocated to stratum h
$n$: Total planned sample size
$N_{h}$: Number of units in stratum h
$N$: Total population size

Proportional allocation. Each stratum contributes observations in proportion to its share of the population, ensuring representation without oversampling any subgroup.

Check yourself

PracticeCORE

A retailer has 10,000 customers categorised as low, medium, or high spenders. It randomly selects 100 customers from each spending category. Which sampling method is this, and what is its main advantage?

Select an answer to check your understanding.