Stratified Random Sampling

What Is Stratified Random Sampling?

Stratified random sampling is a probability sampling method in which a population is first divided into distinct, non-overlapping subgroups, called strata, based on shared characteristics. A random sample is then drawn separately from each stratum.

The central idea is simple:
instead of treating the population as one undifferentiated group, we acknowledge that it is composed of meaningful subgroups and ensure that each subgroup is represented in the sample.

Why Stratified Random Sampling Is Used

In many real-world populations, individuals differ in important ways—such as age, gender, education, income, or profession—and these differences may be related to the outcome being studied.

If we rely only on simple random sampling, some groups may be:

underrepresented,
overrepresented, or
entirely missed by chance.

Stratified random sampling is used to:

improve representation of key subgroups,
increase precision of estimates,
reduce sampling error, and
allow explicit comparisons between groups.

Basic Terminology

Population: the entire group of interest.
Sample: a subset of the population used for analysis.
Stratum (plural: strata): a subgroup of the population whose members share a defining characteristic.
Sampling frame: a list or mechanism that identifies all members of the population.

A crucial requirement is that:

every population member belongs to exactly one stratum,
strata do not overlap, and
all strata together cover the entire population.

How Stratified Random Sampling Works (Step by Step)

Define the population
Identify the full group you want to study.
Choose stratification variables
Select characteristics that are:
- relevant to the research question, and
- available for every population member
  Examples include age group, gender, education level, income bracket, or region.
Divide the population into strata
Each individual is assigned to one and only one stratum.
Decide the sample size for each stratum
This can be done using:
- proportionate stratification, or
- disproportionate stratification.
Perform random sampling within each stratum
Use simple random sampling independently inside each stratum.
Combine the sampled observations
The final sample is the union of all stratum-specific samples.

Proportionate Stratified Random Sampling

In proportionate stratification, the sample size from each stratum is proportional to that stratum’s size in the population.

If:

total population size is $N$,
total sample size is $n$,
stratum $h$ has population size $N_h$,

then the stratum sample size is:

$n_h = \frac{n}{N} \times N_h$

Key properties

The sample mirrors the population structure.
Estimates are often more precise than those from simple random sampling.
No additional weighting is needed during analysis.

Example

If:

population size = $180{,}000$,
sample size = $50{,}000$,
one age group contains $90{,}000$ people,

then the sample from that stratum is:

$n_h = \frac{50{,}000}{180{,}000} \times 90{,}000 = 25{,}000$

Disproportionate Stratified Random Sampling

In disproportionate stratification, the sample sizes of strata do not match their population proportions.

This approach is used when:

some strata are very small but substantively important,
rare subgroups must be studied in detail,
the research focus prioritizes certain groups.

Consequences

Some strata are over-sampled, others under-sampled.
Statistical weights are required to recover population-level estimates.
Analysis is more complex but often more informative for subgroup comparisons.

Stratified Sampling vs. Simple Random Sampling

Simple Random Sampling

Every individual has the same probability of selection.
No explicit subgroup control.
Easy to implement.
Can produce unbalanced subgroup representation by chance.