Stratified Random Sampling

Stratified Random Sampling

Key takeaways

• Stratified random sampling divides a population into homogeneous subgroups (strata) and draws random samples from each stratum.
• Proportionate stratification samples each stratum in proportion to its population share; disproportionate (or oversampling) intentionally changes those shares.
• This method improves precision for estimates of subgroup and overall population characteristics but requires a reliable way to classify every population member into a single stratum.

What it is

Stratified random sampling is a probability sampling technique in which the population is partitioned into distinct, non-overlapping subgroups (strata) based on shared characteristics such as age, gender, geography, or major. Random samples are then drawn independently from each stratum and combined for analysis. The approach ensures that all important subgroups are represented in the sample.

When to use it

Use stratified sampling when:
* You want precise estimates for specific subgroups as well as the overall population.
* The population is heterogeneous but can be meaningfully divided into homogeneous strata.
* You can identify and classify every population member into exactly one stratum.

Use simple random sampling instead when subgroup information is unavailable or strata cannot be clearly defined.

How it works — steps

1. Define the target population and obtain a sampling frame (list of members).
2. Choose stratification variables (characteristics that define strata).
3. Partition the population into non-overlapping strata.
4. Determine the sample size for each stratum (proportionate or disproportionate).
5. Select a random sample from each stratum (e.g., simple random sampling within each stratum).
6. Combine the stratum samples for analysis and apply weighting if strata were sampled disproportionately.

Proportionate vs. disproportionate stratification

• Proportionate (proportional) stratified sampling: each stratum’s sample size is proportional to its share of the population. This preserves the population composition in the sample and often yields more precise overall estimates.
• Formula: n_h = (N_h / N) × n
  where n_h = sample size for stratum h, N_h = population size of stratum h, N = total population, n = total sample size.
• Example: Population N = 180,000, sample n = 50,000, stratum N_h = 90,000 → n_h = (90,000/180,000)×50,000 = 25,000.
• Disproportionate stratified sampling: stratum sample sizes do not match population shares. Useful when rare subgroups need more precise estimates (oversampling). Analysis typically requires weighting to produce unbiased overall estimates.

Advantages

• Ensures representation of key subgroups, including small or rare groups.
• Often reduces sampling error and increases precision relative to simple random sampling, especially when strata differ substantially.
• Allows separate analysis and tailored insights for each stratum.

Disadvantages and limitations

• Requires a complete sampling frame and reliable classification of every unit into a single stratum.
• Not suitable when members fit multiple strata (overlap) unless strata are redefined; overlaps can bias selection probabilities.
• More complex to design and implement than simple random sampling and may raise costs and logistical burdens.
• If disproportionate sampling is used, proper weighting is necessary during analysis to obtain unbiased population estimates.

Example

A research team wants a sample of n = 4,000 college students to reflect U.S. major distributions. Population proportions: English 12%, Science 28%, Computer Science 24%, Engineering 21%, Math 15%. For proportionate stratified sampling:
* English: 0.12 × 4,000 = 480
Science: 0.28 × 4,000 = 1,120
Computer Science: 0.24 × 4,000 = 960
Engineering: 0.21 × 4,000 = 840
Math: 0.15 × 4,000 = 600
Random samples are then drawn from each major to create a combined, representative sample.

Applications

• Survey research (demographic analysis, opinion polls)
• Market research (customer segments)
• Public health studies (age, risk groups)
• Finance (index-replication techniques, stratified portfolio sampling)

Bottom line

Stratified random sampling is a powerful method for producing representative and precise samples when a population can be partitioned into distinct, meaningful strata. It improves subgroup estimates and overall accuracy but requires clear classification of every population member, careful design, and, when necessary, weighting to correct for disproportionate sampling.