Stratified Sampling

Stratified sampling is a probability sampling technique in which the target population is divided into mutually exclusive, exhaustive subgroups (strata) based on a characteristic relevant to the research question, and a random sample is drawn independently from each stratum.^[1][3] This ensures that each subgroup is represented in the sample in known proportions and, when the strata differ on the outcome, can improve the precision of population estimates compared to simple random sampling of the same size.^[1][3]

When important subgroups exist within a population (such as different age groups, geographic regions, or disease severity levels), simple random sampling may, by chance, over or underrepresent certain subgroups, particularly in smaller samples. Stratified sampling guarantees that every defined subgroup appears in the sample in a planned number and, when the subgroups differ on the outcome, can produce more precise estimates of population parameters. It also enables subgroup specific analyses with adequate sample sizes. Stratified sampling is widely used in national surveys, clinical research, and epidemiological studies. When strata are sampled at different rates, analyses that ignore the design, such as unweighted estimates, give biased population estimates.^[3]

The researcher first identifies one or more stratification variables that are expected to influence the outcome. The population is then divided into strata based on these variables. Within each stratum, a simple random sample (or systematic sample) is drawn independently.

Proportionate stratification allocates the sample to each stratum in proportion to the stratum's share of the population.^[1][3] Disproportionate stratification samples strata at different rates, for example giving more sample units to smaller strata to ensure adequate representation for subgroup analysis. Each respondent then receives a design weight equal to the inverse of their stratum's sampling fraction, so that the analysis produces correct population estimates.^[3] Optimal (Neyman) allocation is a disproportionate design for a single overall estimate: it sets each stratum's sample size in proportion to the stratum's population size multiplied by its standard deviation on the outcome, which gives the smallest standard error for a fixed total sample size when costs per unit are equal.^[1][2]

The overall estimate combines the stratum results, each weighted by the stratum's share of the population, and its variance is the sum, over strata, of the squared population share times the within stratum variance divided by the stratum sample size (leaving out the finite population correction, which is negligible when only a small fraction of each stratum is sampled). Only variation within strata enters this variance.^[1][3]

The gains from stratification are greatest when the stratification variable is strongly associated with the outcome variable and when strata are internally homogeneous but different from each other. Under these conditions, stratified sampling with proportionate or optimal allocation reduces the standard error of estimates compared to simple random sampling, effectively increasing the precision of the study without increasing the total sample size.^[1][3]

Use stratified sampling when the population contains distinct subgroups that you want to ensure are represented, when the outcome is expected to vary across subgroups, and when subgroup specific estimates are needed. It is appropriate when a sampling frame with the stratification variable is available. Stratified sampling is not necessary when the population is homogeneous with respect to the outcome, or when no prior information about subgroup differences exists to guide the choice of stratification variable.

A national health survey aims to estimate the prevalence of diabetes across four age groups (18 to 39, 40 to 54, 55 to 69, and 70 and older), which make up 40%, 27%, 21% and 12% of the adult population. Proportionate allocation of 8,000 respondents would give 3,200, 2,160, 1,680 and 960. Instead, using disproportionate stratified sampling from a population registry, the survey draws 2,000 respondents from each age group to ensure adequate precision for subgroup estimates. Suppose the prevalence is 4%, 11%, 20% and 26% in the four groups. Simply pooling all 8,000 respondents would give 15.25%, because older people are oversampled. Weighting each group by its population share gives the national estimate: 0.40 × 4% + 0.27 × 11% + 0.21 × 20% + 0.12 × 26% = 11.89%. Its standard error is about 0.34 percentage points, slightly smaller than the 0.36 points a simple random sample of 8,000 would give, because stratifying by age takes the differences between age groups out of the standard error, and the oversampled older groups are also the ones with the largest within group variance (26% × 74% = 0.19 against 4% × 96% = 0.04 in the youngest group). The oldest group's own estimate has a standard error of about 0.98 points, against 1.42 points with the 960 respondents proportionate allocation would give it.