Stratified Sampling

Stratified Sampling Lecturer: Chad Jensen

Sampling Methods • SRS (simple random sample) • Systematic • Convenience • Judgment • Quota • Snowball • Stratified Sampling

What is Stratified Sampling? Stratification is the process of grouping members of the population into relatively homogeneous subgroups before sampling.

Advantages • Provides greater precision than a SRS (simple random sample) of the same size • Often requires a smaller sample, which saves money • Can guard against an "unrepresentative" sample • Focuses on important subpopulations but ignores irrelevant ones

Disadvantages • Can be difficult to select relevant stratification variables • Often requires more administrative work than an SRS • Not useful when there are no homogeneous subgroups • Can be expensive

Proportionate Stratification • Each Stratum has the same sampling fraction. • Can provide better precision than a SRS of the same size. • Gains in precision are greatest when values within strata are homogeneous. • Gains in precision accrue to all survey measures.

Proportionate Stratum nh = ( Nh / N ) * n • nh = is the sample size for stratum h. • Nh = is the population size of stratum h. • N = the total population size • n = the total sample size

Disproportionate Stratification • The sampling fraction may vary from one stratum to the next. • If variances differ across strata, disproportionate stratification can provide better precision than proportionate stratification, when sample points are correctly allocated to strata. • The researcher can maximize precision for a single important survey measure. • Gains in precision may not accrue to other survey measures.

Disproportionate Stratum nh = n * ( Nh * Sh ) / [ Σ ( Ni * Si ) ] • nh = sample size for stratum h. • n = total sample size • Nh = population size of stratum h. • Sh = Standard deviation of stratum h

Proportionate vs. Disproportionate Disproportionate can be a better choice (e.g., less cost, more precision) if sample elements are assigned correctly to strata. • Example: Given a fixed budget or fixed sample size, how should sample be allocated to get the most precision from a stratified sample?

Proportionate vs. Disproportionate Recommendation: • If costs and variances are about equal across strata, choose proportionate stratification. • If they differ, consider disproportionate stratification.

Example • The state administers a reading test to a sample of 36 third graders. • The school system has 20,000 third graders • 10,000 boys and 10,000 girls.

Proportionate Stratum nh = ( Nh / N ) * n • 18 boys = (10,000/20,000) *36 • 18 girls = (10,000/20,000) *36

Disproportionate Stratum nh = n * ( Nh * Sh ) / [ Σ ( Ni * Si ) ] • 21.83 boys = 36 * ( 10,000 * 10.27 ) / [ ( 10,000 * 10.27 ) + ( 10,000 * 6.67 ) ] • 14 girls = (36 – 22 boys)

Conclusion • How can you use stratified sampling in your project?

Questions? Comments? Concerns? Emotional Outburst?

Stratified Sampling