1. Stratified Sampling Lecturer: Chad Jensen

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

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

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

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

6. Proportionate Stratification Each Stratum has the same sampling fraction. 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.

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

8. Disproportionate Stratification The sampling fraction may vary from one stratum to the next. 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.

9. Disproportionate Stratum n h = n * ( N h * S h ) / [ Σ ( N i * S i ) ] n h = n * ( N h * S h ) / [ Σ ( N i * S i ) ] n h = sample size for stratum h. n h = sample size for stratum h. n = total sample size n = total sample size N h = population size of stratum h. N h = population size of stratum h. S h = Standard deviation of stratum h S h = Standard deviation of stratum h

10. 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?

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

12. Example Stratum Mean Score Standard Deviation Boys7010.27 Girls806.66 The state administers a reading test to a sample of 36 third graders. The state administers a reading test to a sample of 36 third graders. The school system has 20,000 third graders The school system has 20,000 third graders 10,000 boys and 10,000 girls. 10,000 boys and 10,000 girls.

13. Proportionate Stratum n h = ( N h / N ) * n n h = ( N h / N ) * n 18 boys = (10,000/20,000) *36 18 boys = (10,000/20,000) *36 18 girls = (10,000/20,000) *36 18 girls = (10,000/20,000) *36

14. Disproportionate Stratum Stratum Mean Score Standard Deviation Boys7010.27 Girls806.66 n h = n * ( N h * S h ) / [ Σ ( N i * S i ) ] n h = n * ( N h * S h ) / [ Σ ( N i * S i ) ] 21.83 boys = 36 * ( 10,000 * 10.27 ) / [ ( 10,000 * 10.27 ) + ( 10,000 * 6.67 ) ] 21.83 boys = 36 * ( 10,000 * 10.27 ) / [ ( 10,000 * 10.27 ) + ( 10,000 * 6.67 ) ] 14 girls = (36 – 22 boys) 14 girls = (36 – 22 boys)

15. Conclusion How can you use stratified sampling in your project? How can you use stratified sampling in your project?

16. Questions? Comments? Concerns? Emotional Outburst?