Stratification Strategies for Efficient Sample Allocation
Explore the recommended stratification strategies - proportional, optimal, and equal allocation - to determine the most efficient sample size allocation for a total sample size of 800 across different strata.
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Presentation Transcript
Exercise #2 Given the information below, what stratification strategy would you recommend to the government for a total sample size of 800? Calculate the sample size for each strata under proportional and equal allocation to inform your answer. Stratum 1 Capital City ?1= 7500 ?1= 1000 ?1= 200 Stratum 2 Mountain ?2= 2500 ?2= 200 ?2= 25 ? = 10,000 ?1= ?2
Proportional Allocation ? = ? ? ? ?1= ? ?1 ? = 800 7500 1000= 600 ?2= ? ?2 ? = 800 2500 1000= 200
Equal Allocation ? =? ? ? ?=800 2 = 400 ?1= ?2=
Optimal Allocation ? ? ? = ? ? =1 ? ? ?1?1 (7500)(200) ?1= ? = 800 (7500)(200) + (2500)(25)= 768 ?1?1+ ?2?2 ?2?2 (2500)(25) ?2= ? = 800 (7500)(200) + (2500)(25)= 32 ?1?1+ ?2?2
Summary of results N % Mean x sd n Var(x) e(srs) RSE equal allocation strata 1 strata 2 National 7500 2500 10000 0.75 0.25 1000 200 800 200 25 400 400 800 100 10 1 8 1.0% 0.6% 0.9% 2 1 56 proportional allocation 600 200 800 strata 1 strata 2 National 7500 2500 10000 0.75 0.25 1000 200 800 200 25 67 3 38 8 2 6 0.8% 0.9% 0.8% 1 optimal allocation strata 1 strata 2 National 7500 2500 10000 0.75 0.25 1000 200 800 200 25 768 32 800 52 20 31 7 4 6 0.7% 2.2% 0.7% 1
What do you recommend? It depends. Proportional allocation Simplest form of sample allocation. Provides self-weighting sample. Efficient sample design for national- level results when variability is similar for the different strata. Optimal allocation Generates the most efficient. allocation at the national level for one variable. People really like the name. Equal allocation Easy to explain. Generates same level of precision is required for each stratum. Practical allocation Most common sample design for complex, multi-indicator sample surveys.
