Stratification in Sampling Designs
Learn about the concept of stratification in sampling, its importance, and practical examples in the context of surveys and research. Explore different levels of stratification in the Pacific region and understand sample allocation methods for more accurate data collection.
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Stratification February 18, 2019 Noumea, NEW CALEDONIA
Stratification The population is divided up into subgroups or strata . A separate sample of units is then selected from each stratum. There are two primary reasons for using a stratified sampling design: To potentially reduce sampling error by gaining greater control over the composition of the sample. To ensure that particular groups within a population are adequately represented in the sample. These objectives are often contradictory in practice. The sampling fraction generally varies across strata. Sampling weights need to be used to analyze the data.
Stratification Establishment survey Stratification of establishments by economic activity and employment size National household survey Geographic domains regions, provinces Urban/rural Socio-economic groups Agricultural survey Agro-ecological zones Land use Farm size
Stratification in the Pacific Example 1 : Samoa has 4 levels of stratification Apia Urban Area Rest of Upolu North West Upolu Savaii
Stratification in the Pacific Example 2 : Vanuatu has 8 levels of stratification 1. Torba 2. Sanma-urban (Luganville) 3. Sanma-rural 4. Penama 5. Malampa 6. Shefa-urban (Port Vila) 7. Shefa-rural 8. Tafea
Sample allocation under stratified sampling Each stratum is treated as an independent population Estimate of stratified total is sum of stratum totals ? ? ? ? = ? =1 Estimate of stratified mean is weighted combination of stratum means ? ? 2 2 1 ? ? ?2??? ? ?2??? ??? ? = ? ? ? =1 =1 H = Number of strata h = stratum number Nh =Population size in stratum h nh = sample size in stratum h
Stratification Common examples of sample allocation among the strata: Proportional allocation Equal allocation Optimum allocation Practical allocation
Proportional allocation The sample allocated to each stratum is proportionally to the number of units in the frame for the stratum: N N h = n n h Simplest form of sample allocation. Provides self-weighting sample. Efficient sample design for national-level results when variability is similar for the different strata.
Equal allocation Each stratum is allocated an equal number of sample units: ? ? ? = H = Number of Strata Used when same level of precision is required for each stratum. Example: estimates of similar quality required for each region.
Neyman or optimal allocation Provides minimum total error and minimum cost for a fixed sample size: ? ? ? ? ? ? ? = ? ? =1 sh = estimated standard deviation in stratum h ch = cost per unit in stratum h If cost is unknown: ? ? ? ? = ? =1 ? ?
Practical allocation criteria For national household surveys, sometimes allocation is a compromise between proportional, equal and Neyman allocation; e.g. we start with a proportional allocation and then we increase the sample size in the smaller regions. In countries with high proportion of rural population, sometimes a higher sampling rate is used for the urban stratum, to increase the urban sample size and because of the lower cost of data collection in urban areas.
Second Stage Stratification Sometimes it is desirable to stratify the sample in the last stage (household or individual level). Examples: male/female headed households, program beneficiaries, households with orphans and vulnerable children (OVCs). Beware of the dangers. Second stage stratification increases the need for close supervision of field teams.
Weighting under stratified sample designs A proportionally allocated sample is self-weighted. In non-proportionally allocated samples, we must use weights to account for different sampling fractions by stratum.
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, equal, and optimal 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
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.
