Formalizing the Concepts: STRATIFICATION

These objectives are often contradictory in practice Sampling weights need to be used to analyze the data Sampling weights need to be used to analyze the data Stratification The population is divided up into subgroups or “strata”. The population is divided up into subgroups or “strata”. A separate sample of units is then selected from each stratum. A separate sample of units is then selected from each stratum. There are two primary reasons for using a stratified sampling design: 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 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.To ensure that particular groups within a population are adequately represented in the sample. The sampling fraction generally varies across strata. The sampling fraction generally varies across strata.

Examples of Stratification Establishment survey Establishment survey Stratification of establishments by economic activity and employment sizeStratification of establishments by economic activity and employment size National household survey National household survey Geographic domains – regions, provincesGeographic domains – regions, provinces Urban/ruralUrban/rural Socio-economic groupsSocio-economic groups Agricultural survey Agricultural survey Agro-ecological zonesAgro-ecological zones Land useLand use Farm sizeFarm size

Estimation under stratified random sampling Each stratum is treated as an independent population Each stratum is treated as an independent population Estimate of stratified total is sum of stratum totals Estimate of stratified total is sum of stratum totals Estimate of stratified mean is weighted combination of stratum means Estimate of stratified mean is weighted combination of stratum means Variance calculated independently for each stratum Variance calculated independently for each stratum

Estimation under stratified random sampling L = Number of strata h = stratum number N h =Population size in stratum h n h = sample size in stratum h In other words, we need to weight!

Sample allocation under stratified sampling Three major types of sample allocation of sample units among the strata: Three major types of sample allocation of sample units among the strata: Proportional allocationProportional allocation Equal allocationEqual allocation “Optimum” allocation“Optimum” allocation

Proportional allocation The sample allocated to each stratum is proportionally to the number of units in the frame for the stratum: The sample allocated to each stratum is proportionally to the number of units in the frame for the stratum: Simplest form of sample allocation Simplest form of sample allocation Provides self-weighting sample Provides self-weighting sample Efficient sample design for national-level results when variability is similar for the different strata 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: Each stratum is allocated an equal number of sample units: Used when same level of precision is required for each stratum Used when same level of precision is required for each stratum Example: reliable survey estimates required for each region Example: reliable survey estimates required for each region

Neyman allocation S h = standard deviation in stratum h S h = standard deviation in stratum h c h = cost per unit in stratum h c h = cost per unit in stratum h Provides minimum total error and minimum cost for a fixed sample size Provides minimum total error and minimum cost for a fixed sample size

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 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 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

Weighting under stratified, multi-stage sample designs A proportionally allocated sample is self-weighted A proportionally allocated sample is self-weighted In non proportionally allocated samples, we must use weights to account for different sampling fractions by stratum In non proportionally allocated samples, we must use weights to account for different sampling fractions by stratum

Concept of Stratification (cont’d)  Domain of inference  Separate sample is selected in each stratum Sample design may be different in each stratumSample design may be different in each stratum  Stratification increases efficiency of sample design Uses known information about the populationUses known information about the population Eliminates variability between strataEliminates variability between strata As a result, decreases the sampling errorAs a result, decreases the sampling error