Objectives and Use of Stratification in Sample Design
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1 Regioal Traiig Course o Agricultural Cost of Productio Statistics November 2016, Daejeo, Republic of Korea Objectives ad Use of Stratificatio i Sample Desig Cotets Strata ad Clusters Sigle Stage Cluster samplig epsem selectio ad estimatio Selectio metod (sigle stage) epsem ad PPSWR ad PPS systematic Estimatio uder PPS cluster samplig 2
2 Strata ad Clusters 3 Strata ad Clusters Clusterig ad Stratificatio i Sample Desig Typically, sample surveys coducted by NSOs ivolve subdividig te populatio ito strata ad clusters. Te sampler s objective is to get te rigt combiatio of stratificatio ad clusterig to get te required estimates at te desired level of accuracy wit te give resources. 4
3 Strata ad Clusters Strata ad Clusters Bot stratificatio ad clusterig ivolve subdividig te populatio ito mutually exclusive groups. Sub divisios of te populatio are called clusters or strata depedig upo te samplig procedure adopted. Te term cluster is used i te cotext of cluster samplig ad multi stage (cluster) samplig. 5 Strata ad Clusters Sample Desig Selectio Pla Sample Selectio Pla = Samplig System AND Samplig Sceme Samplig system Elemet samplig Cluster samplig Stratified samplig Multi-stage samplig* Samplig sceme Simple radom samplig Systematic samplig PPS *Select cluster first, te select elemets witi selected clusters 6
4 Coice of Strata ISEC ISI 7 Clusterig ad Stratificatio Stratificatio A powerful tool for improvig efficiecy. I complex surveys, te clusters (PSUs) are usually stratified. Ofte te ultimate stage uits (ouseolds / oldigs) are also stratified. Permits idepedet selectio ad estimatio for eac stratum at all stages of selectio. Appropriate allocatio of samples improve efficiecy of te estimates. 8
5 Clusterig ad Stratificatio Objectives of Stratificatio To obtai estimates of iger efficiecy for give per uit of cost Providig separate estimates required for eac subdivisio of te populatio domai estimates Usig differet samplig procedures for differet subpopulatio, to (i) icrease efficiecy of te estimates (ii) orgaize te field work 9 Clusterig ad Stratificatio Defiig Strata 1. Coice of stratificatio variables (locatio, output etc.): Homogeeous witi strata; Heterogeeous across strata Higly correlated wit study variables (output wit cropped area or irrigatio status etc.) 2. Number of strata Depeds o availability of stratifyig iformatio i samplig frame: less iformatio, fewer strata At least two samplig uits per stratum to be able to compute samplig error 10
6 Coice of Strata Coice of Strata To icrease precisio relative to SRS Form strata wit stratum uits omogeeous wit respect to survey variable (omogeeous witi stratum) Stratum meas of caracteristic of iterest varies widely amog strata (eterogeeous across strata) To provide separate estimates for smaller domais Place eac domai i a stratum or set of strata Apply appropriate samplig rate or sample desig to acieve eeded sample size ad precisio. 11 Clusterig ad Stratificatio Stratificatio variables: Examples Houseold / Holdigs surveys At te First Stage Urba/rural Locatio: regio; provice At te Secod Stage (for selectio of ouseolds/ oldigs) Affluet / o affluet Houseolds reportig cultivatio, aimal usbadry, poultry, orticulture etc. Holdigs of differet size classes 12
7 Allocatio of Sample Size to Strata ISEC ISI 13 Stratificatio Allocatio Allocatio Sample over Strata Give a total sample size,, ow sould tis be allocated amog te strata? Maximize precisio for fixed cost OR Miimize cost for required precisio 1 2 H N 1 N 2 N N H 1 2 H SIAP 14 18/11/2016
8 Stratificatio Allocatio Sample Allocatio to Strata Alteratives Metods: Uiform or equal allocatio Proportioate allocatio Disproportioate allocatio Optimum allocatio (miimum variace), fixed sample size Cost optimum allocatio (ot discussed!) 18/11/ Stratificatio Allocatio Sample Allocatio to Strata I proportioate stratificatio, a uiform samplig fractio is applied to eac strata; tat is, te sample size selected from eac stratum is made proportioate to te populatio size of te stratum I disproportioate stratificatio, differet samplig rates are used deliberately i differet strata 18/11/
9 Stratificatio Allocatio Proportioate Allocatio I proportioate stratificatio, N is specified to be te same for eac stratum. Tis implies tat te overall samplig fractio is N Te umber of elemets take from te t stratum is N N N N 18/11/ Stratificatio Allocatio Proportioate Allocatio VSRS V prop Tus, for proportioate stratified deff < 1 For a give total variability i te populatio, te gai is greater if: te strata mea are more eterogeeous (more uequal strata mea) OR te elemet values witi te strata are more omogeeous
10 Stratificatio Allocatio Optimum Allocatio Uses widely differet samplig rates for te various strata. Objective: to acieve te least variace for te overall mea for te give sample size (Neyma s allocatio); as well as give per uit of cost i differet strata. Witout cost cosideratio, te allocatio is N N Tis gives better efficiecy as compared to proportioate allocatio: V SRS V prop V opt Taks 20
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