Sampling Frames and Sample Design Pres. 5

1. Sampling Frames andSample DesignPres. 5

2. Sample Frames & Sample Design Objectives: Important to define objectives before designing a sample Items to estimate – coverage error, duplication, omissions, etc. Geographic level – national, sub-national (province or district, urban/rural, etc.) Demographic characteristics – sex, age, person, household, etc. Confidence level Margin of error

3. Sample Frames & Sample Design Frames: Material from which a sample is drawn Each unit to be included in the universe There should be no duplicates Each unit should be well defined and distinguishable from other units (it should be unique) Should be updated

4. Sampling Strategies Probability household surveys It is usual to make inferences in a PES for a number of analytical domains Relatively large samples necessary in each domain for reliable estimates Stratified cluster sample design-common First-stage units or Primary Sampling Units (PSUs) - many countries use geographically contiguous land areas usually called area clusters or EAs PPS systematic sample selection Second-stage, common to canvass all persons in selected households

5. Importance of Stratification Population subdivided into heterogeneous groups that are internally homogenous Stratification based on variables correlated with the extent of coverage-geopolitical subdivisions Internal homogeneity can be maintained with regard to socio-demographic variables e.g. urban stratum Common strata may include: rural, urban, provinces etc.

6. Multi-stage Cluster Sampling Usually used when sampling hierarchical populations The hierarchical levels are called stages First stage units are called primary sampling units (PSUs) e.g. EAs Second stage units are called secondary sampling units (SSUs) e.g. households Last stage units are called ultimate sampling units (USUs) e.g. persons within households which can be selected from EAs

7. Why Area sampling? • At national level only a frame of EAs is required • Data collection is more efficient • Lower costs compared to simple random sampling (SRS) • Supervision is easier • However, estimates are prone to higher variability compared to SRS

8. Choices of PSUs • Must have clearly identifiable and stable boundaries • Must completely cover the relevant population • Preferably must have measures of size • They should be mapped • Must cover the whole country • The number of PSUs must be relatively large

9. Common problems with EAs • Incomplete coverage • Inadequate maps • Poor measures of size or lack of them

10. PES sample design • A single-stage stratified clustered sample design is commonly adopted • When the PSUs i.e. EAs are selected all households in selected EAs are canvassed, or more rarely only a sample (e.g. 1 every 5). • This is beneficial for matching operation

11. Sample Size Sample size depends on estimate requirements Geographic level (national, province, urban/rural) Demographic (sex, age) Reliability Confidence level

12. Sample Size To estimate samplesize in the case of proportions you must: Know the occurrence of the event in the population by domain of estimation Specify a confidence interval (e.g 95%) Specify the margin of error or precision (e.g 1%)

13. Sample Size (contd.) To estimate samplesize in the case of proportions, the following formula can be used:

14. Sample size (contd.) From that it is deduced :

15. Sample Size (contd.) Example: To estimate percentage of households omitted in the census (expected about 5%); confidence interval at 95% (t=1.96) for a margin of error of 2 % The sample size works out to be:

16. Sample Size (contd.) Adjusting for non-response, e.g. 10%: Adjusting for the design effect for a complex sample design Design effect of 2 is a default value : 2 x 507 =1,014 This may apply to each province (analysis) domains. If they are five provinces Sample size will be 5 x 1,014 = 5,070

17. Sample selection procedures For greater convenience and efficiency, the sample of PSUs should be selected using a systematic procedure. If there are good measures of size, probability proportional to size (PPS) should be used to increase the efficiency of the sample design. Otherwise, the selection should be made with equal probabilities

18. Sample selection procedures -- PPS 1) Order the EAs geographically (and, if applicable, by other stratification characteristic) to allow implicit stratification  2) Record for each EA i of the stratum h the measure of size Mhi, typically the number of households or persons from the census mapping operation  3) Cumulate the size measures down the list of EAs, the last cumulated number will be equal to the total number of households (or persons) in stratum h (Mh)  4) Determine the number of EAs (nh) to be selected in a stratum according to the allocation

19. Sample selection procedures –- PPS (contd.)  5) Determine the sampling interval (Ih) by:  6) Obtain a random number (Ah) between 1 and Ih inclusively;  7) Determine the selected EAs as follows: Shi=Ah + (i-1) x Ih, for i = 1,...,nh, rounded up to the next integer The i-th EA selected will be the one for which the cumulated measure is closest to Shi without exceeding it.

20. Illustration: Selection of Eight EAs with probability Proportional to size

21. Sample Allocation – 2009 Kenyan PES

22. Thank You!