1. Copyright 2010, The World Bank Group. All Rights Reserved. Part 2 Sample Design Produced in Collaboration between World Bank Institute and the Development Data Group (DECDG)

2. Copyright 2010, The World Bank Group. All Rights Reserved. Sample Size Sample size must be selected to meet:  reliability criteria  cost constraints Steps to determine sample size 1. Set reliability criteria and budget constraints 2. Develop an equation to express the relationship between reliability and sample size 3. Develop an equation to express the relationship between cost and sample size 4. Select sample size that satisfies both equations 2

3. Copyright 2010, The World Bank Group. All Rights Reserved. CV, a Measure of Reliability CV – Coefficient of Variation Relative measure of an estimate’s accuracy Generally expressed in %; e.g., 10% CV Better to have small CVs than large CVs 3

4. Copyright 2010, The World Bank Group. All Rights Reserved. Estimate of CV 4

5. Copyright 2010, The World Bank Group. All Rights Reserved. Estimated Standard Error se(x) Square root of the estimated variance Often compared to a simple random sample of size n from a population N Design effect de accounts for differences of a particular sample from the “ideal” of simple random sampling

6. Copyright 2010, The World Bank Group. All Rights Reserved. Estimated Standard Error se(x) For a proportion p, the parameter s 2 takes the simple form np(1- p)/(n-1) A “safe” design effect de=4 can be useful

7. Copyright 2010, The World Bank Group. All Rights Reserved. Factors Affecting Sample Size National & Subnational Reliability Response Rates Clustering (households sampled, not persons, can sample clusters of households) Type of Sampling (Stratification? 2-stage? Are first-stage areas small or large?) Advanced Techniques –Sample Rotation –Population controls in estimation

8. Copyright 2010, The World Bank Group. All Rights Reserved. Sample Size Formulas

9. Copyright 2010, The World Bank Group. All Rights Reserved. Sample Size Formulas In previous slide, large letters that represent assumed “known” values replace estimates S 2 = NP(1-P)/(N-1) in second formula for a proportion P P is a proportion with respect to N, for ex: – UE/N = unemployment /(adult population) – NOT the unemployment rate UER – UER = UE/(labor force)

10. Copyright 2010, The World Bank Group. All Rights Reserved. Final Sample Size Determination Several variables of interest? National and subnational reliability criteria? If the sample size is too costly, then rethink –Relax reliability criteria? –Increase allowed cost?