Copyright 2010, The World Bank Group. All Rights Reserved. Part 2 Sample Design Produced in...

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)


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


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


Estimate of CV

4

x

xse

xcv

)(

Estimate ForceLabor

EstimateError Standard)(


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

xNxN

nN

n

sNdex

1)v(

22


Estimated Standard Error se(x)

• For a proportion p, the parameter s2 takes the simple form np(1-p)/(n-1)

• A “safe” design effect de=4 can be useful

1

)1(v(Np)

2

N

nN

n

ppNde


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


Sample Size Formulas

)1/(1

)1/(1222

3

222

22

NPdePNCVX

NPPdeNn

SNdeCVX

SdeNn


Sample Size Formulas

• In previous slide, large letters that represent assumed “known” values replace estimates

• S2 = 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)


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?

Copyright 2010, The World Bank Group. All Rights Reserved. Part 2 Sample Design Produced in...

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