Formalizing the Concepts: DESIGN EFFECTS

Cluster effect where: ρ = intraclass correlation coefficient – measure of homogeneity within a cluster m = number of units per cluster C = number of clusters

Cluster effect (continued) The cluster effect increases with the intraclass correlation coefficient ( ρ ) and the number of sampling units per cluster The cluster effect increases with the intraclass correlation coefficient ( ρ ) and the number of sampling units per cluster The intraclass correlation coefficient is The intraclass correlation coefficient is Very high (> 0.2) for variables of infrastructureVery high (> 0.2) for variables of infrastructure High (~ 0.05) for socioeconomic variablesHigh (~ 0.05) for socioeconomic variables Low (< 0.02) for demographic variablesLow (< 0.02) for demographic variables Typical number of households per cluster: Typical number of households per cluster: 10 to 15 sample households for socioeconomic and LSMS surveys10 to 15 sample households for socioeconomic and LSMS surveys 20 to 25 households for Demographic Surveys20 to 25 households for Demographic Surveys

Design Effects The cluster effect measures the inefficiency of two- stage sampling relative to SRS The cluster effect measures the inefficiency of two- stage sampling relative to SRS ceff = e TSS / e SRSceff = e TSS / e SRS In a more complex sample design (with many stages, stratification, etc.) In a more complex sample design (with many stages, stratification, etc.) deff = e COMPLEX / e SRSdeff = e COMPLEX / e SRS The design effect can also be interpreted as The design effect can also be interpreted as deff = n/ n SRSdeff = n/ n SRS Some researchers use Some researchers use deft = deff = e COMPLEX /e SRSdeft = deff = e COMPLEX /e SRS Design effect Size of the SRS that would have given the same error

Importance of Design Effects Necessary to calculate sampling errors and design effects based on actual sample design Necessary to calculate sampling errors and design effects based on actual sample design If deff is ignored, the sampling errors will be underestimated, and the conclusions from any test of hypothesis or analysis will be biasedIf deff is ignored, the sampling errors will be underestimated, and the conclusions from any test of hypothesis or analysis will be biased Statistical software will always assume simple random sampling unless told otherwise Statistical software will always assume simple random sampling unless told otherwise In Stata standard errors and deffs for complex designs can be calculated using the svy commands. In Stata standard errors and deffs for complex designs can be calculated using the svy commands.