English title: Design Effects

Author(s): Siegfried Gabler - Matthias Ganninger -

Language: English

Type: Book chapter

Year: 2008

## Abstract

In large-scale sample surveys inferences are usually based on the standard randomization principle in survey sampling. Under such an approach, the responses are treated as fixed and the randomness is assumed to solely come from the probability mechanism that generates the sample. For example, in simple random sampling (SRS), the sample mean is unbiased with randomization-based variance given by Var(bar{y})_{srs} = (1-f) (S^2)/n. where n, N and f = n/N denote the sample size, the population size and the sampling fraction, respectively and S^2 is the finite population variance with the divisor N-1. Usually f is negligible and can be dropped from the formula. In any such case, the above equality provides a conservative formula for the variance. In most cases, however, complex sample designs (indicated by the subscript CSD in the following) are applied rather than SRS. In such a situation, the sample mean can still be an unbiased estimator under the usual randomization approach if the sampling design is epsem, i.e. each sampling unit in the finite population has the same chance f of being selected. However, the variance of the sample mean usually underestimates the true randomization variance of under the complex sample design. To account for this underestimation, Kish proposed the following variance inflation factor, commonly known as design effect: DEFF_R = Var_CSD(\bar{y})/Var_SRS(\bar{y}), where subscript R denotes the perspective of the randomization framework. Although in the vast majority of empirical applications the design effect is considered for the usual sample mean (as above and in the following), the above ratio can be defined more generally for the variances of any estimator under any complex design. In practice, DEFF_R is unknown and some approximations and estimations are employed to assess its magnitude.

From page no: 193

To page no: 197

Anthology: Encyclopedia of Survey Research Methods