The Design Effect: Bias and Variance Estimation

The estimation of the sample size is a crucial part of the planning process of a survey and it can be accomplished in different ways, some of them require information not available or that may be obtained with a substantial cost. The estimation of the sample size can be done by using the design effect estimator proposed by Kish. This estimator is also used as an efficiency measure for a probability sampling plan and to build confidence intervals. Even though the design effect estimator is widely used in practice, little is known about its statistical properties and there are no variance estimators available. In this paper we show that the design effect estimator is biased, we give an expression for an upper bound to the ratio of the bias to the standard error and a method to estimate the variance. With these elements it is possible to improve the precision of the estimators during the planning and estimation stage of a survey. This also results in a better resource allocation during the planning stage of a survey.