Estimation of Some Proportion in a Clustered Population

The aim of this paper is to show that the traditional design-based estimator for the proportion of population units, associated with at least one subunit having an attribute of interest using the two-stage sampling design, is biased. We face such a situation in the Adult Education Survey of official statistics of the European countries when estimating the share of individuals in non-formal education, involved in job-related learning activities. The alternative design and model-based estimators are proposed.