Repräsentativität von Subgruppen bei geschichteten Zufallsstichproben

The concept of a representative sample can be found in nearly every survey description. In general, this means that the sample is a miniature of the population. A scientific definition of the term should include all important aspects of a sample survey. In this paper such a definition is discussed. Besides the theoretical aspects of the sample design such as the sampling method and the estimation technique, it comprises practical aspects occurring also in population surveys such as nonresponse and untruthful answering. Given this sample design, the chosen sample number determines the survey’s sampling error. The question of the necessary sample number for a certain efficiency of the estimator is discussed. Based on that, the question on the sample numbers in subgroups of a stratified random sample, relevant in practice, is considered. These sample numbers have to allow for representativeness in each subgroup. The solution of this problem can be described by a convex minimization program under box constraints and linear inequality constraints. A numerical example illustrates the proposed procedure. Copyright Springer-Verlag Berlin Heidelberg 2013