1. INTRODUCTION TO THE NONRESPONSE PROBLEM 1. Introduction to the Nonresponse Problem This thesis concerns itself with the question to what extent do surveys suffer from nonresponse and which strategies are suitable for necessary corrections of nonresponse bias. As an introduction to this question, the first chapter discusses the conflicting principles between the imaginary idealised sample (as assumed in the mathematical theory of probability) and the real world of survey research with the many possible sources of errors and focuses upon the nonresponse problem. The second chapter examines a nonresponse follow-up study which was conducted as part of the East German Life History Study. The exploration of the nonrespondents has two aims: firstly, to obtain knowledge about the data and to collect robust descriptions and secondly, to isolate variables as candidates in order to explain nonresponse. On the basis of the exploratory chapter, hypotheses about nonresponse behaviour shall be formulated. The third chapter presents a model to predict nonresponse. The fourth chapter discusses possible corrections for nonresponse in multivariate relationships: weighting strategies and the Heckman sample selection model which will be illustrated by an example. The final chapter gives a brief review of the findings. 1.1 The Ideal World: Mathematical Theory In the social sciences, surveys are used to generalise information obtained from a concrete collection of observations which build the sample to an abstract total population. Kish (1965) calls it "a hypothetical infinite set of elements generated by a theoretical model". The mathematical theory of probability forms the basis of our statistical inferences. It was formulated by Kolmogorov' in 1933. He transferred the intuitive idea of uncertainty about what will happen to the set theoretic axioms of probability theory. Kolmogorov constructed the concept of an event as a possible result of an experiment and the concept of probability as a measure. Guided by this approach to probability, two theorems are important for understanding the idea of sampling: the law of large numbers (there are a weak law and a strong law) and the central limit theoremâ€œ. I will not cite them as formularies as e.g. given and proven by Feller (1950). To understand their implications on the concept of sampling, I will concentrate on the following simplified summary: Kolmogorov, A. N. (1956). Foundations of the Theory of Probability. Second English Edition. See Axioms, pp.2,14-16. The correct mathematical formulations as well as the proofs can be found in: Feller, William (1950). Probability Theory and Its Applications, Volume I. pp.155-156,191-196. See also Kolmogorov (1956:61-64,66- 68). 4