## Full text: Wehner, Sigrid: Exploring trends and patterns of nonresponse

```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 theorem“. 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).
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