A sample is a subset of a population that has been selected under certain criteria. Typically, the sample is subjected to examinations or surveys , the results of which should say something about the population from which the sample was taken.
A sample survey (partial survey) as an alternative to the full survey is used if the investigation of all individuals or objects in a population is not practical. This is the case with very large populations and / or when the sample elements are rendered unusable by the investigation (e.g. in quality analyzes). If the sample is to be representative of its population, the selection process used must meet certain conditions. The random sample is of particular importance here .
The word random sample originally comes from iron smelting and referred to the tapping at the blast furnace to take a sample of the liquid metal. But there were also random checks on sacks of grain . To take a grain sample , a cone-shaped probe was pushed ( pricked ) into the unopened jute sack and a sample was taken without damaging the sack.
A selection process is the way in which the elements of the sample are selected as appropriately as possible. There are different selection procedures, which are described below.
A random sample is necessary if the sample is to be representative , i.e. H. if it is intended to draw conclusions about the population based on the induction principle (see also extrapolation ). Random samples are often used in statistical applications (e.g. in scientific , medical and psychological research, in quality controls or in market research ), since it is often not possible to examine the population (e.g. the entire population or all specimens of a certain product ) .
With a random selection (also called probability selection or random sample), each element of the population has a definable (usually the same) probability of being included in the sample ( inclusion probability ). The combinatorics can give clues for sensible selection methods.
In empirical research , a distinction is made between several random sampling methods, for example
- single-stage and multi-stage procedures (grading)
- stratified random sample (stratification)
- Cluster sample (clustering)
In a systematic sampling , known information about the cases to be selected is used. The selection is made on the basis of lists and defined rules. Mathematical-statistical models, such as the calculation of the inclusion probability, cannot be used with conscious choices. Systematic selection processes occur in the commercial sector, for example, when representativeness is not important. (see also quota sample ).
In the case of random samples , elements from the population (e.g. from an interviewer ) are included in the sample more or less at random. The choice is at the discretion of the interviewer - or the test person ( self-selection ).
- Recovery method
- Design effect
- Importance sampling
- Spot checks for consumption meters
- Theoretical sampling
- Josef Bleymüller, Günther Gehlert, Herbert Gülicher (2002): Statistics for economists. 14th edition. Munich, ISBN 3-8006-3115-6 (Chapters 12 and 13)
- Elisabeth Noelle-Neumann , Thomas Petersen (1996): All, not everyone . Munich
- Hoffmeyer-Zlotnik, Jürgen HP: Sampling in Survey Practice - The different results of random samples in face-to-face surveys. Faulbaum, F .; Wolf, C (2006): 19-36.
- Peter Atteslander : Methods of Empirical Social Research . 2003, ISBN 3-11-017817-6 , pp. 305 ( limited preview in Google Book Search).
- Jürgen Raithel: Quantitative Research: A Practical Course . 2., through Edition. VS Verlag für Sozialwissenschaften , Wiesbaden 2008, ISBN 978-3-531-16181-5 , p. 56 ( limited preview in Google Book search).
- Literature on the subject of sampling in the catalog of the German National Library
- Sample and population
- Page no longer available , search in web archives: Handout Statistics Lecture, WU Vienna, 2003 (PDF, 424 KiB) ) (