# Population

The population (also population , statistical mass , collective or total scope of survey ) is a term used in statistics and is described by it. The population is the set of all objects about which a statement is to be made. Universes are often only incompletely recorded and only roughly described, for example through a partial survey in the descriptive statistics, or a random survey using stochastics .

## definition

In statistics , the population denotes the set of all statistical units (also feature carriers , investigation unit , survey unit ) with matching identification criteria (factual, spatial and temporal). The statistical unit is the carrier of the information for the statistical investigation. Statistical units can be natural units (people, animals, plants, workpieces), but also artificial units, for example socio-economic units (families, households, companies) or events.

“A population can contain a finite or an infinite number of elements. Theoretical populations are often ( uncountable ) infinite, such as B. with continuous random variables. Real populations are mostly very large, but always finite. ”Accordingly, a distinction is also made between finite populations and infinite populations . One also speaks of a closed population and an open population . "The finite population is referred to as closed, the infinite as an open."

## Collection and survey of populations

### Complete coverage of populations

The complete recording of populations is possible using descriptive statistics . It is also known as full survey or census designated, the term survey is misleading in this case because it from empiricism originated.

An example of a fully comprehensible population are all persons (statistical units) who are registered with their main residence (material identification) in Berlin (local identification) on January 1, 2009 (temporal identification). Depending on how the population is narrowed down using a time criterion, one speaks either of existing masses or movement masses :

Stock
We speak of a stock when the stock of feature carriers is determined at a fixed point in time. This is useful for feature carriers with a certain retention period ("e.g. the inventory of a company on December 31, 2006").
Movement mass
We speak of a movement mass when the elements are events, the amount of which is limited by specifying a certain period of time (“e.g. the number of births in a city in 2006”).

Also opinion polls can completely map populations in circumstances. This is possible if all statistical units are actually questioned, for example an opinion poll in a sports club, which is only intended to represent the opinion of this one sports club (and not, for example, inferring the opinion of other sports clubs from this). Examples of the complete coverage of large populations are population censuses , as well as the counting of votes in national elections .

Universes are often very large and can only be recorded with great effort or not at all. If full coverage is not achieved using descriptive statistics, this is called a partial survey .

### Survey using stochastics

Methods of stochastics , in particular mathematical statistics , are used to at least approximately describe populations that have not been fully recorded . On the basis of data collection from a sample that is assumed to be representative of the population , inferences are made about the actual population being sought. This is in the empirical research, among other things as a population or target population ( English target population hereinafter).

For example, in electoral research, the entire population entitled to vote is not asked about their party preference, but a sample is collected that reflects the conditions in the population in terms of their characteristics (age, gender, residence, etc.). The data collected through random sampling are extrapolated to the population using statistical methods and thus result in an election prognosis . In this case, the population is defined as the number of people who will vote for a specific party (identification feature) on a specific election date. In this case, however, the entire population is also fully recorded by counting all the votes cast after the actual election. This example also shows that the empirical description of populations is not always independent of the actual population: just collecting election prognoses can influence voting behavior and thus the actual populations. The effect is difficult to characterize and is therefore considered undesirable in democratic elections. It is avoided as much as possible by, for example, not publishing election forecasts while voting.

The defined target population (e.g. all Germans over the age of 18) is often not identical with the actual population from which the sample is drawn, for example for an election survey. This is because some elements of the population have no or a smaller chance of getting into the sample than others. This includes people in institutions (e.g. student dormitories , penal institutions, barracks), mobile people such as inland waterwaymen, but also some homeless people ( undercoverage ). In practice, the conclusion of the sample about the target population is made more difficult by nonresponse (also referred to as dropout). This is understood to mean the non-response to a survey by elements of the population that have already entered the sample.

## Individual evidence

1. a b Georg Bol: Descriptive Statistics: Textbook and Workbook . 6th edition. Oldenbourg Wissenschaftsverlag, Munich 2004, ISBN 3-486-57612-7 , p. 9–15 ( limited preview in Google Book Search).
2. Manfred Kühlmeyer: Statistical evaluation methods for engineers . Springer , 2001, ISBN 3-540-41097-X ( online [accessed September 13, 2012]).
3. ^ Göran Kauermann, Helmut Küchenhoff: Samples. Methods and practice with R . 1st edition. Springer, Berlin Heidelberg 2011, ISBN 978-3-642-12317-7 , pp. 5 ( limited preview in Google Book search).
4. Peter Pflaumer, Joachim Hartung, Barbara Heine: Statistics for economics and social sciences. Descriptive statistics . 3. Edition. Oldenbourg Wissenschaftsverlag, Munich 2005, ISBN 978-3-486-57779-2 , p. 13 ( limited preview in Google Book search).
5. ^ Peter P. Eckstein: Repetitorium Statistics . 6th edition. Gabler, 2006, p. 4 .
6. Horst Rinne: Pocket book of statistics . 4th edition. Scientific publishing house Harri Deutsch, Munich 2008, ISBN 978-3-8171-1827-4 , pp. 11 ( limited preview in Google Book search).
7. ^ Walter Assenmacher: Inductive statistics . 1st edition. Springer, Berlin 2000, ISBN 978-3-540-67145-9 , pp. 185 ( limited preview in Google Book search).
8. ^ Lothar Sachs , Jürgen Hedderich: Applied statistics . 12th edition. Springer, Berlin 2006, ISBN 978-3-540-32160-6 , pp.  12 ( limited preview in Google Book search).
9. ^ Käthe Schneider: The participation and non-participation of adults in further training. Theory-like statement to explain the initiation of action . 12th edition. Klinkhardt, Bad Heilbrunn 2004, ISBN 978-3-7815-1338-9 , pp. 51 ( limited preview in Google Book search).
10. Karl Bosch: Basic Knowledge of Statistics: Introduction to the basics of statistics with numerous examples, exercises and solutions . Oldenbourg Wissenschaftsverlag, Munich 2007, ISBN 978-3-486-58253-6 , p. 6 ( limited preview in Google Book search).
11. ^ Peter Pflaumer, Joachim Hartung, Barbara Heine: Statistics for economics and social sciences. Descriptive statistics . 3. Edition. Oldenbourg Wissenschaftsverlag, Munich 2005, ISBN 978-3-486-57779-2 , p. 11 ( limited preview in Google Book search).
12. Rainer Schnell: On the factual population in “general population surveys”: undercoverage, those who are difficult to reach and those who cannot be questioned . In: Cologne journal for sociology and social psychology . tape 43 . Oldenbourg Wissenschaftsverlag, Munich 1991, p. 106-137 .