# sample

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 .

## etymology

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.

## Selection process

A random sample of a car is subjected to a drug search. One speaks of a random sample if z. B. every tenth car is checked and it is assumed that the cars come in a random order. A systematic selection would be to check all red vehicles. It would be an arbitrary selection if the officer selects vehicles without criteria.

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.

### Random selection

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 ) .

Strictly speaking, the methods of inductive statistics can only be used for random selections . The type of sampling has an influence on the informative value.

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

In opinion polls, for example, respondents are selected using the random route method and the Sweden key. Another option is the RLD procedure .

### Conscious choice

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 ).

### Arbitrary selection

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 ).