# Sample (statistics)

As a sample is called a subset of a population that has been selected from a particular point.

The word sample is originally from the iron smelting and described the tapping of the blast furnace for taking a sample of the liquid metal. But even with sacks of grain, there were samples. To collect a sample of grain was a cone-shaped probe inserted into the non- open jute bag ( pin ), and thus a sample is taken, without the bag was damaged.

## Selection

A selection process is the way how the elements of the sample are selected appropriately as possible. There are various selection procedures are described below.

### Random selection

A random sample is necessary if the sample is to be representative, that is, if is to be closed by the induction principle to the population of her ( see also extrapolation ). With random sampling is carried out frequently in applications of statistics ( such as in the scientific, medical and psychological research, quality control, or market research ), because it is not often possible to the population (such as the total population, or all instances of a particular product ) to investigate.

Only with random selections are strictly the methods of inductive statistics applicable. The type of sampling affects the explanatory power.

(Also called selection probability or random sample ) In a random sample, each member of the population a specifiable (usually the same ) probability to reach the sample ( inclusion probability ). The combinatorics can provide clues for rational selection methods.

In the empirical multiple random sampling can be distinguished, for example,

- Single-stage and multi-stage process (steps )
- Stratified random sample ( stratification )
- Lump - sample ( clumping )

In the opinion of the research respondents are selected, for example with the random route method and the Swede key. A further possibility is the RLD process.

### Conscious selection

In a systematic sampling known information about the cases to be selected already be used. The selection is made on the basis of lists and established rules. Mathematical and statistical models, such as the calculation of the inclusion probability, are not applicable to conscious choices. Systematic selection procedure as before in the commercial sector, if it does not arrive on representativeness.

### Arbitrary selection

For arbitrary sample elements from the population to be included in the sample ( approximately by an interviewer ) more or less arbitrary. The selection is at the discretion of the interviewer - or even the subjects ( self-selection ).