A set of homogeneous objects is often investigated with respect to any feature that characterizes them, measured quantitatively or qualitatively.
For example, if there is a batch of parts, then the quantitative attribute may be the size of the part according to GOST, and the qualitative one may be the standard part.
If necessary, their verification of compliance with standards sometimes resort to a continuous examination, but in practice this is extremely rare. For example, if the general population contains a huge number of studied objects, then it is almost impossible to conduct a continuous survey. In this case, a certain number of objects (elements) are selected from the entire population and they are examined. Thus, there is a general and selective population.
General is the totality of all objects that are examined or studied. The general population, as a rule, contains a finite number of elements, but if it is too large, then in order to simplify mathematical calculations, it is assumed that the entire population consists of countless objects.
A sample or a sample population is a part of the selected elements from the entire population. The selection may be repeated or non-repeated. In the first case, it is returned to the general population, in the second - not. In practice, they often use repeated random selection.
The population and the sample must be linked by representativeness. Speaking differently, in order for the characteristics of the sample population to be able to confidently determine the characteristics of the entire population, it is necessary that the elements of the sample represent them as accurately as possible. In other words, the sample should be representative (representative).
A sample will be more or less representative if it is made randomly from a very large number of the entire population. This can be argued on the basis of the so-called law of large numbers. Moreover, all elements have an equal probability of falling into the sample.
Various selection options are available. All these methods can, in principle, be divided into two options:
- Option 1. Elements are selected when the population is not divided into parts. This option includes simple random repeated and non-repeated selections.
- Option 2. The general population is divided into parts and elements are selected. These include typical, mechanical and serial selections.
Simple random - selection, in which elements are retrieved one at a time from the entire population in a random manner.
Typical is a selection in which elements are not selected from the entire population, but from all its "typical" parts.
Mechanical is such a selection when the entire population is divided into the number of groups equal to the number of elements that should be in the sample, and, accordingly, one element is selected from each group. For example, if you need to select 25% of the parts manufactured by the machine, then every fourth part is selected, and if you want to select 4% of the parts, then every twenty-fifth part is selected and so on. It is necessary to say that sometimes mechanical selection may not provide sufficient representativeness of the sample.
Serial - this is such a selection in which elements are selected from the entire set of "series", subjected to continuous research, and not one at a time. For example, when parts are manufactured by a large number of automatic machines, a thorough examination is carried out only in relation to the products of several machines. Serial selection is used if the trait under investigation has insignificant variability in different series.
In order to reduce the error, mathematical and statistical methods are used to estimate the general population using a sample. Moreover, selective control can be either single-stage or multi-stage, which increases the reliability of the examination.