Statistical population

In statistics, a population is a complete set of items that share at least one property in common that is the subject of a statistical analysis.^[1] For example, the population of German people share a common geographic origin, language, literature, and genetic heritage, among other traits, that distinguish them from people of different nationalities. As another example, the Milky Way galaxy comprises a star population. In contrast, a statistical sample is a subset drawn from the population to represent the population in a statistical analysis.^[2] If a sample is chosen properly, characteristics of the entire population that the sample is drawn from can be inferred from corresponding characteristics of the sample.

Subpopulation

A subset of a population is called a subpopulation if they share one or more additional properties. For example, if the population is all Egyptian people, a subpopulation is all Egyptian males; if the population is all pharmacies in the world, a subpopulation is all pharmacies in Egypt.

In contrast, a subset of a population that does not require the sharing of any additional property is called a sample.

Descriptive statistics may yield different results for different subpopulations. For instance, a particular medicine may have different effects on different subpopulations, and these effects may be obscured or dismissed if such special subpopulations are not identified and examined in isolation.

Similarly, one can often estimate parameters more accurately if one separates out subpopulations: the distribution of heights among people is better modeled by considering men and women as separate subpopulations, for instance.

Populations consisting of subpopulations can be modeled by mixture models, which combine the distributions within subpopulations into an overall population distribution. Even if subpopulations are well-modeled by given simple models, the overall population may be poorly fit by a given simple model – poor fit may be evidence for existence of subpopulations. For example, given two equal subpopulations, both normally distributed, if they have the same standard deviation and different means, the overall distribution will exhibit low kurtosis relative to a single normal distribution – the means of the subpopulations fall on the shoulders of the overall distribution. If sufficiently separated, these form a bimodal distribution, otherwise it simply has a wide peak. Further, it will exhibit overdispersion relative to a single normal distribution with the given variation. Alternatively, given two subpopulations with the same mean and different standard deviations, the overall population will exhibit high kurtosis, with a sharper peak and heavier tails (and correspondingly shallower shoulders) than a single distribution.

See also

• Sample (statistics)
• Sampling (statistics)

References

External links

• Statistical Terms Made Simple