Statistical population

In statistics, a population is a set of similar items or events which is of interest for some question or experiment. A statistical population can be a group of actually existing objects (e.g. the set of all stars within the Milky Way galaxy) or a hypothetical and potentially infinite group of objects conceived as a generalization from experience (e.g. the set of all possible hands in a game of poker). A common aim of statistical analysis is to produce information about some chosen population.

In statistical inference, a subset of the population (a statistical sample) is chosen to represent the population in a statistical analysis. If a sample is chosen properly, characteristics of the entire population that the sample is drawn from can be estimated from corresponding characteristics of the sample.

A subset of a population that shares one or more additional properties is called a subpopulation. 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. By contrast, a sample is a subset of a population that is not chosen to share any additional property.

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.

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