Statistical Population

A Statistical Population is an entire set of items, events, subjects or measurements from which a sample can be drawn for a statistical experiment or random trial.

• AKA: Population.
• Context:
  • It is can be denoted as a sequence of all [math]\displaystyle{ N }[/math]possible outcomes [math]\displaystyle{ \{X_1,X_2, \cdots, X_N\} }[/math] of the random variable [math]\displaystyle{ X }[/math].
  • It can be sampled to create a Population Sample.
  • It can be composed of Population Subsets, such as an observed population and an unobserved population.
  • It can (typically) have a Population Parameter.
  • It can range from being a Finite Population to being a Infinite Population.
• Example(s):
  • Population 1: All the planetary systems in the Universe.
  • Population 2: All college students in the USA.
  • A Labor Population, for labor statistics.
  • …
• Counter-Example(s):
  • a Random Sample.
  • A Random Sample drawn from Populaton 1: planetary systems detected by the space observatory Kepler.
  • A Random Sample drawn from Population 2: A group of selected college students in the USA.
• See: Probability Space, Random Experiment Sample Space, Overdispersion, Selection Bias.

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References

2016

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/statistical_population Retrieved:2015-2-23.
  • 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.

• (Stat Trek, 2016) ⇒ "Populations and Samples", © 2011, Encyclopedia of Mathematics] Retrieved October 11, 2016, from http://stattrek.com/sampling/populations-and-samples.aspx
  • QUOTE: The main difference between a population and sample has to do with how observations are assigned to the data set. A population includes all of the elements from a set of data. A sample consists of one or more observations from the population.

Depending on the sampling method, a sample can have fewer observations than the population, the same number of observations, or more observations. More than one sample can be derived from the same population.

Other differences have to do with nomenclature, notation, and computations. For example, a measurable characteristic of a population, such as a mean or standard deviation, is called a parameter; but a measurable characteristic of a sample is called a statistic.

• (Minitab, 2016) ⇒ http://support.minitab.com/en-us/minitab/17/topic-library/basic-statistics-and-graphs/introductory-concepts/basic-concepts/sample-and-population/
  • QUOTE: A sample is a subset of people, items, or events from a larger population that you collect and analyze to make inferences. To represent the population well, a sample should be randomly collected and adequately large.

To understand the basic foundation for hypothesis testing and other types of inferential statistics, it’s important to understand how a sample and a population differ.

A population is a collection of people, items, or events about which you want to make inferences. It is not always convenient or possible to examine every member of an entire population. For example, it is not practical to count the bruises on all apples picked at an orchard. It is possible, however, to count the bruises on a set of apples taken from that population. This subset of the population is called a sample.

If the sample is random and large enough, you can use the information collected from the sample to make inferences about the population. For example, you could count the number of apples with bruises in a random sample and then use a hypothesis test to estimate the percentage of all the apples that have bruises.

• (StatGuide,2016) ⇒ Statistical Analysis Glossary: http://www.quality-control-plan.com/StatGuide/sg_glos.htm
  • QUOTE: The population is the universe of all the objects from which a sample could be drawn for an experiment. If a representative random sample is chosen, the results of the experiment should be generalizable to the population from which the sample was drawn, but not necessarily to a larger population. For example, the results of medical studies on males may not be generalizable for females.

2006

• (Dubnicka, 2006k) ⇒ Suzanne R. Dubnicka. (2006). “Introduction to Statistics - Handout 11." Kansas State University, Introduction to Probability and Statistics I, STAT 510 - Fall 2006.
  • QUOTE: The population is the set of all possible subjects (individuals or objects) of interest. A sample is a subset of the population which are actually observed or measured. Ideally, we would like to use the sample to draw conclusions about the entire population; this is known as inference or statistical inference. In order to draw valid conclusions about the population of interest from the sample, the sample must be representative of the population. One way to guarantee this is to take a random sample from the population (more specifically, a simple random sample). A Simple Random Sample|simple random sample guarantees that each subject in a population has an equal chance of being selected.

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