Statistical parameter: Difference between revisions

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{{Short description|Quantity that indexes a parametrized family of probability distributions}}

{{Other uses|Parameter (disambiguation)}}

{{redirect|True value|the company|True Value|the logical value|Truth value}}In [[statistics]], as opposed to its general [[parameter|use in mathematics]], a '''parameter''' is any measured quantity of a [[statistical population]] that summarisessummarizes or describes an aspect of the population, such as a [[mean]] or a [[standard deviation]]. If a population exactly follows a known and defined distribution, for example the [[normal distribution]], then a small set of parameters can be measured which completelyprovide describesa comprehensive description of the population, and can be considered to define a [[probability distribution]] for the purposes of extracting [[Sample (statistics)|sample]]s from this population.

{{redirect|True value|the company|True Value|the logical value|Truth value}}

[[File:World population distribution.svg|thumb|World population distribution]]

A "parameter" is to a [[statistical population|population]] as a "[[statistic]]" is to a [[statistical sample|sample]]; that is to say, a parameter describes the '''true value''' calculated from the full population (such as the [[population mean]]), whereas a statistic is an estimated measurement of the parameter based on a subsamplesample (such as the [[sample mean]], which is the mean of gathered data per sampling, called sample). Thus a "statistical parameter" can be more specifically referred to as a '''population parameter'''.<ref name="ESS06">{{citation| title= Parameter | encyclopedia= [[Encyclopedia of Statistical Sciences]] | editor1-first= S. | editor1-last= Kotz | editor1-link= Samuel Kotz |display-editors=etal | year= 2006 | publisher= [[Wiley (publisher)|Wiley]]}}.</ref><ref>Everitt, B. S.; Skrondal, A. (2010), ''The Cambridge Dictionary of Statistics'', [[Cambridge University Press]].</ref>

In [[statistics]], as opposed to its general [[parameter|use in mathematics]], a '''parameter''' is any measured quantity of a [[statistical population]] that summarises or describes an aspect of the population, such as a [[mean]] or a [[standard deviation]]. If a population exactly follows a known and defined distribution, for example the [[normal distribution]], then a small set of parameters can be measured which completely describes the population, and can be considered to define a [[probability distribution]] for the purposes of extracting [[Sample (statistics)|sample]]s from this population.

A parameter is to a [[statistical population|population]] as a [[statistic]] is to a [[statistical sample|sample]]; that is to say, a parameter describes the '''true value''' calculated from the full population, whereas a statistic is an estimated measurement of the parameter based on a subsample. Thus a "statistical parameter" can be more specifically referred to as a '''population parameter'''.<ref name="ESS06">{{citation| title= Parameter | encyclopedia= [[Encyclopedia of Statistical Sciences]] | editor1-first= S. | editor1-last= Kotz | editor1-link= Samuel Kotz |display-editors=etal | year= 2006 | publisher= [[Wiley (publisher)|Wiley]]}}.</ref><ref>Everitt, B. S.; Skrondal, A. (2010), ''The Cambridge Dictionary of Statistics'', [[Cambridge University Press]].</ref>

==Discussion==

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==Examples==

During an election, there may be specific percentages of voters in a country who would vote for each particular candidate – these percentages would be statistical parameters. It is impractical to ask every voter before an election occurs what their candidate preferences are, so a sample of voters will be polled, and a statistic (also called an [[estimator]]) – that is, the percentage of the subsamplesample of polled voters – will be measured instead. The statistic, along with an estimation of its accuracy (known as its [[sampling error]]), is then used to make inferences about the true statistical parameters (the percentages of all voters).

Similarly, in some forms of testing of manufactured products, rather than destructively testing all products, only a sample of products are tested. Such tests gather statistics supporting an inference that the products meet specifications.