Editing Statistic

{{short description|Single measure of some attribute of a sample}}
{{other uses|Statistics (disambiguation)}}
A '''statistic''' (singular) or '''sample statistic''' is any quantity computed from values in a [[Sample (statistics)|sample]] which is considered for a statistical purpose. Statistical purposes include [[Estimation|estimating]] a [[Statistical population|population]] parameter, describing a sample, or evaluating a hypothesis. The [[Arithmetic mean|average (or mean)]] of sample values is a statistic. The term statistic is used both for the function (e.g., a calculation method of the average) and for the value of the function on a given sample (e.g., the result of the average calculation). When a statistic is being used for a specific purpose, it may be referred to by a name indicating its purpose.

When a statistic is used for estimating a population parameter, the statistic is called an ''[[estimator]]''. A population parameter is any characteristic of a population under study, but when it is not feasible to directly measure the value of a population parameter, statistical methods are used to infer the likely value of the parameter on the basis of a statistic computed from a sample taken from the population. For example, the [[sample mean]] is an [[Bias of an estimator|unbiased estimator]] of the [[population mean]]. This means that the [[expected value]] of the sample mean equals the true population mean.{{sfn|Kokoska|2015|p=296-308}}

A ''[[descriptive statistic]]'' is used to summarize the sample data. A ''[[test statistic]]'' is used in [[statistical hypothesis testing]]. A single statistic can be used for multiple purposes{{snd}}for example, the sample mean can be used to estimate the population mean, to describe a sample data set, or to test a hypothesis.

==Examples==
Some examples of statistics are:
* "In a recent survey of Americans, '''52%''' of women say global warming is happening."

In this case, "52%" is a statistic, namely the percentage of women in the survey sample who believe in global warming. The population is the [[Set (mathematics)|set]] of all women in the United States, and the population parameter being estimated is the percentage of ''all'' women in the United States, not just those surveyed, who believe in global warming.

* "The manager of a large hotel located near Disney World indicated that 20 selected guests had a mean length of stay equal to '''5.6''' days."

In this example, "5.6 days" is a statistic, namely the mean length of stay for our sample of 20 hotel guests. The population is the set of all guests of this hotel, and the population parameter being estimated is the mean length of stay for ''all'' guests.{{sfn|Kokoska|2015|p=296-297}} Whether the estimator is unbiased in this case depends upon the sample selection process; see [[Renewal theory#The inspection paradox|the inspection paradox]].

There are a variety of functions that are used to calculate statistics. Some include:
* [[Sample mean]], [[sample median]], and [[Mode (statistics)|sample mode]]
* [[Sample variance]] and sample [[standard deviation]]
* Sample [[quantile]]s besides the [[median]], e.g., [[quartile]]s and [[percentile]]s
* [[Test statistic]]s, such as [[t-statistic]], [[chi-squared statistic]], [[F-test|f statistic]]
* [[Order statistic]]s, including sample maximum and minimum
* Sample [[moment (mathematics)|moments]] and functions thereof, including [[kurtosis]] and [[skewness]]
* Various [[Functional (mathematics)|functionals]] of the [[empirical distribution function]]

==Properties==
===Observability===
Statisticians often contemplate a [[parameterized family]] of [[probability distribution]]s, any member of which could be the distribution of some measurable aspect of each member of a population, from which a sample is drawn randomly. For example, the parameter may be the average height of 25-year-old men in North America. The height of the members of a sample of 100 such men are measured; the average of those 100 numbers is a statistic. The average of the heights of all members of the population is not a statistic unless that has somehow also been ascertained (such as by measuring every member of the population). The average height that would be calculated using ''all'' of the individual heights of ''all'' 25-year-old North American men is a parameter, and not a statistic.

===Statistical properties===
Important potential properties of statistics include [[completeness (statistics)|completeness]], [[consistent estimator|consistency]], [[sufficiency (statistics)|sufficiency]], [[estimator bias|unbiased]]ness, [[minimum mean square error]], low [[variance]], [[Robust statistics|robustness]], and computational convenience.

===Information of a statistic===
Information of a statistic on model parameters can be defined in several ways. The most common is the [[Fisher information]], which is defined on the statistic model induced by the statistic. [[Kullback information]] measure can also be used.

==See also==
{{Wiktionary|statistic}}
* [[Statistics]]
* [[Statistical theory]]
* [[Descriptive statistics]]
* [[Statistical hypothesis testing]]
* [[Summary statistic]]
* [[Well-behaved statistic]]

==References==
{{reflist}}
{{refbegin}}
* {{cite book |last=Kokoska |first=Stephen |title=Introductory Statistics: A Problem-Solving Approach |edition=2nd |year=2015 |publisher=W. H. Freeman and Company |location=New York |isbn=978-1-4641-1169-3 }}
* Parker, Sybil P (editor in chief). "Statistic". McGraw-Hill Dictionary of Scientific and Technical Terms. Fifth Edition. McGraw-Hill, Inc. 1994. {{isbn|0-07-042333-4}}. Page 1912.
* DeGroot and Schervish. "Definition of a Statistic". Probability and Statistics. International Edition. Third Edition. Addison Wesley. 2002. {{isbn|0-321-20473-5}}. Pages 370 to 371.
{{refend}}

{{Statistics|inference}}

[[Category:Sample statistics|*]]