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{{StatsPsy}}
 
{{StatsPsy}}
   
A '''statistic''' (singular) is the result of applying a statistical [[algorithm]] to a [[Data set|set of data]]. In the calculation of the [[arithmetic mean]], for example, the algorithm directs us to sum all the [[data]] values and divide by the number of data items. In this case, we call the mean a statistic. To be complete in describing any use of a statistic, one must describe both the procedure and the data set.
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A '''statistic''' (singular) is the result of applying a [[function (mathematics)|function]] (statistical [[algorithm]]) to a [[Data set|set of data]].
   
The popular use of the term to mean a single measurement, or ''[[datum]]'', differs from this meaning. A statistician would normally call an individual person's height a statistic only if that person were chosen randomly from some population of interest, but more often would use the term to refer to, for example, the [[median]] height of a group of people.
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More formally, statistical theory defines a '''statistic''' as a function of a [[sample (statistics)|sample]] where the function itself is independent of the sample's distribution.
   
Often the concept is defined by saying that a statistic is an ''observable'' [[random variable]]. Statisticians often contemplate a parametrized family of [[probability distribution]]s, any member of which could be the distribution of some measurable aspect of each member of a [[statistical population]] from which a sample is drawn randomly. The value of the parameter is ''not observable'', since it depends on the whole population rather than on the sample. 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). The ''difference'' between that observable sample average and the unobservable population average is an example of a random variable that is not a statistic; the reason it is ''random'' is that the sample was chosen randomly.
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==Examples==
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In the calculation of the [[arithmetic mean]], for example, the algorithm consists of summing all the [[data]] values and dividing this sum by the number of data items. Thus the arithmetic mean is a statistic.
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Other examples of statistics include
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* [[sample median]]
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* [[Sample variance]] and sample [[standard deviation]]
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* Sample [[quantile]]s besides the [[median]], e.g., [[quartile]]s and [[percentile]]s
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* [[t statistic]]s, [[chi-square statistic]]s
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* [[Order statistic]]s
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* [[p-value]]s
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* Sample [[moment (mathematics)|moments]], including [[Kurtosis]] and [[skewness]]
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* Various [[Functional (mathematics)|functionals]] of the [[empirical distribution function]]
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==Usage note==
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Strictly speaking, the popular use of "'''statistic'''" to mean a single measurement, or ''[[datum]]'', is correct, as the function used can be deemed the [[identity function]]. In practice however, a statistician would usually not call an individual such measurement a statistic and rather would use the term to refer to, for example, the [[mean]] of several such measurements.
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==Properties==
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===Observability===
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A '''statistic''' is an ''observable'' [[random variable]], which differentiates it from a ''parameter'', an unobservable quantity describing a property of a [[statistical population]].
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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. The average height of ''all'' (in the sense of ''genetically possible'') 25-year-old North American men is a ''parameter'' and not a '''statistic'''.
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===Statistical properties===
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Important potential properties of statistics are [[completeness (statistics)|completeness]], [[sufficiency (statistics)|sufficiency]] and [[estimator bias|unbiased]]ness.
   
 
==See also==
 
==See also==
 
*[[Statistics]]
 
*[[Statistics]]
 
*[[Statistical theory]]
 
*[[Statistical theory]]
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*[[Descriptive statistics]]
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[[Category:Statistical theory]]
   
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{{enWP|Statistic}}

Latest revision as of 15:47, May 15, 2007

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A statistic (singular) is the result of applying a function (statistical algorithm) to a set of data.

More formally, statistical theory defines a statistic as a function of a sample where the function itself is independent of the sample's distribution.

ExamplesEdit

In the calculation of the arithmetic mean, for example, the algorithm consists of summing all the data values and dividing this sum by the number of data items. Thus the arithmetic mean is a statistic.

Other examples of statistics include

Usage noteEdit

Strictly speaking, the popular use of "statistic" to mean a single measurement, or datum, is correct, as the function used can be deemed the identity function. In practice however, a statistician would usually not call an individual such measurement a statistic and rather would use the term to refer to, for example, the mean of several such measurements.

PropertiesEdit

ObservabilityEdit

A statistic is an observable random variable, which differentiates it from a parameter, an unobservable quantity describing a property of a statistical population.

Statisticians often contemplate a parameterized family of probability distributions, 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. The average height of all (in the sense of genetically possible) 25-year-old North American men is a parameter and not a statistic.

Statistical propertiesEdit

Important potential properties of statistics are completeness, sufficiency and unbiasedness.

See alsoEdit

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