http://debianws.lexgopc.com/wiki143/index.php?action=history&feed=atom&title=Count_dataCount data - Revision history2026-05-04T21:01:57ZRevision history for this page on the wikiMediaWiki 1.43.1http://debianws.lexgopc.com/wiki143/index.php?title=Count_data&diff=6243931&oldid=previmported>Biggerj1 at 20:12, 15 April 20252025-04-15T20:12:02Z<p></p>
<p><b>New page</b></p><div>{{short description|Statistical data type}}<br />
{{More citations needed|date=August 2009}}<br />
{{distinguish|Count key data}}<br />
In [[statistics]], '''count data''' is a [[statistical data type]] describing ''[[countable quantity|countable quantities]]'', [[data]] which can take only the ''[[counting number]]s'', non-negative [[integer]] values {0, 1, 2, 3, ...}, and where these integers arise from ''[[counting]]'' rather than [[ranking]]. The statistical treatment of count data is distinct from that of [[binary data]], in which the observations can take only two values, usually represented by 0 and 1, and from [[ordinal data]], which may also consist of integers but where the individual values fall on an arbitrary scale and only the relative ranking is important.{{examples|date=September 2022}}<br />
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==Count variables==<br />
An individual piece of count data is often termed a '''count variable'''. When such a variable is treated as a [[random variable]], the [[Poisson distribution|Poisson]], [[binomial distribution|binomial]] and [[negative binomial distribution|negative binomial]] distributions are commonly used to represent its distribution.<br />
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==Graphical examination==<br />
Graphical examination of count data may be aided by the use of [[data transformation (statistics)|data transformation]]s chosen to have the property of stabilising the sample variance. In particular, the [[square root]] transformation might be used when data can be approximated by a [[Poisson distribution]] (although other transformation have modestly improved properties), while an inverse sine transformation is available when a [[binomial distribution]] is preferred.<br />
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==Relating count data to other variables==<br />
Here the count variable would be treated as a [[dependent variable]]. Statistical methods such as [[least squares]] and [[analysis of variance]] are designed to deal with continuous dependent variables. These can be adapted to deal with count data by using [[data transformation (statistics)|data transformation]]s such as the [[square root]] transformation, but such methods have several drawbacks; they are approximate at best and estimate [[parameter]]s that are often hard to interpret.<br />
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The [[Poisson distribution]] can form the basis for some analyses of count data and in this case [[Poisson regression]] may be used. This is a special case of the class of [[generalized linear model]]s which also contains specific forms of model capable of using the [[binomial distribution]] ([[binomial regression]], [[logistic regression]]) or the [[negative binomial distribution]] where the assumptions of the Poisson model are violated, in particular when the range of count values is limited or when [[overdispersion]] is present.<br />
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==See also==<br />
* [[Index of dispersion]]<br />
* [[Empirical distribution function]]<br />
* [[Frequency distribution]]<br />
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==Further reading==<br />
{{No footnotes|date=November 2009}}<br />
* {{cite book |last=Cameron |first=A. C. |author-link=A. Colin Cameron |first2=P. K. |last2=Trivedi |title=Regression Analysis of Count Data Book |publisher=Cambridge University Press |edition=Second |year=2013 |isbn=978-1-107-66727-3 |url=https://books.google.com/books?id=qVEwBQAAQBAJ }}<br />
* {{cite book |last=Hilbe |first=Joseph M. |authorlink=Joseph Hilbe|year=2011 |title=Negative Binomial Regression |edition=Second |publisher=Cambridge University Press |isbn=978-0-521-19815-8 |url=https://books.google.com/books?id=0Q_ijxOEBjMC }}<br />
* {{cite book |title=Econometric Analysis of Count Data |first=Rainer |last=Winkelmann | publisher=Springer |edition=Fifth |year=2008 |isbn=978-3-540-77648-2 |doi=10.1007/978-3-540-78389-3 }}<br />
* Transition models for count data: a flexible alternative to fixed distribution models https://link.springer.com/article/10.1007/s10260-021-00558-6<br />
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{{DEFAULTSORT:Count Data}}<br />
[[Category:Statistical data types]]<br />
[[Category:Countable quantities]]<br />
[[Category:Units of amount]]</div>imported>Biggerj1