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((short description|Statistical data type))
((More citations needed|date=August 2009))
((distinguish|Count key data))
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))

==Count variables==
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.

==Graphical examination==
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.

==Relating count data to other variables==
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.

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.

==See also==
* [[Index of dispersion]]
* [[Empirical distribution function]]
* [[Frequency distribution]]

==Further reading==
((No footnotes|date=November 2009))
* ((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 ))
* ((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 ))
* ((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 ))

((DEFAULTSORT:Count Data))
[[Category:Statistical data types]]
[[Category:Countable quantities]]
[[Category:Units of amount]]

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