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Instatistics,count data is astatistical data type describingcountable quantities,data which can take only thecounting numbers, non-negativeinteger values {0, 1, 2, 3, ...}, and where these integers arise fromcounting rather thanranking. The statistical treatment of count data is distinct from that ofbinary data, in which the observations can take only two values, usually represented by 0 and 1, and fromordinal data, which may also consist of integers but where the individual values fall on an arbitrary scale and only the relative ranking is important.^{[example needed]}

An individual piece of count data is often termed acount variable. When such a variable is treated as arandom variable, thePoisson,binomial andnegative binomial distributions are commonly used to represent its distribution.

Graphical examination of count data may be aided by the use ofdata transformations chosen to have the property of stabilising the sample variance. In particular, thesquare root transformation might be used when data can be approximated by aPoisson distribution (although other transformation have modestly improved properties), while an inverse sine transformation is available when abinomial distribution is preferred.

Here the count variable would be treated as adependent variable. Statistical methods such asleast squares andanalysis of variance are designed to deal with continuous dependent variables. These can be adapted to deal with count data by usingdata transformations such as thesquare root transformation, but such methods have several drawbacks; they are approximate at best and estimateparameters that are often hard to interpret.

ThePoisson distribution can form the basis for some analyses of count data and in this casePoisson regression may be used. This is a special case of the class ofgeneralized linear models which also contains specific forms of model capable of using thebinomial distribution (binomial regression,logistic regression) or thenegative binomial distribution where the assumptions of the Poisson model are violated, in particular when the range of count values is limited or whenoverdispersion is present.

• Index of dispersion
• Empirical distribution function
• Frequency distribution

This article includes alist of references,related reading, orexternal links,but its sources remain unclear because it lacksinline citations. Please helpimprove this article byintroducing more precise citations.(November 2009) (Learn how and when to remove this message)

• Cameron, A. C.; Trivedi, P. K. (2013).Regression Analysis of Count Data Book (Second ed.). Cambridge University Press.ISBN 978-1-107-66727-3.
• Hilbe, Joseph M. (2011).Negative Binomial Regression (Second ed.). Cambridge University Press.ISBN 978-0-521-19815-8.
• Winkelmann, Rainer (2008).Econometric Analysis of Count Data (Fifth ed.). Springer.doi:10.1007/978-3-540-78389-3.ISBN 978-3-540-77648-2.

• Statistical data types
• Countable quantities
• Units of amount

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