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<title>Count data</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Count data</span></span>

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</style><div role="note" class="hatnote navigation-not-searchable">Not to be confused with <a href="Count_key_data" title="Count key data">Count key data</a>.</div>

<p>In <a href="Statistics" title="Statistics">statistics</a>, <b>count data</b> is a <a href="Statistical_data_type" title="Statistical data type">statistical data type</a> describing <i><a href="Countable_quantity" class="mw-redirect" title="Countable quantity">countable quantities</a></i>, <a href="Data" title="Data">data</a> which can take only the <i><a href="Counting_number" class="mw-redirect" title="Counting number">counting numbers</a></i>, non-negative <a href="Integer" title="Integer">integer</a> values {0, 1, 2, 3, ...}, and where these integers arise from <i><a href="Counting" title="Counting">counting</a></i> rather than <a href="Ranking" title="Ranking">ranking</a>. The statistical treatment of count data is distinct from that of <a href="Binary_data" title="Binary data">binary data</a>, in which the observations can take only two values, usually represented by 0 and 1, and from <a href="Ordinal_data" title="Ordinal data">ordinal data</a>, which may also consist of integers but where the individual values fall on an arbitrary scale and only the relative ranking is important.

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<div class="mw-heading mw-heading2"><h2 id="Count_variables">Count variables</h2></div>

<p>An individual piece of count data is often termed a <b>count variable</b>. When such a variable is treated as a <a href="Random_variable" title="Random variable">random variable</a>, the <a href="Poisson_distribution" title="Poisson distribution">Poisson</a>, <a href="Binomial_distribution" title="Binomial distribution">binomial</a> and <a href="Negative_binomial_distribution" title="Negative binomial distribution">negative binomial</a> distributions are commonly used to represent its distribution.

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<div class="mw-heading mw-heading2"><h2 id="Graphical_examination">Graphical examination</h2></div>

<p>Graphical examination of count data may be aided by the use of <a href="Data_transformation_(statistics)" title="Data transformation (statistics)">data transformations</a> chosen to have the property of stabilising the sample variance. In particular, the <a href="Square_root" title="Square root">square root</a> transformation might be used when data can be approximated by a <a href="Poisson_distribution" title="Poisson distribution">Poisson distribution</a> (although other transformation have modestly improved properties), while an inverse sine transformation is available when a <a href="Binomial_distribution" title="Binomial distribution">binomial distribution</a> is preferred.

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<div class="mw-heading mw-heading2"><h2 id="Relating_count_data_to_other_variables">Relating count data to other variables</h2></div>

<p>Here the count variable would be treated as a <a href="Dependent_variable" class="mw-redirect" title="Dependent variable">dependent variable</a>. Statistical methods such as <a href="Least_squares" title="Least squares">least squares</a> and <a href="Analysis_of_variance" title="Analysis of variance">analysis of variance</a> are designed to deal with continuous dependent variables. These can be adapted to deal with count data by using <a href="Data_transformation_(statistics)" title="Data transformation (statistics)">data transformations</a> such as the <a href="Square_root" title="Square root">square root</a> transformation, but such methods have several drawbacks; they are approximate at best and estimate <a href="Parameter" title="Parameter">parameters</a> that are often hard to interpret.

</p><p>The <a href="Poisson_distribution" title="Poisson distribution">Poisson distribution</a> can form the basis for some analyses of count data and in this case <a href="Poisson_regression" title="Poisson regression">Poisson regression</a> may be used. This is a special case of the class of <a href="Generalized_linear_model" title="Generalized linear model">generalized linear models</a> which also contains specific forms of model capable of using the <a href="Binomial_distribution" title="Binomial distribution">binomial distribution</a> (<a href="Binomial_regression" title="Binomial regression">binomial regression</a>, <a href="Logistic_regression" title="Logistic regression">logistic regression</a>) or the <a href="Negative_binomial_distribution" title="Negative binomial distribution">negative binomial distribution</a> where the assumptions of the Poisson model are violated, in particular when the range of count values is limited or when <a href="Overdispersion" title="Overdispersion">overdispersion</a> is present.

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<ul><li><a href="Index_of_dispersion" title="Index of dispersion">Index of dispersion</a></li>

<li><a href="Empirical_distribution_function" title="Empirical distribution function">Empirical distribution function</a></li>

<li><a href="Frequency_distribution" class="mw-redirect" title="Frequency distribution">Frequency distribution</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>

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</style><cite id="CITEREFCameronTrivedi2013" class="citation book cs1"><a href="A._Colin_Cameron" title="A. Colin Cameron">Cameron, A. C.</a>; Trivedi, P. K. (2013). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=qVEwBQAAQBAJ"><i>Regression Analysis of Count Data Book</i></a> (Second ed.). Cambridge University Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-107-66727-3</bdi>.</cite></li>

<li><cite id="CITEREFHilbe2011" class="citation book cs1"><a href="Joseph_Hilbe" title="Joseph Hilbe">Hilbe, Joseph M.</a> (2011). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=0Q_ijxOEBjMC"><i>Negative Binomial Regression</i></a> (Second ed.). Cambridge University Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-521-19815-8</bdi>.</cite></li>

<li><cite id="CITEREFWinkelmann2008" class="citation book cs1">Winkelmann, Rainer (2008). <i>Econometric Analysis of Count Data</i> (Fifth ed.). Springer. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-540-78389-3">10.1007/978-3-540-78389-3</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-540-77648-2</bdi>.</cite></li>

<li>Transition models for count data: a flexible alternative to fixed distribution models <a rel="nofollow" class="external free" href="https://link.springer.com/article/10.1007/s10260-021-00558-6">https://link.springer.com/article/10.1007/s10260-021-00558-6</a></li></ul></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2025-04-15" href="https://en.wikipedia.org/wiki/?title=Count_data&oldid=1285789772">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

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