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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Nuisance variable</span></span>

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<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="en" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><p>In the theory of <a href="Stochastic_processes" class="mw-redirect" title="Stochastic processes">stochastic processes</a> in <a href="Probability_theory" title="Probability theory">probability theory</a> and <a href="Statistics" title="Statistics">statistics</a>, a <b>nuisance variable</b> is a <a href="Random_variable" title="Random variable">random variable</a> that is fundamental to the <a href="Probabilistic_model" class="mw-redirect" title="Probabilistic model">probabilistic model</a>, but that is of no particular interest in itself or is no longer of any interest: one such usage arises for the <a href="Chapman%E2%80%93Kolmogorov_equation" title="Chapman–Kolmogorov equation">Chapman–Kolmogorov equation</a>. For example, a model for a <a href="Stochastic_process" title="Stochastic process">stochastic process</a> may be defined conceptually using intermediate variables that are not observed in practice. If the problem is to derive the theoretical properties, such as the mean, variance and covariances of quantities that would be observed, then the intermediate variables are nuisance variables.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p><p>The related term <b>nuisance factor</b> has been used<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> in the context of <a href="Randomized_block_design" class="mw-redirect" title="Randomized block design">block experiments</a>, where the terms in the model representing block-means, often called "factors", are of no interest. Many approaches to the analysis of such experiments, particularly where the <a href="Experimental_design" class="mw-redirect" title="Experimental design">experimental design</a> is subject to randomization, treat these factors as random variables. More recently, "nuisance variable" has been used in the same context.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

</p><p>"Nuisance variable" has been used in the context of statistical surveys to refer information that is not of direct interest but which needs to be taken into account in an analysis.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>

</p><p>In the context of stochastic models, the treatment of nuisance variables does not necessarily involve working with the full joint distribution of all the random variables involved, although this is one approach. Instead, an analysis may proceed directly to the quantities of interest.

</p><p>The term <b>nuisance variable</b> is sometimes also used in more general contexts, simply to designate those variables that are marginalized over when finding a <a href="Marginal_distribution" title="Marginal distribution">marginal distribution</a>.

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<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFEddy2008" class="citation journal cs1"><a href="Sean_Eddy" title="Sean Eddy">Eddy, S. R.</a> (2008). Rost, Burkhard (ed.). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2396288">"A Probabilistic Model of Local Sequence Alignment That Simplifies Statistical Significance Estimation"</a>. <i>PLOS Computational Biology</i>. <b>4</b> (5): e1000069. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2008PLSCB...4E0069E">2008PLSCB...4E0069E</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1371%2Fjournal.pcbi.1000069">10.1371/journal.pcbi.1000069</a></span>. <a href="PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2396288">2396288</a></span>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/18516236">18516236</a>.</cite></span>

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<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">Kendall, M.G., Stuart, A. (1968) <i>The Advanced Theory of Statistics, Volume 3: Design and Analysis, and Time-Series</i>, Griffin. Section 38.14, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-85264-069-2</bdi></span>

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<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">Irving B. Weiner, Donald K. Freedheim, John A. Schinka (2003) <i>Handbook of Psychology: Volume 2</i>,

Wiley. (Chapter 1, page 3) <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-471-38513-1</bdi></span>

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<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite id="CITEREFSandermanCoyneRanchor2006" class="citation journal cs1">Sanderman, R.; Coyne, J. C.; Ranchor, A. V. (2006). "Age: Nuisance variable to be eliminated with statistical control or important concern?". <i>Patient Education and Counseling</i>. <b>61</b> (3): <span class="nowrap">315–</span>316. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.pec.2006.04.002">10.1016/j.pec.2006.04.002</a>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/16731313">16731313</a>.</cite></span>

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