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<title>One-factor-at-a-time method</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">One-factor-at-a-time method</span></span>

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<p>The <b>one-factor-at-a-time method,</b><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> also known as <b>one-variable-at-a-time</b>, <b>OFAT</b>, <b>OF@T</b>,

<b>OFaaT</b>, <b>OVAT</b>, <b>OV@T</b>, <b>OVaaT</b>, or <b>monothetic analysis</b> is a method of <a href="Design_of_experiments" title="Design of experiments">designing experiments</a> involving the testing of factors, or causes, one at a time instead of multiple factors simultaneously.

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

<p>OFAT is favored by non-experts, especially in situations where the data is cheap and abundant.

</p><p>There exist cases where the mental effort required to conduct a complex multi-factor analysis exceeds the effort required to acquire extra data, in which case OFAT might make sense. Furthermore, some researchers have shown that OFAT can be more effective than <a href="Fractional_factorial_design" title="Fractional factorial design">fractional factorials</a> under certain conditions (number of runs is limited, primary goal is to attain improvements in the system, and experimental error is not large compared to factor effects, which must be additive and independent of each other).<sup id="cite_ref-Friedman,_M.,_and_Savage,_L._J._(1947),_“Planning_Experiments_Seeking_Maxima,”_in_Techniques_of_Statistical_Analysis,_eds._C._Eisenhart,_M._W._Hastay,_and_W._A._Wallis,_New_York:_McGraw-Hill,_pp._365-372._2-0" class="reference"><a href="#cite_note-Friedman,_M.,_and_Savage,_L._J._(1947),_“Planning_Experiments_Seeking_Maxima,”_in_Techniques_of_Statistical_Analysis,_eds._C._Eisenhart,_M._W._Hastay,_and_W._A._Wallis,_New_York:_McGraw-Hill,_pp._365-372.-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Cuthbert_Daniel_3-0" class="reference"><a href="#cite_note-Cuthbert_Daniel-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

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

<p>In contrast, in situations where data is precious and must be analyzed with care, it is almost always better to

change multiple factors at once. A middle-school-level example illustrating this point is the family of <a href="Balance_puzzle" title="Balance puzzle">balance puzzles</a>, which includes the Twelve Coins puzzle. At the undergraduate level, one could compare

Bevington's<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> <code>GRIDLS</code> versus <code>GRADLS</code>. The latter is far from optimal, but the former, which changes only one variable at a time, is worse. See also the <a href="Factorial_design" class="mw-redirect" title="Factorial design">factorial experimental design</a> methods pioneered by <a href="Ronald_Fisher" title="Ronald Fisher">Sir Ronald A. Fisher</a>. Reasons for disfavoring OFAT include:

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<ol><li>OFAT requires more runs for the same precision in effect estimation</li>

<li>OFAT cannot estimate interactions</li>

<li>OFAT can miss optimal settings of factors.</li></ol>

<p>Designed experiments remain nearly always preferred to OFAT with many types and methods available, in addition to fractional factorials which, though usually requiring more runs than OFAT, do address the three concerns above.<sup id="cite_ref-Czitrom_5-0" class="reference"><a href="#cite_note-Czitrom-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> One modern design over which OFAT has no advantage in number of runs is the <a href="Plackett-Burman_design" class="mw-redirect" title="Plackett-Burman design">Plackett-Burman</a> which, by having all factors vary simultaneously (an important quality in experimental designs),<sup id="cite_ref-Czitrom_5-1" class="reference"><a href="#cite_note-Czitrom-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> gives generally <a href="Efficiency_(statistics)" title="Efficiency (statistics)">greater precision in effect estimation</a>.

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<ul><li><a href="Ceteris_paribus" title="Ceteris paribus">Ceteris paribus</a></li></ul>

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

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</style><cite id="CITEREFRazaviGupta2015" class="citation journal cs1">Razavi, Saman; Gupta, Hoshin V. (2015). <a rel="nofollow" class="external text" href="https://doi.org/10.1002%2F2014wr016527">"What do we mean by sensitivity analysis? The need for comprehensive characterization of "global" sensitivity in Earth and Environmental systems models"</a>. <i>Water Resources Research</i>. <b>51</b> (5): <span class="nowrap">3070–</span>3092. <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/2015WRR....51.3070R">2015WRR....51.3070R</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/10.1002%2F2014wr016527">10.1002/2014wr016527</a></span>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0043-1397">0043-1397</a>.</cite></span>

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<li id="cite_note-Friedman,_M.,_and_Savage,_L._J._(1947),_“Planning_Experiments_Seeking_Maxima,”_in_Techniques_of_Statistical_Analysis,_eds._C._Eisenhart,_M._W._Hastay,_and_W._A._Wallis,_New_York:_McGraw-Hill,_pp._365-372.-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-Friedman,_M.,_and_Savage,_L._J._(1947),_“Planning_Experiments_Seeking_Maxima,”_in_Techniques_of_Statistical_Analysis,_eds._C._Eisenhart,_M._W._Hastay,_and_W._A._Wallis,_New_York:_McGraw-Hill,_pp._365-372._2-0">^</a></b></span> <span class="reference-text">Friedman, M., and Savage, L. J. (1947), “Planning Experiments Seeking Maxima,” in Techniques of Statistical Analysis, eds. C. Eisenhart, M. W. Hastay, and W. A. Wallis, New York: McGraw-Hill, pp. 365-372.</span>

</li>

<li id="cite_note-Cuthbert_Daniel-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-Cuthbert_Daniel_3-0">^</a></b></span> <span class="reference-text">Daniel, C. (1973),“One-at-a-Time Plans,” Journal of the American Statistical Association 68, 353-360</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">Bevington and Robinson, <i>Data Reduction and Error Analysis for the Physical Sciences</i>, 2nd Ed. McGraw–Hill (1992)</span>

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<li id="cite_note-Czitrom-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-Czitrom_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Czitrom_5-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><cite id="CITEREFCzitrom1999" class="citation journal cs1"><a href="Veronica_Czitrom" title="Veronica Czitrom">Czitrom, Veronica</a> (1999). "One-Factor-at-a-Time Versus Designed Experiments". <i>American Statistician</i>. <b>53</b> (2): <span class="nowrap">126–</span>131. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F2685731">10.2307/2685731</a>. <a href="JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/2685731">2685731</a>.</cite></span>

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