One-factor-at-a-time method: Difference between revisions

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{{Short description|Method of designing experiments}}

The '''one-factor-at-a-time method''' (or OFAT) is a method of [[design of experiments|designing experiments]] involving the testing of [[factor]]s, or causes, one at a time instead of all simultaneously. Prominent text books and academic papers currently favor [[factorial design|factorial experimental designs]], a method pioneered by [[Ronald Fisher|Sir Ronald A. Fisher]], where multiple factors are changed at once. The reasons stated for favoring the use of factorial design over OFAT are:

The '''one-factor-at-a-time method,'''<ref>{{Cite journal|last1=Razavi|first1=Saman|last2=Gupta|first2=Hoshin V.|date=2015|title=What do we mean by sensitivity analysis? The need for comprehensive characterization of "global" sensitivity in Earth and Environmental systems models|journal=Water Resources Research|language=en|volume=51|issue=5|pages=3070–3092|doi=10.1002/2014wr016527|bibcode=2015WRR....51.3070R |issn=0043-1397|doi-access=free}}</ref> also known as '''one-variable-at-a-time''', '''OFAT''', '''OF@T''',

'''OFaaT''', '''OVAT''', '''OV@T''', '''OVaaT''', or '''monothetic analysis''' is a method of [[design of experiments|designing experiments]] involving the testing of factors, or causes, one at a time instead of multiple factors simultaneously.

==Advantages==

1. OFAT requires more runs for the same precision in effect estimation<br />

2. OFAT cannot estimate interactions<br />

3. OFAT can miss optimal settings of factors

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

Despite these criticisms, some researchers have articulated a role for OFAT and showed they can be more effective than [[Fractional factorial design|fractional factorials]] 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).<ref name=" 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.

"> 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.</ref><ref name= "Cuthbert Daniel"> Daniel , C. (1973) ,“One-at-a-Time Plans,” Journal of the American Statistical Association 68, 353-360</ref> Designed experiments remain nearly always preferred to OFAT with many types and methods available,<ref>See Category: Experimental design, at bottom.</ref> in addition to fractional factorials which, though usually requiring more runs than OFAT, do address the three concerns above.<ref>[http://www.questia.com/googleScholar.qst?docId=5001888588 Czitrom (1999) "One-Factor-at-a-Time Versus Designed Experiments", American Statistician, 53, 2.]</ref> <!--formerly http://www.amstat.org/publications/tas/czitrom.pdf--> One modern design over which OFAT has no advantage in number of runs is the [[Plackett-Burman_design|Plackett-Burman]] which, by having all factors vary simultaneously (an important quality in experimental designs),<ref>Ibid. Czitrom.</ref> gives generally [[Efficiency (statistics)|greater precision in effect estimation]].

DespiteThere theseexist criticisms,cases somewhere researchersthe havemental articulatedeffort required to conduct a rolecomplex formulti-factor analysis exceeds the effort required to acquire extra data, in which case OFAT andmight showedmake theysense. Furthermore, some researchers have shown that OFAT can be more effective than [[Fractional factorial design|fractional factorials]] 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).<ref name=" 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.

== References==

">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.</ref><ref name= "Cuthbert Daniel">Daniel, C. (1973),“One-at-a-Time Plans,” Journal of the American Statistical Association 68, 353-360</ref>

{{reflist}}

==Disadvantages==

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

[[Category:Experimental design]]

change multiple factors at once. A middle-school-level example illustrating this point is the family of [[balance puzzle]]s, which includes the Twelve Coins puzzle. At the undergraduate level, one could compare

Bevington's<ref>Bevington and Robinson, ''Data Reduction and Error Analysis for the Physical Sciences'', 2nd Ed. McGraw&ndash;Hill (1992)</ref> <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 [[factorial design|factorial experimental design]] methods pioneered by [[Ronald Fisher|Sir Ronald A. Fisher]]. Reasons for disfavoring OFAT include:

1. #OFAT requires more runs for the same precision in effect estimation<br />

2. #OFAT cannot estimate interactions<br />

3. #OFAT can miss optimal settings of factors.

"> 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.</ref><ref name= "Cuthbert Daniel"> Daniel , C. (1973) ,“One-at-a-Time Plans,” Journal of the American Statistical Association 68, 353-360</ref> Designed experiments remain nearly always preferred to OFAT with many types and methods available,<ref>See Category: Experimental design, at bottom.</ref> in addition to fractional factorials which, though usually requiring more runs than OFAT, do address the three concerns above.<ref name=Czitrom>[http://www.questia.com/googleScholar.qst?docId{{cite journal |last=Czitrom|first=5001888588Veronica|authorlink= Veronica Czitrom (|year=1999) "|title=One-Factor-at-a-Time Versus Designed Experiments", |journal=American Statistician, |volume=53, |issue=2 |pages=126–131 |doi=10.]<2307/ref>2685731|jstor= 2685731}}<!--formerly http://www.amstat.org/publications/tas/czitrom.pdf--ref> One modern design over which OFAT has no advantage in number of runs is the [[Plackett-Burman_designBurman design|Plackett-Burman]] which, by having all factors vary simultaneously (an important quality in experimental designs),<ref>Ibid. name=Czitrom.< /ref> gives generally [[Efficiency (statistics)|greater precision in effect estimation]].

==See also==

* [[Ceteris paribus]]

== References==

{{reflist}}

[[Category:Design of experiments]]

{{tech-stub}}