Editing Design of experiments (section)

==History==

===Statistical experiments, following Charles S. Peirce===
{{Main|Frequentist statistics}}
{{See also|Randomization}}
A theory of [[statistical inference]] was developed by [[Charles Sanders Peirce|Charles S. Peirce]] in "[[Charles Sanders Peirce bibliography#illus|Illustrations of the Logic of Science]]" (1877–1878)<ref>Peirce, Charles Sanders (1887). "Illustrations of the Logic of Science". Open Court (10 June 2014). {{ISBN|0812698495}}.</ref> and  "[[Charles Sanders Peirce bibliography#SIL|A Theory of Probable Inference]]" (1883),<ref>Peirce, Charles Sanders (1883). "A Theory of Probable Inference". In C. S. Peirce (Ed.), Studies in logic by members of the Johns Hopkins University (p. 126–181). Little, Brown and Co (1883)</ref> two publications that emphasized the importance of randomization-based inference in statistics.<ref name=Stigler78>{{cite journal |last1=Stigler |first1=Stephen M. |author-link=Stephen Stigler |year=1978 |title=Mathematical statistics in the early States |url=http://projecteuclid.org/euclid.aos/1176344123 |journal=Annals of Statistics |volume=6 |issue= 2|pages=239–65 [248] |quote="Indeed, Pierce's work contains one of the earliest explicit endorsements of mathematical randomization as a basis for inference of which I am aware (Peirce, 1957, pages 216–219" | doi=10.1214/aos/1176344123 |jstor=2958876 |mr=483118|doi-access=free }}</ref>

====Randomized experiments====
{{Main|Random assignment}}
{{See also|Repeated measures design}}
Charles S. Peirce randomly assigned volunteers to a [[blinding (medicine)|blinded]], [[repeated measures design|repeated-measures design]] to evaluate their ability to discriminate weights.<ref name="smalldiff">{{Cite journal| last1= Peirce|first1=Charles Sanders|last2=Jastrow|first2=Joseph |author-link1=Charles Sanders Peirce|author-link2=Joseph Jastrow|year=1885|title=On Small Differences in Sensation|url=http://psychclassics.yorku.ca/Peirce/small-diffs.htm| journal=Memoirs of the National Academy of Sciences|volume=3|pages=73–83}}</ref><ref name="telepathy">of
{{Cite journal|first=Ian |last=Hacking|  author-link=Ian Hacking | title=Telepathy: Origins of Randomization in Experimental Design|journal=[[Isis (journal)|Isis]]|issue=3|volume=79|date=September 1988 |pages=427–451|jstor=234674|mr=1013489 | doi=10.1086/354775|s2cid=52201011}}</ref><ref name="stigler">
{{Cite journal|author=Stephen M. Stigler|title=A Historical View of Statistical Concepts in Psychology and Educational Research| journal=American Journal of Education| volume=101|issue=1|date=November 1992|pages=60–70|jstor=1085417|doi=10.1086/444032
|s2cid=143685203|author-link=Stephen M. Stigler}}</ref><ref name="dehue">
{{Cite journal|author=Trudy Dehue|title=Deception, Efficiency, and Random Groups: Psychology and the Gradual Origination of the Random Group Design|journal=[[Isis (journal)|Isis]]|volume=88|issue=4|date=December 1997|pages=653–673|doi=10.1086/383850|pmid=9519574|s2cid=23526321|url=https://www.rug.nl/research/portal/en/publications/deception-efficiency-and-random-groups(459e54f0-1e56-4390-876a-46a33e80621d).html}}</ref>
Peirce's experiment inspired other researchers in psychology and education, which developed a research tradition of randomized experiments in laboratories and specialized textbooks in the 1800s.<ref name="smalldiff"/><ref name="telepathy"/><ref name="stigler"/><ref name="dehue"/>

====Optimal designs for regression models====
{{Main|Response surface methodology}}
{{See also|Optimal design}}
[[Charles Sanders Peirce|Charles S. Peirce]] also contributed the first English-language publication on an [[optimal design]] for [[Regression analysis|regression]] [[statistical model|models]] in 1876.<ref>{{cite journal| author=Peirce, C. S. | year=1876| title=Note on the Theory of the Economy of Research | journal=Coast Survey Report | pages=197–201| author-link=Charles Sanders Peirce}}, actually published 1879, NOAA [http://docs.lib.noaa.gov/rescue/cgs/001_pdf/CSC-0025.PDF#page=222 PDF Eprint] {{Webarchive|url=https://web.archive.org/web/20170302071239/https://docs.lib.noaa.gov/rescue/cgs/001_pdf/CSC-0025.PDF#page=222 |date=2 March 2017 }}.<br /> Reprinted in ''[[Charles Sanders Peirce bibliography#CP|Collected Papers]]'' '''7''', paragraphs 139–157, also in ''[[Charles Sanders Peirce bibliography#W|Writings]]'' '''4''', pp. 72–78, and in {{cite journal| author=Peirce, C. S. |date=July–August 1967
| title=Note on the Theory of the Economy of Research
| journal=Operations Research
|volume=15 | issue=4|pages=643–648
| jstor=168276|doi=10.1287/opre.15.4.643
|author-link=Charles Sanders Peirce
}}</ref> A pioneering [[optimal design]] for [[polynomial regression]] was suggested by [[Joseph Diaz Gergonne|Gergonne]] in 1815. In 1918, [[Kirstine Smith]] published optimal designs for polynomials of degree six (and less).<ref name=GL2009>{{cite journal |last1=Guttorp |first1=P. |last2=Lindgren |first2=G. |title= Karl Pearson and the Scandinavian school of statistics |journal= International Statistical Review |volume=77 |year=2009 |page=64 |doi=10.1111/j.1751-5823.2009.00069.x|citeseerx=10.1.1.368.8328 |s2cid=121294724 }}</ref><ref name="polynomials">{{Cite journal| last1= Smith| first1=Kirstine| author-link1=Kirstine Smith| year=1918| title=On the standard deviations of adjusted and interpolated values of an observed polynomial function and its constants and the guidance they give towards a proper choice of the distribution of observations.| url=https://books.google.com/books?id=UMNLAAAAYAAJ | journal=Biometrika|volume=12| issue=1–2|pages=1–85| doi=10.1093/biomet/12.1-2.1| url-access=subscription}}</ref>

===Sequences of experiments===
{{Main|Sequential analysis}}
{{See also|Multi-armed bandit problem|Gittins index|Optimal design}}
The use of a sequence of experiments, where the design of each may depend on the results of previous experiments, including the possible decision to stop experimenting, is within the scope of [[sequential analysis]], a field that was pioneered<ref>Johnson, N.L. (1961). "Sequential analysis: a survey." ''[[Journal of the Royal Statistical Society]]'', Series A. Vol. 124 (3), 372&ndash;411. (pages 375&ndash;376)</ref> by [[Abraham Wald]] in the context of sequential tests of statistical hypotheses.<ref>Wald, A. (1945) "Sequential Tests of Statistical Hypotheses", [[Annals of Mathematical Statistics]], 16 (2), 117&ndash;186.</ref> [[Herman Chernoff]] wrote an overview of optimal sequential designs,<ref name="ref3"/> while [[Adaptive design (medicine)|adaptive designs]] have been surveyed by S. Zacks.<ref>Zacks, S. (1996) "Adaptive Designs for Parametric Models". In: Ghosh, S. and Rao, C. R., (Eds) (1996). "Design and Analysis of Experiments," ''Handbook of Statistics'', Volume 13. North-Holland. {{ISBN|0-444-82061-2}}.  (pages 151&ndash;180)</ref> One specific type of sequential design is the "two-armed bandit", generalized to the [[multi-armed bandit]], on which early work was done by [[Herbert Robbins]] in 1952.<ref>{{cite journal | doi = 10.1090/S0002-9904-1952-09620-8 | last1 = Robbins | first1 = H. | year = 1952 | title = Some Aspects of the Sequential Design of Experiments | journal = Bulletin of the American Mathematical Society | volume = 58 | issue = 5| pages = 527–535 | doi-access = free }}</ref>