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| {{Use dmy dates|date=July 2013}}
| | It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.<br><br>Here are some common dental emergencies:<br>Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.<br><br>At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.<br><br>Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.<br><br>Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.<br><br>Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.<br><br>Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.<br><br>Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.<br><br>In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.<br><br>If you have any inquiries relating to where and the best ways to use [http://www.youtube.com/watch?v=90z1mmiwNS8 Washington DC Dentist], you can call us at our own webpage. |
| [[Image:Response surface metodology.jpg|thumb|Design of experiments with full factorial design (left), response surface with second-degree polynomial (right)]]
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| In general usage, '''design of experiments (DOE)''' or '''experimental design''' is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in [[statistics]], these terms are usually used for [[controlled experiment]]s. Formal planned experimentation is often used in evaluating [[physical test|physical objects]], [[chemical test|chemical formulations]], structures, components, and materials. Other types of study, and their design, are discussed in the articles on [[computer experiment]]s, [[opinion poll]]s and [[statistical survey]]s (which are types of [[observational study]]), [[natural experiment]]s and [[quasi-experiment]]s (for example, [[quasi-experimental design]]). See [[Experiment]] for the distinction between these types of experiments or studies.
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| In the design of experiments, the experimenter is often interested in the effect of some process or intervention (the "treatment") on some objects (the "[[experimental unit]]s"), which may be people, parts of people, groups of people, plants, animals, etc. Design of experiments is thus a discipline that has very broad application across all the natural and social sciences and engineering.
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| ==History of development==
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| ===Controlled experimentation on scurvy===
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| In 1747, while serving as surgeon on [[HMS Salisbury (1746)|HMS ''Salisbury'']], [[James Lind (physician)|James Lind]] carried out a controlled experiment to develop a cure for [[scurvy]].<ref name="ADC1997">{{Cite journal| last =Dunn | first =Peter | coauthors = | title =James Lind (1716-94) of Edinburgh and the treatment of scurvy | journal =Archive of Disease in Childhood Foetal Neonatal | volume =76 | issue = 1| pages =64–65 | publisher =British Medical Journal Publishing Group | location =United Kingdom |date = January 1997| url =http://fn.bmj.com/cgi/content/full/76/1/F64 | doi = 10.1136/fn.76.1.F64| pmc =1720613 | accessdate =2009-01-17 | pmid=9059193}}</ref>
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| Lind selected 12 men from the ship, all suffering from scurvy. Lind limited his subjects to men who "were as similar as I could have them", that is he provided strict entry requirements to reduce extraneous variation. He divided them into six pairs, giving each pair different supplements to their basic diet for two weeks. The treatments were all remedies that had been proposed:
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| * A quart of cider every day
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| * Twenty five gutts (drops) of ''elixir [[vitriol]]'' (sulphuric acid) three times a day upon an empty stomach
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| * One half-pint of seawater every day
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| * A mixture of garlic, mustard, and horseradish in a lump the size of a nutmeg
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| * Two spoonfuls of vinegar three times a day
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| * Two oranges and one lemon every day
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| The men given [[citrus fruit]]s recovered dramatically within a week. One of them returned to duty after six days, and the others cared for the rest. The other subjects experienced some improvement, but nothing compared to the subjects who ate the citrus fruits, which proved substantially superior to the other treatments. | |
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| ===Statistical experiments, following Charles S. Peirce===
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| {{Main|Frequentist statistics}}
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| {{See also|Randomization}}
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| 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) and "[[Charles Sanders Peirce bibliography#SIL|A Theory of Probable Inference]]" (1883), two publications that emphasized the importance of randomization-based inference in statistics.
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| ====Randomized experiments====
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| {{Main|Random assignment}}
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| {{See also|Repeated measures design}}
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| 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 |authorlink1=Charles Sanders Peirce|authorlink2=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">
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| {{Cite journal|first=Ian |last=Hacking| authorlink=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}}</ref><ref name="stigler">
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| {{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
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| }}</ref><ref name="dehue">
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| {{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}}</ref>
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| 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"/>
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| ====Optimal designs for regression models====
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| {{Main|Response surface methodology}}
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| {{See also|Optimal design}}
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| [[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=[[Charles Sanders Peirce|Peirce, C. S.]] | year=1876| title=Note on the Theory of the Economy of Research | journal=Coast Survey Report | pages=197–201}}, actually published 1879, NOAA [http://docs.lib.noaa.gov/rescue/cgs/001_pdf/CSC-0025.PDF#page=222 PDF Eprint].<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=[[Charles Sanders Peirce|Peirce, C. S.]] | year=1967
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| | title=Note on the Theory of the Economy of Research
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| | journal=Operations Research
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| |volume=15 | issue=4 |month=July–August|pages=643–648
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| | jstor=168276|doi=10.1287/opre.15.4.643
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| }}</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).
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| ===Sequences of experiments===
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| {{Main|Sequential analysis}}
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| {{See also|Multi-armed bandit problem|Gittins index|Optimal design}}
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| 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), 372–411. (pages 375–376)</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), 117–186.</ref> [[Herman Chernoff]] wrote an overview of optimal sequential designs,<ref name="ref3"/> while [[Minimisation (clinical trials)|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 151–180)</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 | url = | journal = Bulletin of the American Mathematical Society | volume = 58 | issue = 5| pages = 527–535 }}</ref>
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| ==Principles of experimental design, following Ronald A. Fisher==
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| A methodology for designing experiments was proposed by [[Ronald Fisher|Ronald A. Fisher]], in his innovative books: "The Arrangement of Field Experiments" (1926) and ''[[The Design of Experiments]]'' (1935). Much of his pioneering work dealt with agricultural applications of statistical methods. As a mundane example, he described how to test the [[hypothesis]] that a certain lady could distinguish by flavour alone whether the milk or the tea was first placed in the cup. These methods have been broadly adapted in the physical and social sciences, and are still used in [[agricultural engineering]]. The concepts presented here differ from the design and analysis of [[computer experiment]]s.
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| ;Comparison
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| :In some fields of study it is not possible to have independent measurements to a traceable [[Standard (metrology)|standard]]. Comparisons between treatments are much more valuable and are usually preferable. Often one compares against a [[scientific control]] or traditional treatment that acts as baseline.
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| ;[[Randomization]]
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| :Random assignment is the process of assigning individuals at random to groups or to different groups in an experiment. The random assignment of individuals to groups (or conditions within a group) distinguishes a rigorous, "true" experiment from an adequate, but less-than-rigorous, "quasi-experiment".<ref>Creswell, J.W. (2008). Educational research: Planning, conducting, and evaluating quantitative and qualitative research (3rd). Upper Saddle River, NJ: Prentice Hall. 2008, p. 300. ISBN 0-13-613550-1</ref> There is an extensive body of mathematical theory that explores the consequences of making the allocation of units to treatments by means of some random mechanism such as tables of random numbers, or the use of randomization devices such as playing cards or dice. Provided the sample size is adequate, the risks associated with random allocation (such as failing to obtain a representative sample in a survey, or having a serious imbalance in a key characteristic between a treatment group and a control group) are calculable and hence can be managed down to an acceptable level. Random does ''not'' mean haphazard, and great care must be taken that appropriate random methods are used.
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| ;[[Replication (statistics)|Replication]]
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| :Measurements are usually subject to variation and [[Measurement uncertainty|uncertainty]]. Measurements are repeated and full experiments are replicated to help identify the sources of variation, to better estimate the true effects of treatments, to further strengthen the experiment's reliability and validity, and to add to the existing knowledge of the topic.<ref>{{cite web|last=Dr. Hani|title=Replication study|url=http://www.experiment-resources.com/replication-study.html|accessdate=27 October 2011|year=2009}}</ref> However, certain conditions must be met before the replication of the experiment is commenced: the original research question has been published in a peer-reviewed journal or widely cited, the researcher is independent of the original experiment, the researcher must first try to replicate the original findings using the original data, and the write-up should state that the study conducted is a replication study that tried to follow the original study as strictly as possible.<ref>{{cite web|last=Burman|first=Leonard E.|title=A call for replication studies|url=http://pfr.sagepub.com|publisher=Public Finance Review|accessdate=27 October 2011|coauthors=Robert W. Reed, James Alm|pages=787–793|format=journal article|doi=10.1177/1091142110385210|year=2010}}</ref>
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| ;[[Blocking (statistics)|Blocking]]
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| :Blocking is the arrangement of experimental units into groups (blocks/lots) consisting of units that are similar to one another. Blocking reduces known but irrelevant sources of variation between units and thus allows greater precision in the estimation of the source of variation under study.
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| ;[[Orthogonality]]
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| [[File:Factorial Design.svg|thumb|Example of orthogonal factorial design]]
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| :Orthogonality concerns the forms of comparison (contrasts) that can be legitimately and efficiently carried out. Contrasts can be represented by vectors and sets of orthogonal contrasts are uncorrelated and independently distributed if the data are normal. Because of this independence, each orthogonal treatment provides different information to the others. If there are ''T'' treatments and ''T'' – 1 orthogonal contrasts, all the information that can be captured from the experiment is obtainable from the set of contrasts.
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| ;[[Factorial experiment]]s
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| :Use of factorial experiments instead of the one-factor-at-a-time method. These are efficient at evaluating the effects and possible [[Interaction (statistics)|interactions]] of several factors (independent variables). Analysis of [[experiment]] design is built on the foundation of the [[analysis of variance]], a collection of models that partition the observed variance into components, according to what factors the experiment must estimate or test.
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| ==Example==
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| [[Image:Balance à tabac 1850.JPG|right|240px]]
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| This example is attributed to [[Harold Hotelling]].<ref name="ref3">[[Herman Chernoff]], ''Sequential Analysis and Optimal Design'', [[Society for Industrial and Applied Mathematics|SIAM]] Monograph, 1972.</ref> It conveys some of the flavor of those aspects of the subject that involve combinatorial designs.
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| Weights of eight objects are measured using a [[pan balance]] and set of standard weights. Each weighing measures the weight difference between objects in the left pan vs. any objects in the right pan by adding calibrated weights to the lighter pan until the balance is in equilibrium. Each measurement has a [[errors and residuals in statistics|random error]]. The average error is zero; the [[standard deviation]]s of the [[probability distribution]] of the errors is the same number σ on different weighings; and errors on different weighings are [[statistical independence|independent]]. Denote the true weights by
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| :<math>\theta_1, \dots, \theta_8.\,</math>
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| We consider two different experiments:
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| # Weigh each object in one pan, with the other pan empty. Let ''X''<sub>''i''</sub> be the measured weight of the ''i''th object, for ''i'' = 1, ..., 8.
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| # Do the eight weighings according to the following schedule and let ''Y''<sub>''i''</sub> be the measured difference for ''i'' = 1, ..., 8:
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| :: <math>
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| \begin{matrix}
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| & \mbox{left pan} & \mbox{right pan} \\
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| \mbox{1st weighing:} & 1\ 2\ 3\ 4\ 5\ 6\ 7\ 8 & \text{(empty)} \\
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| \mbox{2nd:} & 1\ 2\ 3\ 8\ & 4\ 5\ 6\ 7 \\
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| \mbox{3rd:} & 1\ 4\ 5\ 8\ & 2\ 3\ 6\ 7 \\
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| \mbox{4th:} & 1\ 6\ 7\ 8\ & 2\ 3\ 4\ 5 \\
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| \mbox{5th:} & 2\ 4\ 6\ 8\ & 1\ 3\ 5\ 7 \\
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| \mbox{6th:} & 2\ 5\ 7\ 8\ & 1\ 3\ 4\ 6 \\
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| \mbox{7th:} & 3\ 4\ 7\ 8\ & 1\ 2\ 5\ 6 \\
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| \mbox{8th:} & 3\ 5\ 6\ 8\ & 1\ 2\ 4\ 7
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| \end{matrix}
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| </math>
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| : Then the estimated value of the weight θ<sub>1</sub> is
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| :: <math>\widehat{\theta}_1 = \frac{Y_1 + Y_2 + Y_3 + Y_4 - Y_5 - Y_6 - Y_7 - Y_8}{8}. </math>
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| :Similar estimates can be found for the weights of the other items. For example
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| ::<math>\widehat{\theta}_2 = \frac{Y_1 + Y_2 - Y_3 - Y_4 + Y_5 + Y_6 - Y_7 - Y_8}{8}.</math>
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| The question of design of experiments is: which experiment is better?
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| The variance of the estimate ''X''<sub>1</sub> of θ<sub>1</sub> is σ<sup>2</sup> if we use the first experiment. But if we use the second experiment, the variance of the estimate given above is σ<sup>2</sub>/8. Thus the second experiment gives us 8 times as much precision for the estimate of a single item, and estimates all items simultaneously, with the same precision. What the second experiment achieves with eight would require 64 weighings if the items are weighed separately. However, note that the estimates for the items obtained in the second experiment have errors that correlate with each other.
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| Many problems of the design of experiments involve [[combinatorial design]]s, as in this example.
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| ==Discussion topics when setting up an experimental design==
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| An experimental design or randomized clinical trial requires careful consideration of several factors before actually doing the experiment.<ref>Ader, Mellenberg & Hand (2008) "Advising on Research Methods: A consultant's companion"</ref> An experimental design is the laying out of a detailed experimental plan in advance of doing the experiment. Some of the following topics have already been discussed in the principles of experimental design section:
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| 1. How many factors does the design have? and are the levels of these factors fixed or random?
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| 2. Are control conditions needed, and what should they be?
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| 3. Manipulation checks; did the manipulation really work?
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| 4. What are the background variables?
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| 5. What is the sample size. How many units must be collected for the experiment to be generalisable and have enough power?
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| 6. What is the relevance of interactions between factors?
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| 7. What is the influence of delayed effects of substantive factors on outcomes?
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| 8. How do response shifts affect self-report measures?
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| 9. How feasible is repeated administration of the same measurement instruments to the same units at different occasions, with a post-test and follow-up tests?
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| 10. What about using a proxy pretest?
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| 11. Are there lurking variables?
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| 12. Should the client/patient, researcher or even the analyst of the data be blind to conditions?
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| 13. What is the feasibility of subsequent application of different conditions to the same units?
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| 14. How many of each control and noise factors should be taken into account?
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| ==Statistical control==
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| It is best that a process be in reasonable statistical control prior to conducting designed experiments. When this is not possible, proper blocking, replication, and randomization allow for the careful conduct of designed experiments.<ref>Bisgaard, S (2008) "Must a Process be in Statistical Control before Conducting Designed Experiments?", ''Quality Engineering'', ASQ, 20 (2), pp 143 - 176</ref>
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| To control for nuisance variables, researchers institute '''control checks''' as additional measures. Investigators should ensure that uncontrolled influences (e.g., source credibility perception) are measured do not skew the findings of the study. A [[manipulation checks|manipulation check]] is one example of a control check. Manipulation checks allow investigators to isolate the chief variables to strengthen support that these variables are operating as planned.
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| One of the most important requirements of experimental research designs is the necessity of eliminating the effects of [[spurious relationship|spurious]], intervening, and [[antecedent variable]]s. In the most basic model, cause (X) leads to effect (Y). But there could be a third variable (Z) that influences (Y), and X might not be the true cause at all. Z is said to be a spurious variable and must be controlled for. The same is true for [[intervening variable]]s (a variable in between the supposed cause (X) and the effect (Y)), and anteceding variables (a variable prior to the supposed cause (X) that is the true cause). When a third variable is involved and has not been controlled for, the relation is said to be a [[zero order (statistics)|zero order]]{{disambiguation needed|date=August 2012}} relationship. In most practical applications of experimental research designs there are several causes (X1, X2, X3). In most designs, only one of these causes is manipulated at a time.
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| ==Experimental designs after Fisher==
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| Some efficient designs for estimating several main effects were found independently and in near succession by [[Raj Chandra Bose]] and K. Kishen in 1940 at the [[Indian Statistical Institute]], but remained little known until the [[Plackett-Burman design]]s were published in ''[[Biometrika]]'' in 1946. About the same time, [[C. R. Rao]] introduced the concepts of [[orthogonal array]]s as experimental designs. This concept played a central role in the development of [[Taguchi methods]] by [[Genichi Taguchi]], which took place during his visit to Indian Statistical Institute in early 1950s. His methods were successfully applied and adopted by Japanese and Indian industries and subsequently were also embraced by US industry albeit with some reservations.
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| In 1950, [[Gertrude Mary Cox]] and [[William Gemmell Cochran]] published the book ''Experimental Designs,'' which became the major reference work on the design of experiments for statisticians for years afterwards.
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| Developments of the theory of [[linear model]]s have encompassed and surpassed the cases that concerned early writers. Today, the theory rests on advanced topics in [[linear algebra]], [[algebraic statistics|algebra]] and [[combinatorial design|combinatorics]].
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| As with other branches of statistics, experimental design is pursued using both [[frequentist statistics|frequentist]] and [[Bayesian experimental design|Bayesian]] approaches: In evaluating statistical procedures like experimental designs, [[frequentist statistics]] studies the [[sampling distribution]] while [[Bayesian statistics]] updates a [[Bayesian probability|probability distribution]] on the parameter space.
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| Some important contributors to the field of experimental designs are [[Charles Sanders Peirce|C. S. Peirce]], [[R. A. Fisher]], [[Frank Yates|F. Yates]], [[C. R. Rao]], [[R. C. Bose]], [[Jagdish N. Srivastava|J. N. Srivastava]], [[Shrikhande S. S.]], [[D. Raghavarao]], [[William G. Cochran|W. G. Cochran]], [[Oscar Kempthorne|O. Kempthorne]], W. T. Federer, V. V. Fedorov, A. S. Hedayat, [[John Nelder|J. A. Nelder]], [[Rosemary A. Bailey|R. A. Bailey]], [[Jack Kiefer (mathematician)|J. Kiefer]], W. J. Studden, A. Pázman, F. Pukelsheim, [[David R. Cox|D. R. Cox]], H. P. Wynn, A. C. Atkinson, [[G. E. P. Box]] and [[Genichi Taguchi|G. Taguchi]].{{citation needed|date=November 2011}} The textbooks of D. Montgomery and R. Myers have reached generations of students and practitioners.<ref>{{cite book | last = Montgomery | first = Douglas
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| | title = Design and analysis of experiments
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| | publisher = John Wiley & Sons, Inc | location = Hoboken, NJ
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| | edition = 8th
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| | year = 2013 | isbn = 9781118146927 }}</ref>
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| <ref>
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| {{cite book
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| | last1 = Walpole | first1 = Ronald E.
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| | last2 = Myers | first2 = Raymond H.
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| | last3 = Myers | first3 = Sharon L.
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| | last4 = Ye | first4 = Keying
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| | title = Probability & statistics for engineers & scientists
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| | publisher = Pearson Prentice Hall | location = Upper Saddle River, NJ
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| | edition = 8
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| | year = 2007 | isbn = 978-0131877115 }}</ref>
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| <ref>
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| {{cite book
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| | last1 = Myers | first1 = Raymond H.
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| | last2 = Montgomery | first2 = Douglas C.
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| | last3 = Vining | first3 = G. Geoffrey
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| | last4 = Robinson | first4 = Timothy J.
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| | title = Generalized linear models : with applications in engineering and the sciences
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| | publisher = Wiley | location = Hoboken, N.J
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| | edition = 2
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| | year = 2010 | isbn = 978-0470454633 }}</ref>
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| ==Human participant experimental design constraints==
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| Laws and ethical considerations preclude some carefully designed
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| experiments with human subjects. Legal constraints are dependent on
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| [[Human subject research|jurisdiction]]. Constraints may involve
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| [[institutional review board]]s, [[informed consent]]
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| and [[confidentiality]] affecting both clinical (medical) trials and
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| behavioral and social science experiments.<ref>
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| {{cite book | last1 = Moore | first1 = David S.
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| | last2 = Notz | first2 = William I.
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| | title = Statistics : concepts and controversies
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| | publisher = W.H. Freeman | location = New York | year = 2006
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| | isbn = 9780716786368 | edition = 6th
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| | pages = Chapter 7: Data ethics}}</ref>
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| In the field of toxicology, for example, experimentation is performed
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| on laboratory ''animals'' with the goal of defining safe exposure limits
| |
| for ''humans''.<ref>
| |
| {{cite book | last = Ottoboni | first = M. Alice
| |
| | title = The dose makes the poison : a plain-language guide to toxicology
| |
| | publisher = Van Nostrand Reinhold | location = New York, N.Y
| |
| | year = 1991 | isbn = 0442006608 | edition = 2nd }}</ref> Balancing
| |
| the constraints are views from the medical field.<ref>{{cite book
| |
| | last = Glantz | first = Stanton A.
| |
| | title = Primer of biostatistics | edition = 3rd | year = 1992 |
| |
| isbn = 0-07-023511-2 }}</ref> Regarding the randomization of patients,
| |
| "... if no one knows which therapy is better, there is no ethical
| |
| imperative to use one therapy or another." (p 380) Regarding
| |
| experimental design, "...it is clearly not ethical to place subjects
| |
| at risk to collect data in a poorly designed study when this situation
| |
| can be easily avoided...". (p 393)
| |
| | |
| ==See also==
| |
| {{Portal|Statistics}}
| |
| <div style="-moz-column-count:3; column-count:3;">
| |
| * [[Adversarial collaboration]]
| |
| * [[Bayesian experimental design]]
| |
| * [[Clinical trial]]
| |
| *[[Computer experiment]]
| |
| * [[Control variable]]
| |
| * [[Controlling for a variable]]
| |
| * [[Experimetrics]]: application of [[econometrics]] to [[economics]] experiments.
| |
| * [[Factor analysis]]
| |
| * [[First-in-man study]]
| |
| * [[Glossary of experimental design]]
| |
| * [[Instrument effect]]
| |
| * [[Law of large numbers]]
| |
| * [[Manipulation checks]]
| |
| * [[Multifactor design of experiments software]]
| |
| * [[Probabilistic design]]
| |
| * [[Protocol (natural sciences)]]
| |
| * [[Quasi-experimental design]]
| |
| * [[Randomized block design]]
| |
| * [[Randomized controlled trial]]
| |
| * [[Research design]]
| |
| * [[Robust Parameter Design (RPD)|Robust Parameter Design]]
| |
| * [[Plackett–Burman design#Supersaturated designs|Supersaturated]] design
| |
| * [[Survey sampling]]
| |
| * [[Taguchi methods]]
| |
| | |
| </div>
| |
| | |
| ==Notes==
| |
| {{Reflist|30em}}
| |
| | |
| ==References==
| |
| *[[Charles Sanders Peirce|Peirce, C. S.]] (1877–1878), "Illustrations of the Logic of Science" (series), ''Popular Science Monthly'', vols. 12-13. Relevant individual papers:
| |
| ** (1878 March), "The Doctrine of Chances", ''Popular Science Monthly'', v. 12, March issue, pp. [http://books.google.com/books?id=ZKMVAAAAYAAJ&jtp=604 604]–615. ''Internet Archive'' [http://www.archive.org/stream/popscimonthly12yoummiss#page/612/mode/1up Eprint].
| |
| ** (1878 April), "The Probability of Induction", ''Popular Science Monthly'', v. 12, pp. [http://books.google.com/books?id=ZKMVAAAAYAAJ&jtp=705 705]–718. ''Internet Archive'' [http://www.archive.org/stream/popscimonthly12yoummiss#page/715/mode/1up Eprint].
| |
| ** (1878 June), "The Order of Nature", ''Popular Science Monthly'', v. 13, pp. [http://books.google.com/books?id=u8sWAQAAIAAJ&jtp=203 203]–217.''Internet Archive'' [http://www.archive.org/stream/popularsciencemo13newy#page/203/mode/1up Eprint].
| |
| ** (1878 August), "Deduction, Induction, and Hypothesis", ''Popular Science Monthly'', v. 13, pp. [http://books.google.com/books?id=u8sWAQAAIAAJ&jtp=470 470]–482. ''Internet Archive'' [http://www.archive.org/stream/popularsciencemo13newy#page/470/mode/1up Eprint].
| |
| *[[Charles Sanders Peirce|Peirce, C. S.]] (1883), "A Theory of Probable Inference", ''Studies in Logic'', pp. [http://books.google.com/books?id=V7oIAAAAQAAJ&pg=PA126 126-181], Little, Brown, and Company. (Reprinted 1983, John Benjamins Publishing Company, ISBN 90-272-3271-7)
| |
| | |
| ==Further reading==
| |
| * {{Cite book|author=[http://stats.lse.ac.uk/atkinson/ Atkinson, A. C.] and [http://www.maths.manchester.ac.uk/~adonev/ Donev, A. N.] and [http://support.sas.com/publishing/bbu/companion_site/index_author.html#tobias Tobias, R. D.]|title=Optimum Experimental Designs, with SAS |url=http://books.google.se/books?id=oIHsrw6NBmoC|publisher=[http://www.us.oup.com/us/catalog/general/subject/Mathematics/ProbabilityStatistics/~~/dmlldz11c2EmY2k9OTc4MDE5OTI5NjYwNg== Oxford University Press]|year=2007 |pages=511+xvi |isbn=978-0-19-929660-6 |doi=}}
| |
| * {{Cite book|authorlink=Rosemary A. Bailey|first=R.A.|last=Bailey|title=Design of Comparative Experiments|publisher=Cambridge University Press|year=2008 |isbn=978-0-521-68357-9|url=http://www.maths.qmul.ac.uk/~rab/DOEbook}} Pre-publication chapters are available on-line.
| |
| * Box, G. E. P., & Draper, N. R. (1987). ''Empirical model-building and response surfaces''. New York: Wiley.
| |
| * [[George E. P. Box|Box, G. E.]], Hunter,W.G., Hunter, J.S., Hunter,W.G., "Statistics for Experimenters: Design, Innovation, and Discovery", 2nd Edition, Wiley, 2005, ISBN 0-471-71813-0
| |
| * {{Cite book
| |
| |author=Caliński, Tadeusz and Kageyama, Sanpei
| |
| |title=Block designs: A Randomization approach, Volume '''I''': Analysis
| |
| |series=Lecture Notes in Statistics
| |
| |volume=150
| |
| |publisher=Springer-Verlag
| |
| |location=New York
| |
| |year=2000
| |
| |isbn=0-387-98578-6
| |
| }}
| |
| * {{Cite book| title=Design and Analysis of Experiments | series=Handbook of Statistics| volume=13|editor=Ghosh, S. and [[Calyampudi Radhakrishna Rao|Rao, C. R.]] | publisher=North-Holland| year=1996| isbn=0-444-82061-2}}
| |
| *{{Cite book
| |
| |author=Goos, Peter and Jones, Bradley
| |
| |year=2011
| |
| |title=[http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0470744618.html Optimal Design of Experiments: A Case Study Approach]
| |
| |publisher=Wiley
| |
| |isbn=978-0-470-74461-1}}
| |
| * {{cite journal|first=Ian |last=Hacking| authorlink=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}}
| |
| *{{Cite book
| |
| |author=Hinkelmann, Klaus and [[Oscar Kempthorne|Kempthorne, Oscar]]
| |
| |year=2008
| |
| |title=Design and Analysis of Experiments
| |
| |volume=I and II
| |
| |edition=Second
| |
| |publisher=[http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0470385510.html Wiley]
| |
| |isbn=978-0-470-38551-7}}
| |
| **{{Cite book
| |
| |author=Hinkelmann, Klaus and [[Oscar Kempthorne|Kempthorne, Oscar]]
| |
| |year=2008
| |
| |title=Design and Analysis of Experiments, Volume I: Introduction to Experimental Design
| |
| |url=http://books.google.com/?id=T3wWj2kVYZgC&printsec=frontcover
| |
| |edition=Second
| |
| |publisher=[http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0471727563.html Wiley]
| |
| |isbn=978-0-471-72756-9
| |
| }}
| |
| **{{Cite book
| |
| |author=Hinkelmann, Klaus and [[Oscar Kempthorne|Kempthorne, Oscar]]
| |
| |year=2005
| |
| |title=Design and Analysis of Experiments, Volume 2: Advanced Experimental Design
| |
| |url=http://books.google.com/books?id=GiYc5nRVKf8C
| |
| |edition=First
| |
| |publisher=[http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0471551775.html Wiley]
| |
| |isbn=978-0-471-55177-5
| |
| }}
| |
| * Mason, R. L., Gunst, R. F., & Hess, J. L. (1989). ''Statistical design and analysis of experiments with applications to engineering and science''. New York: Wiley.
| |
| * [[Judea Pearl|Pearl, Judea]]. ''Causality: Models, Reasoning and Inference'', Cambridge University Press, 2000.
| |
| * [[Charles Sanders Peirce|Peirce, C. S.]] (1876), "Note on the Theory of the Economy of Research", Appendix No. 14 in ''Coast Survey Report'', pp. 197–201, [http://docs.lib.noaa.gov/rescue/cgs/001_pdf/CSC-0025.PDF#page=222 NOAA PDF Eprint]. Reprinted 1958 in ''Collected Papers of Charles Sanders Peirce'' '''7''', paragraphs 139–157 and in 1967 in ''[http://or.journal.informs.org/cgi/content/abstract/15/4/643 Operations Research]'' '''15''' (4): pp. 643–648, [http://www.jstor.org/stable/168276 abstract at JSTOR]. {{cite journal| doi=10.1287/opre.15.4.643| title=Note on the Theory of the Economy of Research| year=1967| last1=Peirce| first1=C. S.| journal=Operations Research| volume=15| issue=4| pages=643}}
| |
| * {{cite journal
| |
| | author=Smith, Kirstine
| |
| |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 the Observations| year=1918
| |
| | journal=[[Biometrika]]
| |
| | volume=12
| |
| | pages=1–85
| |
| | jstor=2331929
| |
| | issue=1
| |
| * Taguchi, G. (1987). ''Jikken keikakuho'' (3rd ed., Vol I & II). Tokyo: Maruzen. English translation edited by D. Clausing. ''System of experimental design''. New York: UNIPUB/Kraus International.
| |
| }}
| |
| | |
| ==External links==
| |
| *A [http://www.itl.nist.gov/div898/handbook/pri/section1/pri1.htm chapter] from a [http://www.itl.nist.gov/div898/handbook/ "NIST/SEMATECH Handbook on Engineering Statistics"] at [[National Institute of Standards and Technology|NIST]]
| |
| *[http://www.itl.nist.gov/div898/handbook/pri/section3/pri3362.htm Box–Behnken designs] from a [http://www.itl.nist.gov/div898/handbook/ "NIST/SEMATECH Handbook on Engineering Statistics"] ] at [[National Institute of Standards and Technology|NIST]]
| |
| *[http://www.curiouscat.net/library/designofexperiments.cfm Articles on Design of Experiments]
| |
| *[http://www.statease.com/articles.html Case Studies and Articles on Design of Experiments (DOE)]
| |
| *[http://www.questia.com/googleScholar.qst?docId=5001888588 Czitrom (1999) "One-Factor-at-a-Time Versus Designed Experiments", American Statistician, 53, 2.]
| |
| *[http://www.iasri.res.in/design Design Resources Server] a mobile library on Design of Experiments. The server is dynamic in nature and new additions would be posted on this site from time to time.
| |
| *[http://www.research.att.com/~njas/gosset/index.html Gosset: A General-Purpose Program for Designing Experiments]
| |
| *[http://www.wright.edu/~dvoss/book/DeanVoss.html SAS Examples for Experimental Design]
| |
| *[http://sumowiki.intec.ugent.be Matlab '''SU'''rrogate '''MO'''deling Toolbox - SUMO Toolbox] – Matlab code for Design of Experiments + Sequential Design + Surrogate Modeling
| |
| *[http://web.cs.dal.ca/~peter/designdb/ Design DB]: A database of combinatorial, statistical, experimental block designs
| |
| *[http://obdoe.com/student/DOEResources/Assistant/assistantintro.php The I-Optimal Design Assistant]: a free on-line library of I-Optimal designs
| |
| *[http://norvig.com/experiment-design.html Warning Signs in Experimental Design and Interpretation] by Peter Norvig, chief of research at Google
| |
| *[http://www.socialresearchmethods.net/kb/desexper.php Knowledge Base, Research Methods]: A good explanation of the basic idea of experimental designs
| |
| *[http://www.juliantrubin.com/fairguide/scientificmethod.html The Controlled Experiment vs. The Comparative Experiment]: "How to experiment" for science fair projects
| |
| *[http://dx.doi.org/10.1109/MCS.2010.937677 Spall, J. C. (2010), “Factorial Design for Choosing Input Values in Experimentation: Generating Informative Data for System Identification,” IEEE Control Systems Magazine, vol. 30(5), pp. 38–53.] General introduction from a systems perspective
| |
| *[http://www.etas.com/en/products/ascmo.php DOE used for engine calibration reduces fuel consumption by 2 to 4 percent]
| |
| {{Library resources box
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| |label=Experimental design}}
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| {{Experimental design|state=collapsed}}
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| {{Design}}
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| {{Statistics|collection|state=collapsed<!-- expanded -->}}
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| {{Medical research studies|state=collapsed}}
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| {{DEFAULTSORT:Design Of Experiments}}
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| [[Category:Design of experiments]]
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| [[Category:Statistical methods]]
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| [[Category:Statistical theory]]
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| [[Category:Industrial engineering]]
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| [[Category:Systems engineering]]
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| [[Category:Quality control]]
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