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Design of experiments with fullfactorial design (left), responsesurface with second­degreepolynomial (right)

Design of experimentsFrom Wikipedia, the free encyclopedia

For the book, see The Design of Experiments.

In general usage, design of experiments (DOE) orexperimental design is the design of any information­gatheringexercises where variation is present, whether under the fullcontrol of the experimenter or not. However, in statistics, theseterms are usually used for controlled experiments. Formalplanned experimentation is often used in evaluating physicalobjects, chemical formulations, structures, components, andmaterials. Other types of study, and their design, are discussed inthe articles on computer experiments, opinion polls and statisticalsurveys (which are types of observational study), naturalexperiments and quasi­experiments (for example, quasi­experimental design). See Experiment for the distinction betweenthese types of experiments or studies.

In the design of experiments, the experimenter is often interested in the effect of some process orintervention (the "treatment") on some objects (the "experimental units"), which may be people, parts ofpeople, groups of people, plants, animals, etc. Design of experiments is thus a discipline that has verybroad application across all the natural and social sciences and engineering.

Contents

1 History1.1 Systematic clinical trials1.2 Statistical experiments, following Charles S. Peirce

1.2.1 Randomized experiments1.2.2 Optimal designs for regression models

1.3 Sequences of experiments2 Fisher's principles3 Example4 Avoiding false positives5 Discussion topics when setting up an experimental design6 Statistical control7 Experimental designs after Fisher8 Human participant experimental design constraints9 See also10 Notes11 References12 Further reading13 External links

History

Systematic clinical trials

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In 1747, while serving as surgeon on HMS Salisbury, James Lind carried out a systematic clinical trialto compare remedies for scurvy.[1]

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 extraneousvariation. He divided them into six pairs, giving each pair different supplements to their basic diet fortwo weeks. The treatments were all remedies that had been proposed:

A quart of cider every day.Twenty five gutts (drops) of vitriol (sulphuric acid) three times a day upon an empty stomach.One half­pint of seawater every day.A mixture of garlic, mustard, and horseradish in a lump the size of a nutmeg.Two spoonfuls of vinegar three times a day.Two oranges and one lemon every day.

The citrus treatment stopped after six days when they ran out of fruit, but by that time one sailor was fitfor duty while the other had almost recovered. Apart from that, only group one (cider) showed someeffect of its treatment. The remainder of the crew presumably served as a control, but Lind did not reportresults from any control (untreated) group.

Statistical experiments, following Charles S. Peirce

Main article: Frequentist statisticsSee also: Randomization

A theory of statistical inference was developed by Charles S. Peirce in "Illustrations of the Logic ofScience" (1877–1878) and "A Theory of Probable Inference" (1883), two publications that emphasizedthe importance of randomization­based inference in statistics.

Randomized experiments

Main article: Random assignmentSee also: Repeated measures design

Charles S. Peirce randomly assigned volunteers to a blinded, repeated­measures design to evaluate theirability to discriminate weights.[2][3][4][5] Peirce's experiment inspired other researchers in psychology andeducation, which developed a research tradition of randomized experiments in laboratories andspecialized textbooks in the 1800s.[2][3][4][5]

Optimal designs for regression models

Main article: Response surface methodologySee also: Optimal design

Charles S. Peirce also contributed the first English­language publication on an optimal design forregression models in 1876.[6] A pioneering optimal design for polynomial regression was suggested byGergonne in 1815. In 1918 Kirstine Smith published optimal designs for polynomials of degree six (andless).

Sequences of experiments

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Ronald Fisher

Main article: Sequential analysisSee also: Multi­armed bandit problem, Gittins index and Optimal design

The use of a sequence of experiments, where the design of each may depend on the results of previousexperiments, including the possible decision to stop experimenting, is within the scope of Sequentialanalysis, a field that was pioneered[7] by Abraham Wald in the context of sequential tests of statisticalhypotheses.[8] Herman Chernoff wrote an overview of optimal sequential designs,[9] while adaptivedesigns have been surveyed by S. Zacks.[10] One specific type of sequential design is the "two­armedbandit", generalized to the multi­armed bandit, on which early work was done by Herbert Robbins in1952.[11]

Fisher's principles

A methodology for designing experiments was proposed by RonaldFisher, in his innovative books: The Arrangement of FieldExperiments (1926) and The Design of Experiments (1935). Much ofhis pioneering work dealt with agricultural applications of statisticalmethods. As a mundane example, he described how to test the ladytasting tea hypothesis, that a certain lady could distinguish byflavour alone whether the milk or the tea was first placed in the cup.These methods have been broadly adapted in the physical and socialsciences, are still used in agricultural engineering and differ from thedesign and analysis of computer experiments.

ComparisonIn some fields of study it is not possible to have independentmeasurements to a traceable metrology standard. Comparisonsbetween treatments are much more valuable and are usuallypreferable, and often compared against a scientific control ortraditional treatment that acts as baseline.

RandomizationRandom assignment is the process of assigning individuals at random to groups or to differentgroups in an experiment. The random assignment of individuals to groups (or conditions within agroup) distinguishes a rigorous, "true" experiment from an observational study or "quasi­experiment".[12] There is an extensive body of mathematical theory that explores the consequencesof making the allocation of units to treatments by means of some random mechanism such astables of random numbers, or the use of randomization devices such as playing cards or dice.Assigning units to treatments at random tends to mitigate confounding, which makes effects dueto factors other than the treatment to appear to result from the treatment. The risks associated withrandom allocation (such as having a serious imbalance in a key characteristic between a treatmentgroup and a control group) are calculable and hence can be managed down to an acceptable levelby using enough experimental units. The results of an experiment can be generalized reliably fromthe experimental units to a larger statistical population of units only if the experimental units are arandom sample from the larger population; the probable error of such an extrapolation depends onthe sample size, among other things.

Statistical replicationMeasurements are usually subject to variation and measurement uncertainty; thus they arerepeated and full experiments are replicated to help identify the sources of variation, to betterestimate the true effects of treatments, to further strengthen the experiment's reliability andvalidity, and to add to the existing knowledge of the topic.[13] However, certain conditions must be

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Example of orthogonal factorialdesign

met before the replication of the experiment is commenced: the original research question hasbeen published in a peer­reviewed journal or widely cited, the researcher is independent of theoriginal experiment, the researcher must first try to replicate the original findings using theoriginal data, and the write­up should state that the study conducted is a replication study that triedto follow the original study as strictly as possible.[14]

BlockingBlocking is the arrangement of experimental units into groups (blocks/lots) consisting of units thatare similar to one another. Blocking reduces known but irrelevant sources of variation betweenunits and thus allows greater precision in the estimation of the source of variation under study.

Orthogonality

Orthogonality concerns the forms of comparison(contrasts) that can be legitimately and efficiently carriedout. Contrasts can be represented by vectors and sets oforthogonal contrasts are uncorrelated and independentlydistributed if the data are normal. Because of thisindependence, each orthogonal treatment providesdifferent information to the others. If there are T treatmentsand T – 1 orthogonal contrasts, all the information that canbe captured from the experiment is obtainable from the setof contrasts.

Factorial experimentsUse of factorial experiments instead of the one­factor­at­a­time method. These are efficient atevaluating the effects and possible interactions of several factors (independent variables). Analysisof experiment design is built on the foundation of the analysis of variance, a collection of modelsthat partition the observed variance into components, according to what factors the experimentmust estimate or test.

Example

This example is attributed to Harold Hotelling.[9] It conveyssome of the flavor of those aspects of the subject that involvecombinatorial designs.

Weights of eight objects are measured using a pan balance andset of standard weights. Each weighing measures the weightdifference between objects in the left pan vs. any objects in theright pan by adding calibrated weights to the lighter pan untilthe balance is in equilibrium. Each measurement has a randomerror. The average error is zero; the standard deviations of theprobability distribution of the errors is the same number σ ondifferent weighings; and errors on different weighings areindependent. Denote the true weights by

We consider two different experiments:

1. Weigh each object in one pan, with the other pan empty. Let Xi be the measured weight of the ithobject, for i = 1, ..., 8.

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2. Do the eight weighings according to the following schedule and let Yi be the measured differencefor i = 1, ..., 8:

Then the estimated value of the weight θ1 is

Similar estimates can be found for the weights of the other items. For example

The question of design of experiments is: which experiment is better?

The variance of the estimate X1 of θ1 is σ2 if we use the first experiment. But if we use the second

experiment, the variance of the estimate given above is σ2/8. Thus the second experiment gives us 8times as much precision for the estimate of a single item, and estimates all items simultaneously, withthe same precision. What the second experiment achieves with eight would require 64 weighings if theitems are weighed separately. However, note that the estimates for the items obtained in the secondexperiment have errors that correlate with each other.

Many problems of the design of experiments involve combinatorial designs, as in this example andothers.[15]

Avoiding false positives

False positive conclusions, often resulting from the pressure to publish or the author's own confirmationbias, are an inherent hazard in many fields, and experimental designs with undisclosed degrees offreedom are a problem.[16] This can lead to conscious or unconscious "p­hacking": trying multiple thingsuntil you get the desired result. It typically involves the manipulation ­ perhaps unconsciously ­ of theprocess of statistical analysis and the degrees of freedom until they return a figure below the p<.05 levelof statistical significance.[17][18] So the design of the experiment should include a clear statementproposing the analyses to be undertaken.

Clear and complete documentation of the experimental methodology is also important in order tosupport replication of results.[19]

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Discussion topics when setting up an experimental design

An experimental design or randomized clinical trial requires careful consideration of several factorsbefore actually doing the experiment.[20] An experimental design is the laying out of a detailedexperimental plan in advance of doing the experiment. Some of the following topics have already beendiscussed in the principles of experimental design section:

1. How many factors does the design have? and are the levels of these factors fixed or random?2. Are control conditions needed, and what should they be?3. Manipulation checks; did the manipulation really work?4. What are the background variables?5. What is the sample size. How many units must be collected for the experiment to be generalisable

and have enough power?6. What is the relevance of interactions between factors?7. What is the influence of delayed effects of substantive factors on outcomes?8. How do response shifts affect self­report measures?9. How feasible is repeated administration of the same measurement instruments to the same units at

different occasions, with a post­test and follow­up tests?10. What about using a proxy pretest?11. Are there lurking variables?12. Should the client/patient, researcher or even the analyst of the data be blind to conditions?13. What is the feasibility of subsequent application of different conditions to the same units?14. How many of each control and noise factors should be taken into account?

Statistical control

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 conductof designed experiments.[21] To control for nuisance variables, researchers institute control checks asadditional measures. Investigators should ensure that uncontrolled influences (e.g., source credibilityperception) do not skew the findings of the study. A manipulation check is one example of a controlcheck. Manipulation checks allow investigators to isolate the chief variables to strengthen support thatthese variables are operating as planned.

One of the most important requirements of experimental research designs is the necessity of eliminatingthe effects of spurious, intervening, and antecedent variables. In the most basic model, cause (X) leads toeffect (Y). But there could be a third variable (Z) that influences (Y), and X might not be the true causeat all. Z is said to be a spurious variable and must be controlled for. The same is true for interveningvariables (a variable in between the supposed cause (X) and the effect (Y)), and anteceding variables (avariable prior to the supposed cause (X) that is the true cause). When a third variable is involved and hasnot been controlled for, the relation is said to be a zero order relationship. In most practical applicationsof experimental research designs there are several causes (X1, X2, X3). In most designs, only one ofthese causes is manipulated at a time.

Experimental designs after Fisher

Some efficient designs for estimating several main effects were found independently and in nearsuccession by Raj Chandra Bose and K. Kishen in 1940 at the Indian Statistical Institute, but remainedlittle known until the Plackett­Burman designs were published in Biometrika in 1946. About the sametime, C. R. Rao introduced the concepts of orthogonal arrays as experimental designs. This concept

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played a central role in the development of Taguchi methods by Genichi Taguchi, which took placeduring his visit to Indian Statistical Institute in early 1950s. His methods were successfully applied andadopted by Japanese and Indian industries and subsequently were also embraced by US industry albeitwith some reservations.

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 yearsafterwards.

Developments of the theory of linear models have encompassed and surpassed the cases that concernedearly writers. Today, the theory rests on advanced topics in linear algebra, algebra and combinatorics.

As with other branches of statistics, experimental design is pursued using both frequentist and Bayesianapproaches: In evaluating statistical procedures like experimental designs, frequentist statistics studiesthe sampling distribution while Bayesian statistics updates a probability distribution on the parameterspace.

Some important contributors to the field of experimental designs are C. S. Peirce, R. A. Fisher, F. Yates,C. R. Rao, R. C. Bose, J. N. Srivastava, Shrikhande S. S., D. Raghavarao, W. G. Cochran, O.Kempthorne, W. T. Federer, V. V. Fedorov, A. S. Hedayat, J. A. Nelder, R. A. Bailey, J. Kiefer, W. J.Studden, A. Pázman, F. Pukelsheim, D. R. Cox, H. P. Wynn, A. C. Atkinson, G. E. P. Box and G.Taguchi. The textbooks of D. Montgomery and R. Myers have reached generations of students andpractitioners.[22] [23] [24]

Human participant experimental design constraints

Laws and ethical considerations preclude some carefully designed experiments with human subjects.Legal constraints are dependent on jurisdiction. Constraints may involve institutional review boards,informed consent and confidentiality affecting both clinical (medical) trials and behavioral and socialscience experiments.[25] In the field of toxicology, for example, experimentation is performed onlaboratory animals with the goal of defining safe exposure limits for humans.[26] Balancing theconstraints are views from the medical field.[27] Regarding the randomization of patients, "... if no oneknows 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 apoorly designed study when this situation can be easily avoided...". (p 393)

See also

Adversarial collaborationBayesian experimental designClinical trialComputer experimentControl variableControlling for a variableExperimetrics (econometrics­related experiments)Factor analysisFirst­in­man studyGlossary of experimental designGrey box modelInstrument effectLaw of large numbers

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Manipulation checksMultifactor design of experiments softwareProbabilistic designProtocol (natural sciences)Quasi­experimental designRandomized block designRandomized controlled trialResearch designRobust parameter designSupersaturated designSurvey samplingSystem identificationTaguchi methods

Notes1. Dunn, Peter (January 1997). "James Lind (1716­94) of Edinburgh and the treatment of scurvy"

(http://fn.bmj.com/cgi/content/full/76/1/F64). Archive of Disease in Childhood Foetal Neonatal (UnitedKingdom: British Medical Journal Publishing Group) 76 (1): 64–65. doi:10.1136/fn.76.1.F64(https://dx.doi.org/10.1136%2Ffn.76.1.F64). PMC 1720613(https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1720613). PMID 9059193(https://www.ncbi.nlm.nih.gov/pubmed/9059193). Retrieved 2009­01­17.

2. Peirce, Charles Sanders; Jastrow, Joseph (1885). "On Small Differences in Sensation"(http://psychclassics.yorku.ca/Peirce/small­diffs.htm). Memoirs of the National Academy of Sciences 3: 73–83.

3. Hacking, Ian (September 1988). "Telepathy: Origins of Randomization in Experimental Design". Isis 79 (3):427–451. doi:10.1086/354775 (https://dx.doi.org/10.1086%2F354775). JSTOR 234674(https://www.jstor.org/stable/234674). MR 1013489 (https://www.ams.org/mathscinet­getitem?mr=1013489).

4. Stephen M. Stigler (November 1992). "A Historical View of Statistical Concepts in Psychology andEducational Research". American Journal of Education 101 (1): 60–70. doi:10.1086/444032(https://dx.doi.org/10.1086%2F444032). JSTOR 1085417 (https://www.jstor.org/stable/1085417).

5. Trudy Dehue (December 1997). "Deception, Efficiency, and Random Groups: Psychology and the GradualOrigination of the Random Group Design". Isis 88 (4): 653–673. doi:10.1086/383850(https://dx.doi.org/10.1086%2F383850). PMID 9519574 (https://www.ncbi.nlm.nih.gov/pubmed/9519574).

6. Peirce, C. S. (1876). "Note on the Theory of the Economy of Research". Coast Survey Report: 197–201.,actually published 1879, NOAA PDF Eprint (http://docs.lib.noaa.gov/rescue/cgs/001_pdf/CSC­0025.PDF#page=222).Reprinted in Collected Papers 7, paragraphs 139–157, also in Writings 4, pp. 72–78, and in Peirce, C. S.(July–August 1967). "Note on the Theory of the Economy of Research". Operations Research 15 (4): 643–648. doi:10.1287/opre.15.4.643 (https://dx.doi.org/10.1287%2Fopre.15.4.643). JSTOR 168276(https://www.jstor.org/stable/168276).

7. Johnson, N.L. (1961). "Sequential analysis: a survey." Journal of the Royal Statistical Society, Series A. Vol.124 (3), 372–411. (pages 375–376)

8. Wald, A. (1945) "Sequential Tests of Statistical Hypotheses", Annals of Mathematical Statistics, 16 (2), 117–186.

9. Herman Chernoff, Sequential Analysis and Optimal Design, SIAM Monograph, 1972.10. 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. North­Holland. ISBN 0­444­82061­2. (pages 151–180)

11. Robbins, H. (1952). "Some Aspects of the Sequential Design of Experiments". Bulletin of the AmericanMathematical Society 58 (5): 527–535. doi:10.1090/S0002­9904­1952­09620­8(https://dx.doi.org/10.1090%2FS0002­9904­1952­09620­8).

12. Creswell, J.W. (2008). Educational research: Planning, conducting, and evaluating quantitative and qualitativeresearch (3rd). Upper Saddle River, NJ: Prentice Hall. 2008, p. 300. ISBN 0­13­613550­1

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13. Dr. Hani (2009). "Replication study" (http://www.experiment­resources.com/replication­study.html).Retrieved 27 October 2011.

14. Burman, Leonard E.; Robert W. Reed; James Alm (2010). "A call for replication studies"(http://pfr.sagepub.com) (journal article). Public Finance Review. pp. 787–793. doi:10.1177/1091142110385210(https://dx.doi.org/10.1177%2F1091142110385210). Retrieved 27 October 2011.

15. Jack Sifri (8 December 2014). "How to Use Design of Experiments to Create Robust Designs With HighYield" (https://www.youtube.com/watch?v=hfdZabCVwzc). youtube.com. Retrieved 2015­02­11.

16. Simmons, Joseph; Leif Nelson; Uri Simonsohn (November 2011). "False­Positive Psychology: UndisclosedFlexibility in Data Collection and Analysis Allows Presenting Anything as Significant"(http://pss.sagepub.com/content/22/11/1359.full). Psychological Science (Washington DC: Association forPsychological Science) 22 (11): 1359–1366. doi:10.1177/0956797611417632(https://dx.doi.org/10.1177%2F0956797611417632). ISSN 0956­7976 (https://www.worldcat.org/issn/0956­7976). PMID 22006061 (https://www.ncbi.nlm.nih.gov/pubmed/22006061). Retrieved 29 January 2012.

17. "Science, Trust And Psychology In Crisis" (http://www.kplu.org/post/science­trust­and­psychology­crisis).KPLU. 2014­06­02. Retrieved 2014­06­12.

18. "Why Statistically Significant Studies Can Be Insignificant" (http://www.psmag.com/navigation/nature­and­technology/statistically­significant­studies­arent­necessarily­significant­82832/). Pacific Standard. 2014­06­04. Retrieved 2014­06­12.

19. Chris Chambers (2014­06­10). "Physics envy: Do ‘hard’ sciences hold the solution to the replication crisis inpsychology?" (http://www.theguardian.com/science/head­quarters/2014/jun/10/physics­envy­do­hard­sciences­hold­the­solution­to­the­replication­crisis­in­psychology). theguardian.com. Retrieved 2014­06­12.

20. Ader, Mellenberg & Hand (2008) "Advising on Research Methods: A consultant's companion"21. Bisgaard, S (2008) "Must a Process be in Statistical Control before Conducting Designed Experiments?",

Quality Engineering, ASQ, 20 (2), pp 143 ­ 17622. Montgomery, Douglas (2013). Design and analysis of experiments (8th ed.). Hoboken, NJ: John Wiley &

Sons, Inc. ISBN 9781118146927.23. Walpole, Ronald E.; Myers, Raymond H.; Myers, Sharon L.; Ye, Keying (2007). Probability & statistics for

engineers & scientists (8 ed.). Upper Saddle River, NJ: Pearson Prentice Hall. ISBN 978­0131877115.24. Myers, Raymond H.; Montgomery, Douglas C.; Vining, G. Geoffrey; Robinson, Timothy J. (2010).

Generalized linear models : with applications in engineering and the sciences (2 ed.). Hoboken, N.J: Wiley.ISBN 978­0470454633.

25. Moore, David S.; Notz, William I. (2006). Statistics : concepts and controversies (6th ed.). New York: W.H.Freeman. pp. Chapter 7: Data ethics. ISBN 9780716786368.

26. Ottoboni, M. Alice (1991). The dose makes the poison : a plain­language guide to toxicology (2nd ed.). NewYork, N.Y: Van Nostrand Reinhold. ISBN 0442006608.

27. Glantz, Stanton A. (1992). Primer of biostatistics (3rd ed.). ISBN 0­07­023511­2.

References

Peirce, C. S. (1877–1878), "Illustrations of the Logic of Science" (series), Popular ScienceMonthly, vols. 12­13. Relevant individual papers:

(1878 March), "The Doctrine of Chances", Popular Science Monthly, v. 12, March issue,pp. 604 (https://books.google.com/books?id=ZKMVAAAAYAAJ&jtp=604)–615. InternetArchive Eprint (https://archive.org/stream/popscimonthly12yoummiss#page/612/mode/1up).(1878 April), "The Probability of Induction", Popular Science Monthly, v. 12, pp. 705(https://books.google.com/books?id=ZKMVAAAAYAAJ&jtp=705)–718. Internet ArchiveEprint (https://archive.org/stream/popscimonthly12yoummiss#page/715/mode/1up).(1878 June), "The Order of Nature", Popular Science Monthly, v. 13, pp. 203(https://books.google.com/books?id=u8sWAQAAIAAJ&jtp=203)–217.Internet ArchiveEprint (https://archive.org/stream/popularsciencemo13newy#page/203/mode/1up).(1878 August), "Deduction, Induction, and Hypothesis", Popular Science Monthly, v. 13,pp. 470 (https://books.google.com/books?id=u8sWAQAAIAAJ&jtp=470)–482. InternetArchive Eprint (https://archive.org/stream/popularsciencemo13newy#page/470/mode/1up).

Peirce, C. S. (1883), "A Theory of Probable Inference", Studies in Logic, pp. 126­181(https://books.google.com/books?id=V7oIAAAAQAAJ&pg=PA126), Little, Brown, and

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Company. (Reprinted 1983, John Benjamins Publishing Company, ISBN 90­272­3271­7)

Further reading

Atkinson, A. C. (http://stats.lse.ac.uk/atkinson/) and Donev, A. N.(http://www.maths.manchester.ac.uk/~adonev/) and Tobias, R. D.(http://support.sas.com/publishing/bbu/companion_site/index_author.html#tobias) (2007).Optimum Experimental Designs, with SAS (http://books.google.se/books?id=oIHsrw6NBmoC).Oxford University Press(http://www.us.oup.com/us/catalog/general/subject/Mathematics/ProbabilityStatistics/~~/dmlldz11c2EmY2k9OTc4MDE5OTI5NjYwNg==). pp. 511+xvi. ISBN 978­0­19­929660­6.Bailey, R.A. (2008). Design of Comparative Experiments(http://www.maths.qmul.ac.uk/~rab/DOEbook). Cambridge University Press. ISBN 978­0­521­68357­9. Pre­publication chapters are available on­line.Box, G. E. P., & Draper, N. R. (1987). Empirical model­building and response surfaces. NewYork: Wiley.Box, G. E., Hunter,W.G., Hunter, J.S., Hunter,W.G., "Statistics for Experimenters: Design,Innovation, and Discovery", 2nd Edition, Wiley, 2005, ISBN 0­471­71813­0Caliński, Tadeusz and Kageyama, Sanpei (2000). Block designs: A Randomization approach,Volume I: Analysis. Lecture Notes in Statistics 150. New York: Springer­Verlag. ISBN 0­387­98578­6.George Casella (2008). Statistical design(http://www.springer.com/statistics/statistical+theory+and+methods/book/978­0­387­75964­7).Springer. ISBN 978­0­387­75965­4.Ghosh, S. and Rao, C. R., ed. (1996). Design and Analysis of Experiments. Handbook of Statistics13. North­Holland. ISBN 0­444­82061­2.Goos, Peter and Jones, Bradley (2011). Optimal Design of Experiments: A Case Study Approach(http://eu.wiley.com/WileyCDA/WileyTitle/productCd­0470744618.html). Wiley. ISBN 978­0­470­74461­1.Hacking, Ian (September 1988). "Telepathy: Origins of Randomization in Experimental Design".Isis 79 (3): 427–451. doi:10.1086/354775 (https://dx.doi.org/10.1086%2F354775).JSTOR 234674 (https://www.jstor.org/stable/234674). MR 1013489(https://www.ams.org/mathscinet­getitem?mr=1013489).Hinkelmann, Klaus and Kempthorne, Oscar (2008). Design and Analysis of Experiments. I and II(Second ed.). Wiley (http://eu.wiley.com/WileyCDA/WileyTitle/productCd­0470385510.html).ISBN 978­0­470­38551­7.

Hinkelmann, Klaus and Kempthorne, Oscar (2008). Design and Analysis of Experiments,Volume I: Introduction to Experimental Design (https://books.google.com/?id=T3wWj2kVYZgC&printsec=frontcover) (Second ed.). Wiley(http://eu.wiley.com/WileyCDA/WileyTitle/productCd­0471727563.html). ISBN 978­0­471­72756­9.Hinkelmann, Klaus and Kempthorne, Oscar (2005). Design and Analysis of Experiments,Volume 2: Advanced Experimental Design (https://books.google.com/books?id=GiYc5nRVKf8C) (First ed.). Wiley(http://eu.wiley.com/WileyCDA/WileyTitle/productCd­0471551775.html). ISBN 978­0­471­55177­5.

Mason, R. L., Gunst, R. F., & Hess, J. L. (1989). Statistical design and analysis of experimentswith applications to engineering and science. New York: Wiley.Pearl, Judea. Causality: Models, Reasoning and Inference, Cambridge University Press, 2000.Peirce, C. S. (1876), "Note on the Theory of the Economy of Research", Appendix No. 14 inCoast Survey Report, pp. 197–201, NOAA PDF Eprint(http://docs.lib.noaa.gov/rescue/cgs/001_pdf/CSC­0025.PDF#page=222). Reprinted 1958 inCollected Papers of Charles Sanders Peirce 7, paragraphs 139–157 and in 1967 in Operations

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Research (http://or.journal.informs.org/cgi/content/abstract/15/4/643) 15 (4): pp. 643–648,abstract at JSTOR (http://www.jstor.org/stable/168276). Peirce, C. S. (1967). "Note on the Theoryof the Economy of Research". Operations Research 15 (4): 643. doi:10.1287/opre.15.4.643(https://dx.doi.org/10.1287%2Fopre.15.4.643).Smith, Kirstine (1918). "On the Standard Deviations of Adjusted and Interpolated Values of anObserved Polynomial Function and its Constants and the Guidance They Give Towards a ProperChoice of the Distribution of the Observations". Biometrika 12 (1): 1–85. doi:10.2307/2331929(https://dx.doi.org/10.2307%2F2331929).Taguchi, G. (1987). Jikken keikakuho (3rd ed., Vol I & II). Tokyo: Maruzen. English translationedited by D. Clausing. System of experimental design. New York: UNIPUB/Kraus International.

External links

A chapter (http://www.itl.nist.gov/div898/handbook/pri/section1/pri1.htm) from a"NIST/SEMATECH Handbook on Engineering Statistics"(http://www.itl.nist.gov/div898/handbook/) at NISTBox–Behnken designs (http://www.itl.nist.gov/div898/handbook/pri/section3/pri3362.htm) from a"NIST/SEMATECH Handbook on Engineering Statistics"(http://www.itl.nist.gov/div898/handbook/) at NISTArticles on Design of Experiments (http://www.curiouscat.net/library/designofexperiments.cfm)Case Studies and Articles on Design of Experiments (DOE)(http://www.statease.com/articles.html)Czitrom (1999) "One­Factor­at­a­Time Versus Designed Experiments", American Statistician, 53,2. (http://www.questia.com/googleScholar.qst?docId=5001888588)Design Resources Server (http://www.iasri.res.in/design) a mobile library on Design ofExperiments. The server is dynamic in nature and new additions would be posted on this site fromtime to time.Gosset: A General­Purpose Program for Designing Experiments(http://www.research.att.com/~njas/gosset/index.html)SAS Examples for Experimental Design (http://www.wright.edu/~dvoss/book/DeanVoss.html)Matlab SUrrogate MOdeling Toolbox ­ SUMO Toolbox (http://sumowiki.intec.ugent.be) –MATLAB code for Design of Experiments + Sequential Design + Surrogate ModelingDesign DB (http://web.cs.dal.ca/~peter/designdb/): A database of combinatorial, statistical,experimental block designsThe I­Optimal Design Assistant(http://obdoe.com/student/DOEResources/Assistant/assistantintro.php): a free on­line library of I­Optimal designsWarning Signs in Experimental Design and Interpretation (http://norvig.com/experiment­design.html) by Peter Norvig, chief of research at GoogleKnowledge Base, Research Methods (http://www.socialresearchmethods.net/kb/desexper.php): Agood explanation of the basic idea of experimental designsThe Controlled Experiment vs. The Comparative Experiment(http://www.juliantrubin.com/fairguide/scientificmethod.html): "How to experiment" for sciencefair projectsSpall, J. C. (2010), "Factorial Design for Choosing Input Values in Experimentation: GeneratingInformative Data for System Identification," IEEE Control Systems Magazine, vol. 30(5), pp. 38–53. (http://dx.doi.org/10.1109/MCS.2010.937677) General introduction from a systemsperspectiveDOE used for engine calibration reduces fuel consumption by 2 to 4 percent(http://www.etas.com/en/products/ascmo.php)

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