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H.3I UN WEARTYOF %]ISCONSRNdr . MA4LIOGRAPIY OF EXPERIMENT DESIGN1950-1167T. Federer aria T. N. Balaamdocument h-s been approved for publicC-ase and sale; its distribution is unlimited.-VMRG Technical S inimary Report # 1080October 1971MR- 19.Reproduced byNATIONAL TECHNICA!,INFORMATION SERVICESprinafield. Va.22131- Address:S.%latheinaticsResearch1'hc LUn vcrsaýi of WisconsinNiadison. Wisconsin S1706

THE UNIVERSITY OF WISCONSINMATHEMATICS RESEARCH CENTERContr.ict No.: DA-31-124-ARO-D-462BIBLIOGRAPHY OF EXPERIMENT DESIGN1950-1967W. T. Federer and L. N. BalaamIThis document has been approved for publicrelease and sale; its distribution is unlimited.MRC Technical Summary Report # 1080October 1971Rr z:eived July 10, 1970I Wicnn 5A0Madison, Wisconsin 53706

All 70-31 TiTnciassiftedDOCU MENT CONTROL DATA - Re*c 1affr.t ofcwe.- So@m.ý"*,,mr"40.0".sf 1dtM"so-ogvaqwwr m. .U nclassifiedNone"LMathematics Research Center,University of Wisconsin, Madiscm, 'Nis. 53706BIBLIOGRAPHY Of' EXPERIMENT DESIGN, 19-50-1967*no specific reportigpodSmayReport:g 2a&U460 ft"Is batwnN440 1"0*1W(Pnima.WV. T. Federer and L N. Balaama0October 1971Contract No.AOAo.3H v*&&CDA-31-124-ARO-D-462NoneE.1080NoneDistribution of this documnant is unlimitted.it. NOTiSPPLZUISTA1VS. srawe.sem ulrafv ACyIw,',Army Research Office-Durham, N C.NoneA classification system for publications on tie design and analysisof experiment and treatment designs has been devised.zublications onIexperiment design, the arrangement of the treatmer.'.s in the experiment,have been classified accordingly and cover the period ,950-1?f.7 inclusively.DD."oovass17Unciaissified AGO OWA

ABSTRACTA bibliography consisting of epproxtrately 1700 literature citations on thevarious aspects of experiment design (the i -rangement of treatments in the experiment) is presented for the years 1950 to 1967, inclusive.A classification systemfor experimeift designs, for treatment designs (the selection of treatments includedin the experiment), and for topics on the philosophy, technique, conduct, andanalyses of experiments, is described.Each literature citation in the bibliographyis coded in the manner indicated by the classification system.Papers on thetheoretical, applied, and practical aspects of experiment design are included.4I!IU1

BIBLIOGfRPHY OF EXPERIMENT DESIGN, 1950-1957byWý T. Federer, Cornell UniversityandL. N. Balaam, Unitvrsity of SydneyI.INTRODUCTIONPublications on the various aspects of experiment design (the arrangement ofthe treatments in a comparative experiment) and the treatment design (the selectionof the treatments included in the experiment) have become numerous during zecentyears.Thus, searching the literature for papers on a particular topic is a difficulttask which can be considerably alleviated by a comprehensive bibliography, especiallyif a classification is included.The general statistics bibliographies by Kendall andDoig [1962, 1965, 1968] are helpful in this connection.specific topics are even more useful.However, bibliographies onThis was the reason for the previous bibliographyprepared by Federer [1964]; this work covered published literature on the design, conduct,and statistical analyses of experimental investigatious prior to 1950; no classificationof citations was presented although a partial classification was presented in the textualpart of the report.The present bibliography contains about 1700 literature citations on experimentdesign for the years 1950 to 1967, Inclusive.A classification of exper ment designsis given in the second section of the paper.Since many of the publications areconcerned with tupics in addition to experiment design, they are further classifiedSponso, ed by the United States Army under Contract No: DA-31-124-ARO-D-462.

into the categories described in sections III and IV. In section III a classificationof treatment designs is presented, and in section III a classification of variousstatistical analyses and of other aspects of experiment and treatment designs isgiven.Bibliographies on the subjects of sections III and IV have been prepared andare to be published in a book, together with the present bibliography and a revisedversion of the pre-1950 bibliography prepared by Federer D1964J.The classification system utilized was to first classify a paper as to whethDrit was chiefly on experiment (experimental) design as E, on treatment design as T,on analyses of experiments as A, on the general conduct of experiments or on specialtopics as C, on bibliographies as related to the design and analysis of experimentsas B, and on sequential and fixed sample size procedures as S.Under each of the main categories of classification as listed above, numbers1,2, .,g15 were used to divide i category into subclasses.A third category ofclassification was to classify a paper as to whether it was on the geneiral conduct,on the application, or on the analysis for an experiment or a treatment design, whichwas coded a, whether it was on the construction procedure for an experiment or atreatment design, which was coded c, or whether the paper contained a numericalexample of an experiment or treatment design which was coded e; this sub-subclassification was utilized for the E and T classifications but not for the A, B, C and 3classifications.As with all bibliographies some references have been omitted accidently andsome publications containing articles on the design and analysis of oxperiments didnot come to the author's attention.Also,the searching was done mostly by title withsome searching being done from summaries or abstracts.In the lattr r;ase the referenceand the checking of the citation came from the abstract.The references at the end-2-#10804

of an artic.19 were scanned to deiermine if any should be included.Quite oftenan entire volume was scanned if it cnntainod one or more appropriate articles forthe bibliography.The following journals were searched in their entirety forreferences tc be included.ography.the title.The abbreviation li.Ged on the right is used in the bibli-The listing is in alphabetical order, omitting articlos and prepositions from(Several additional journals were partially or completely searched.Someof those completely scanned were omitted from the following list because they did notinclude papers on experiment and treatment design.):Agronomy Journal, Vol.42 (1950) to Vol.59 (1967)(U.S,)Agron. JAmerican Society for Quality Control, Technical ConferenceASQC, Tech.Transactions, ninth (1955) to twenty-first (1967) (U.S.)Conf. Trans.The American Statistician, Vol.4 (1950) to Vol.21 (1967) (U.S.)Amer. Stat.Annals of the Institute of Statistical Mathematics, Vol.2(1950) to Vol.19 (1967) (Tokyo, Japan)Ann. Inst.Stat. Math.The Annals of Mathematical Statistics, Vol.21 (1950) toVol.38 (1967) (U.S.)Applied Statistics, Vol.1 (1952) to Vol.16 (1967) (GreatBritain)AppI. Stat.Australian Journal of Agricultural Research, Vol.1 (1950) toVol.18 (1967) (Australia)Australian I.Agri. Res,The Austraiian Journal of Statistics, Vol.1 (1959) to Vol.9a967) (Australia)Australian I.Stat.Biometrics, Vol.6 (1950) to Vol.23 (1967) (International)BiometricsBioemetrie-Praximetrie, Vol.1 (1960) to Vol.3 (1967) (Belgium)BiometrioPraxu mitriebiomietrika, VoI.39 (1950) to Vol.S4 4967) (Great Britain)BiometriksBiorniv.trischz! Zettschrift, Vl.l. (1951) to Vol.9 (1967)(Germany)BMoM. Zeit.Bragantia, Vel .10 (1950) to Vol.2G (1967) (Brazil)Bragantia*48.ln C-3-IAMS3

The British Journal of Statistical Pgychology, Vol.1 (1950)to Vol.19 (1966) (Great Britain)British J. Stat.PsychologyBulletin of the Calcutta Mathematical Society, Vol.42 0950)to Vol.57 (1965) (India)Buil. CalcuttaMath. Soc.Bulletin de l'Institut International de Statistique, Vol.32(1950) to Vol.41 (1966)Bull. ISIBulletin of Mathematical Statistics, Vol.4 (1950) to Vol.12(1967) (Fukuoka, Japan)Bull. Math.Stat.Calcutta Statistical Association Bulletin, Vol.2 (1950) toVol.16 (1967) (India)Calcutta Stat.Assoc. Bull.Canadian Journal of Mathematics, Vol.2 (1950) to Vcl.19(1967) (Canada)Canadian J.Makh.Comptes Rendus, Des Seances de l'Acaddmie des Sciences.Paris, Vol.230 (1950) to Vol.265 (1967) (France)ComptesRendusCrod Science, Vol.1 (1961) to Vol.7 (1967) (U.S.)Crop Sci.Current Science, Vol.19 (1950) to Vol.36 (1967) (India)Current Scd.Der Ztchter, Zeltschrift fUr theoretische und angewandteGenetik, Vol.20 (09 50) to Vol.37 (1967) (Germany)DerZ11chterFstadrstica, joui.aal of the Inter-American StatisticalInstitute, Vol.8 (1950) to Vol.25 (1967)EstadfsticaEuphytica, JouLrnal of Plant Breeding, Voll (1952) to Voi.16(1967) (Nethei-ands)EuphyticaDissertation Abstracts, Vol.i( (1950) to Vol.27 (1967) (U.S.)Dissertation Abs.Genetical Research, Vol.1 (1960) to Vol .10 (1967) (GreatBMUta n)GeneticalRes.Heredity, Vol.4 (1950) to Vol.14 (1960) OGreat iritaln)HeredityIndustrial and Engineering Chemistry, Vcl.42 0950) to Voi.59(1967) (U.S.)Ind. Eng.ChemistryIndustrial Quality Control, Vol.6 0950) to Vol.24 (1967) (U.S.)IQCJournal of the Americanl Statistical Association, Vol.45 0950)to Vol.62 (1967) (U.S.)JASA-4-j#1080-4-

Journal of Combinatorial Theory, Vol.1 (1966) to Vol.3(i367) (U.S.)J. CombirnatorioiTheoryJournal of the Indian Society for Agricultural Statistics,Vol.2 ( J50) to Vol 19 0967) (India)JISASJornlal of the Indian Statistical Association, Vol.1 (1963)to Vol.5 (1967) (India)JISATournal of Research of the National Bureau of Standards,Mt.thematics and Mathematical Physics, SoriesVol.44 (1950) to Vol.71 (1967) (U.S.)B,J. Res.NBSJournal of the Royal Statistical Society, Series A, (General),Vol.113 0.950) to Vol.130 (1967) (Great Britain)JRSSAJournal of the Royal Statistical Society, Serie3 B,(Methodological), Vol.12 (1950) to Vol.29 (1967)(Great Britain)JRSSBJournal of Science of the Hiroshima University, Series A-!NMathematics), Vol.17 (1953) to Vol.31 (1967) (Japan)J. Sci. HiroshimaUniv. Ser. A-IJournal of the Society for Industrial and Applied Mathematics,Vol.1 (1953) to V4.5(1967)(U.S.)J. Soc. Ind.Appl. Math.Mathematics of Computation from 1960, formerly wasMathematical Tables and Aids to Computation, Voi.4(1950) to Vol.21 0967) (U.S.)Math. TablesAids Comp.orMath. Comp.Meihoramento, Estudos da Estaq-o de Melhoramento dePlantas, Vol.4 (1959) to Vol.16 (1963) (Portugal)MelhoramentoMemoirs of the Faculty of Science, Serias A (Mathematics),KylishU University, Vol.6 (1951.) to Vol.21 (1967)(Fukuoka, Japan)Mere. FacultySci.Methods of Information in Medicine, Methodik derInformationin der Medizin, Vol.l 0962) to Vol.5(1966) (Germany)Meth.Med. Inf.Metrika, International Jounial for Theoretical and AppliedStatistics, Vol.1 (1958-) to Vol.12 (1967) (Germany)MetrikaMetron, International Review of Statisticq, Vol.,. to Vol.26 (1967) (France)Metron(1950)Mitteilungsbiatt fUr Mathematiache StalisLik (becameMetrika). Vol.4 (1952) to Vol.9 0957) (Germany)1I0800IMAtteilungablattMath. Stat.-58

Plant Breeding Abstracts, Vol.20 (1950) to Vol.37 (1967)(U.S.)Pl. Br.Abs .Proceedings of the American Mathematical Society, Vo'L.1(1950) to Vol.18 (1967) (U.S.)Proc. Amer.Math. Soc.Proceedings of the American Society for Horticultural Lotence,Vol.55 (1950) to Vol.91 (1967) (U.S.)Proc. Amar.Soc. 1-ort. Sdi.Proceedings of the nth Conference on the Design of Experiments in Army Research Development and Testing, Vol.1(1957) to Vol.12 (196?) (U.S.)Proc. Conf.Design Expt.Army Res. Dev.TestingProceedings of the kth Berkeley Symposium on MathematicalStatis tics and ProbabilityProc. kth BerkeleySymp. Math. Stat.Prob.Psychometrika, Vol.15 (1950) to Vol.32 (1967) (U.S.)PsychometrixaPublications de l'Institut de Statistique de 1'Universitede Paris, V61.1 (1952) to Vol.16 (1967) (France)Pub. Inst. Stat.Univ. ParisQuality Control and Applied Statistics (Abstracts)Vol.11 (1966) to Vol.12 (1967) (U.S.)QC Appi.Stat.Reports of Statistical Application Research, U nion ofJapanese Scientists and Engineers. Vol.1 (1951-2)to Vol.14 (1967) (Japan)ReportsStat. Appl.Res .Revue de l'Institut International de Statistique, Vol.18(1950) to Vol.35 (1967) (International)Rev. ISIRevue de Statistique Appliqu e, Institut de StatIstiqueUniversite de Paris. Vol.1 (1953) to Vol.15 (1967)(France)Rev. Stat.Appl.Sankhy35, The Indian Journal af Statistics, Vol.10 (1950)to Vol.29(1967) (India)SankhySStatistica Neerlandica (named Statisticat prior to Vol. 91955) Vol.4 (1950) to Vol.21 (1967) (Netherlands)StatisticaorStat. NeerlandicaSuid-Afrikaanse Tydskrif vir Landbouwetenskap, Vol .1(1958) to Vol.10 (1967) (South rics, Vol.1 (1959) to Vol.9 (1967) (U.S.)Technornetrics,-6Li-#1080

Trai-ajoy de Estadfistica, Vol.1 (I95O) to Vol.15 (1964)TrabaJosEstad.Zeitschrift far PflanzenzUchtung, Vol.29 (1950) to Vol.58(1967) (Gernmany)Z. Pflanzenzilchtu ngin addition to the above journals the following books and special publicationsccrntainlng a seties of papers represent some of the other sources scanned for paperson experiment design:Riornetrical GeneticsBulletin de l'Institut Agronomique et des Stations de Recherches de Gembloux(Hors Serie) 1960, Volume 1.Cold Spring Harbor Symposia on Quantitative Biol y, Proceedings.Collocues Internationaux du Centre National de la Recherche Scientifioue,No. 10. Le Plan d'bcperience.Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling.Contributions to Statistics: Presented to Professor P. C. Mahalanobis on theOccasion of his 70th BizLhday.Economic and Technical Analysis of Fertilizer Innovations and Resource Use.E.,perii,.ental Designs in Industry.Heterosis.Mathematics and Computer Science in Biologoand Medicine.Statistical Genetics and Plant Breeding. NAS.Statistical Theory of Reliability.Statistics and Mathrmatics in Bioloqy.Stochastic Models in Medicine and Biolo.*1080-7-

II.EXPE.IMENT OR EXPERIMENTAL DESIGNIn the published literature two terms, experimental design and experimentdesign, have been utilized to refer to the arrangement uf treabments in a comparativeexperiment.Perhaps the term experiment design is better grammatical form incomparison with the term treatment design.aAlso, published literature is highlyconfused on the use of the term experimental design in that this term has been usedfor almost all statistical aspects of experimentation from the selection or samplesize and of treatments to the -:onduct and analyses of experiments.This would beone reason for discarding the term experimental design and for using the term experiment design.In general, experiment designs are classified into designs with zero-way,one-way, two-way, etc. elimination of heterogeneity in experimentation.(Asmay be noted from published literature, e.g. reference 2194, one alternate form ofclassification is to denote these designs as one-dimensional, two-dimensional,three-dimensional, etc., respectively; other classifications have been devised.)This refers to the type of blocking in an experiment.The categorization can resultin some confusion for such designs as the split plot (or the split block) experimentdesigns and the lattice square experiment design.The latter experiment design isclassified as having three-way elimination of heterogeneity, i.e., complete blocksand rows and columns within each complete block.using only one-way blocking are possible.In the split-block design analysesSimilarly in a resolvable balanced in-complete block design, an intrablock analysis on treatments and residual is possiblewithout considering the fact that complete blocks were designed into the experiment.-8-1080

The various subclassifications of expeilment designs are listed below asEl, E2, . , E14.1. Zero-way elimination of heterogeneityEli) completely randomized design including*experiments for which the treatments maybe grouped in various ways.2. One-way elimination of heterogeneityE2i) balanced-randomized complete block-balanced incomplete block,both resolvable and noniesolvable.ii) partially balanced-circular-cyclic-group divisible-rectangular lattices-right angular-triangularE3-2, 3, . ., n associate classiii) other incomplete block designs-augmented-calibration-chain block-direct product-extended incomplete block-linked block-reinforced-repetitions of designs with sama treatmentsE4-slipped block-staircase-star-unequal block sizes-unequal replication on treatmentsiv) others-blocking on a trend or gi .dient-constrained randomizationES-n-ary-rotation and -other serially correlated-simple changeover#1080-simple multiresponse-split plot (whole plots in a completelyrandomized design)-supercomplete-systematic-9-

v) missing, mixed-up, or damaged experimentalunits (plots)E63. Two-way elimiiation of heterogeneityi) row-column designs-gradients within blocks for designs withone-way elimination of heterogeneity-latin square and generalized latin square-simple change-over-tied-latin squares-Youden square and extended Youden square-other latin rectangle or row-columnE7ii) row-column designs to measure residual effects-double change-over-rotation-tied double change-overE8iii) others-augmented-balancing in two groups-direct product-multtvariate hierarchical-nested balance-plaid and half-plaid latin square-quasi-latin square-Trojan squareE9iv) missing, mixed-up, or damaged plotsEIO4. Three-way elimination of heterogeneity-i) lattice square, lattice rectangle, and latincube (including missing, mixed-up, anddamaged plots)EllA) others-augmented-graeco-latin square-latin cubemagic latin square,uasi-latin square-split block (or criss-cross)-split and split-split plot-U:VW and U:VW:XYZ plans for two setsof treatmentsE12#1080

S.Four and higher-w.v elimination of heterogeoelty-latin square and cube-hyper-gree-lattice square with split plots-t-restrictional lattice-multidimensional-split, splitsplit. plotE136.Properties of experiment designs-balance and partial zation-replication-sensitivity-othersE14Each of the above categories (except for El4) were frither classified asa , c, arid/or e.The a refers to application and/or analysis, the c refers toconstruction, and the e refers to a numericcl example (mostly nonfictitious)for a particular experiment design.#1080-11-

HII.TRt,&TMENT DESIGNTreatment design reiers to the selection of treatments in an experiment.Many writers in statistical literature, nave used the term experimental designor design of experiments in their discussion oi treatment designs.to some confusion.This has leadThis usage has been espezlally prevalent in connection withfactorial and fractional actoiai reatment designs and sample size determinations.The following classification of treatment designs has been utilized to classifystatistical publications:1. Sek tion f X val.ies a-nd of the X variables inregret sion studies.TI2.Factorial-complete factorial-corfounding in factorial experiments-mixed and fixed effects excluding variancecomponent analysis-quantity x quality interactionT23.Fractional replicationj) reguiar fractions (on-y complete conxfoundingof effects itl aliasing structure)ii)other fractions-response surface, rotatable, centralcomposite, steepest ascent, EVOP,T3T4response curves, PARTAN-12--sinplex, vertices, mixtures, constrainedT5-weighingT6-others (additional or missing r-ombinations,group testing, random balance, randomizedfactorials, compiementation, screenL.- Xvariables)T7iij.) Dosage response (sequential and fixed)TOiv)T9Genetic (diallel crossing systems, parents andcrosses, other genetic treatment designs)#1080

v) Paired, tripled,4.,k -minimum variance, trace, determinant, etc.*-orthogonality-rotatability-unbiasedTiITIOAs with experiment designs, the treatment design categories (except TIO)were further subdivided into the a, c, and e, where these symbols have thesame meaning as for experiment designs.j#1080-13-

IV.TOPICS RELATED TO THE CONDUCT OF EXPERIMENTS ANDON THE ANALYSIS OF EXPERIMENT AND TREATMENT

Canadian Journal of Mathematics, Vol.2 (1950) to Vcl.19 Canadian J. (1967) (Canada) Makh. Comptes Rendus, Des Seances de l'Acaddmie des Sciences. Comptes Paris, Vol.230 (1950) to Vol.265 (1967) (France) Rendus Crod Science, Vol.1 (1961) to Vol.7 (1967) (U.S.) Crop Sci. Current Science, Vol.19 (1950) to Vol.36 (1967) (India) Current Scd. Der .

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