Introduction to Fisher (1926) The Arrangement of Field Experiments

  • T. P. Speed
Part of the Springer Series in Statistics book series (SSS)


In 1919, the Director of Rothamsted Experimental Station, Sir John Russell, invited Ronald Aylmer Fisher, a young mathematician with interests in evolution and genetics, to join the small group of scientists at Rothamsted in order that [see Russell (1966, p. 327)] “after studying our records he should tell me whether they were suitable for proper statistical examination and might be expected to yield more information than we had extracted.” Fisher accepted the invitation and in a very short time Russell realized (loc. cit.) “that he was more than a man of great ability; he was in fact a genius who must be retained.” In the few years that followed, Fisher introduced the subdivision of sums of squares now known as an analysis of variance (anova) table (1923), derived the exact distribution of the (log of the) ratio of two independent chi-squared variates (1924), introduced the principles of blocking and randomization. as well as the randomized block, Latin square, and split-plot experiments, the latter with two anova tables (1925), promoted factorial experiments, and foreshadowed the notion of confounding (1926). Of course Fisher made many contributions to theoretical statistics over this same period [see Fisher (1922)], but the above relate directly to the design and analysis of field experiments, the topic of the paper that follows. It was an incredibly productive period for Fisher, with his ideas quickly transforming agricultural experimentation in Great Britain and more widely, and in major respects these ideas have remained the statistical basis of agricultural experimentation to this day.


Rothamsted Experimental Station Field Experi Young Mathematician Commonwealth Agricultural Bureau Sugar Beet Variety 
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  1. Arnold. G.C. (1985). The Hudson-Gosset correspondence. The New Zealand Statistician. 20. 20–25.Google Scholar
  2. Barbacki, S., and Fisher. R.A. (1936). A test of the supposed precision of systematic arrangements, Ann. Eugen., 7, 189–193.CrossRefGoogle Scholar
  3. Box. J. F. (1978). R.A. Fisher. The Life of a Scientist. Wiley. New York.Google Scholar
  4. Cochran, W.G., (1976). Early development of techniques in comparative experimentation. in On the History of Statistics and Probability ( D.B Owen. ed.). New York: Marcel Dekker, pp. 3–25.Google Scholar
  5. Davis, A W., and Speed. T.P. (1988). An Edgeworth expansion for the distribution of the F-ratio under a randomization model for the randomized block design, in Statistical Decision Theory and Related Topics IV, vol. 2. (S.S. Gupta, and J.O. Berger, eds.). Springer-Verlag. New York, pp. 119 –130.CrossRefGoogle Scholar
  6. Eden, T., and Yates, F. (1933). On the validity of Fisher’s i test when applied to an actual sample of non-normal data, J. Agric. Sci., 23. 6–17.CrossRefGoogle Scholar
  7. Fisher, R.A. (1918). The correlation between relatives on the supposition of Mendelian inheritance. Trans. Roy. Soc. Edinburgh. 52,399–433. (reprinted with a commentary by P.A.P. Moran and C.A.B. Smith as Eugenics Laboratory Memoir XLI. Cambridge University Press, London. 1966 ).Google Scholar
  8. Fisher, R.A. (1922). On the mathematical foundations of theoretical statistics, Philos. Trans. Roy. Soc., Lon. Ser. A. 222. 309–368.CrossRefGoogle Scholar
  9. Fisher. R.A. (1923). Appendix to Gosset (1923).Google Scholar
  10. Fisher, R.A. (1924). On a distribution yielding the error functions of several well known statistics, Proc. Internal. Congress. Math. Toronto, 2. 805–813.Google Scholar
  11. Fisher, R.A. (1925). Statistical Methods for Research Workers, Oliver and Boyd. Edinburgh.Google Scholar
  12. Fisher, R.A. (1935). The Design of Experiments. Oliver and Boyd, Edinburgh.Google Scholar
  13. Fisher, R.A., and Mackenzie. W.A. (1923). Studies in crop variation. II. The manurial response of different potato varieties, J. Agric. Sci., 13, 311–320.CrossRefGoogle Scholar
  14. Fisher, R.A., and Wishart. J. (1930). The arrangement of field experiments and the statistical reduction of the results. Imperial Bur. Soil Sci., Tech. Comm., 10. 23.Google Scholar
  15. Gosset, W S. (“Student”) (1923). On testing varieties of cereals. Biometrika, 15, 271– 293.Google Scholar
  16. Gosset, W S. (“Student”) (1931). Yield trials, in Baillièré’s Encyclopedia of Scientific Agriculture, London, [reprinted as paper 15 in Gosset (1942)].Google Scholar
  17. Gosset. W.S. (“Student”) (1936a). Cooperation in large-scale experiments, J. Roy. Statist. Soc., Suppl., 3. 115–122CrossRefGoogle Scholar
  18. Gosset. W.S. (“Student”) (1936b). The half-drill strip system, Agricultural experiments, letter to Nature, 138, 971.Google Scholar
  19. Gosset. W.S. (“Student”) (1937–8). Comparison between balanced and random arrangements of field plots. Biometrika. 29, 191–208.Google Scholar
  20. Gosset, W.S. (1942). “Student’s” Collected Papers (E.S. Pearson and J. Wishart. eds., with a foreword by L. McMullen). Biometrika Office, University College. London.Google Scholar
  21. Gosset, W.S. (1970). Letters from W.S. Gosset to R A. Fisher ( 1915–1936 ) ( Summaries by R.A. Fisher with a foreword by L. McMullen ). Private circulation.Google Scholar
  22. Goulden, C H. (1931). Modem methods of field experimentation. Scientif. Agri., 11, 681.Google Scholar
  23. Gregory, F.G., Crowther. F. and Lambert, A.R. (1932). The interrelation of factors controlling the production of cotton under irrigation in the Sudan, J. Agric. Sci., 22, 617.Google Scholar
  24. Haines. W.B. (1929). Block 6. Manuring experiment. RRI Experiment Station. First report, Quar. J. Rubber Res. Inst. Malaya., 1. 241–244.Google Scholar
  25. Haines. W.B. (1930a). Block 6. Manuring experiment, RRI Experiment Station. Sec¬ond report. Quar. J. Rubber Res. Inst. Malaya., 2. 31–35.Google Scholar
  26. Haines, W.B. (1930b). Manuring of Rubber—II. Technique of plot experimentation, Quar. J Rubber Res. Inst. Malaya., 2, 51–60.Google Scholar
  27. Hall. A.D. (1925). The principles of agricultural experiments. J. Min. Agric. Great Britain, 32. 202–210.Google Scholar
  28. Hall, P., and Selinger, B. (1986). Statistical significance: Balancing evidence against doubt. Austral. J. Statist., 28, 354–370.zbMATHCrossRefGoogle Scholar
  29. Harrison, C J., Bose, S.S.. and Mahalanobis. P.C. (1935). The effect manurial dressing, weather conditions and manufacturing processes on the quality of tea at Tocklai experimental station, Assam. Sankhyā. 2. 33–42.Google Scholar
  30. Hotelling. H. (1951). The impact of R.A. Fisher on statistics. J. Amer. Statist. Assoc., 46. 35–46.zbMATHCrossRefGoogle Scholar
  31. Kempthorne. O. (1952). The Design and Analysis of Experiments. Wiley. New York.zbMATHGoogle Scholar
  32. Kerr. J.D. (1988). Introduction of statistical design and analysis by the Ouccnsland Board of Sugar Experiment Stations, Austral. J. Statist., 30B, 44–53.MathSciNetGoogle Scholar
  33. Kirk. L.E. (1929). Field plot technique with potatoes with special reference to the Latin square, Scientif. Agri., 9. 719–729.Google Scholar
  34. Mahalanobis. P.C. (1938). Professor Ronald Aylmer Fisher, Sankhyā, 4. 265–272.Google Scholar
  35. Mead, R. (1988). The Design of Experiments: Statistical Principles for Practical Applications. Cambridge University Press. New York.Google Scholar
  36. Mercer. W.B.. and Hall. A.D. (1911). The experimental error of field trials, J. Agric. Sci., 4, 107–132.CrossRefGoogle Scholar
  37. Neyman. J. (1967). R.A. Fisher (1890–1962): An appreciation. Sci., 156. 1456–1460.CrossRefGoogle Scholar
  38. Neyman, J. (1990). On the application of probability theory to agricultural experi¬ments. Essay on principles. Statist. Sci. 5, 465–480. (translation from the original Polish. Rocz. Nauk. Roln X (1923) pp. 27–42 by D. Dabrowska. T.P. Speed, ed.).Google Scholar
  39. Patterson, H.D.. and Silvey. V. (1980). Statutory and recommended list trials of crop varieties in the United Kingdom. J. Roy. Statist. Soc., Ser. A., 143. 219–252CrossRefGoogle Scholar
  40. Patterson. H.D.. Williams, E.R., and Hunter, E.A. (1978). Block designs for variety trials. J. Agric. Sci. Cambridge. 90. 395–400.Google Scholar
  41. Pearce, S.C. (1983). The Agricultural Field Experiment. A Statistical Examination of Theory and Practice. Wiley, New York.Google Scholar
  42. Pitman. E.J.G. (1938). Significance tests which may be applied to samples from any populations: III. The analysis of variance tests, Biometrika, 29, 322–335.zbMATHGoogle Scholar
  43. Richey, F.D. (1930). Some applications of statistical methods to agronomic experiments, J. Amer. Statist. Assoc., 25. 269–283.CrossRefGoogle Scholar
  44. Russell. E.J. (1926). Field experiments: How they are made and what they are. J. Min. Agric. Great Britain. 32. 989–1001.Google Scholar
  45. Russell, E.J. (1966). A History of Agricultural Science in Great Britain. George Allen & Unwin. London.Google Scholar
  46. Savage, LJ. (1976). On rereading R.A. Fisher (J.W. Pratt, ed.). Ann. Statist., 4.441–500.Google Scholar
  47. Seal, H. (1967). The historical development of the Gauss linear model, Biometrika, 54, 1–24.MathSciNetzbMATHGoogle Scholar
  48. Seeger, P., Kristensen, K., and Norell, L. (1987). Experimental designs in two dimensions for official sugar beet variety trials in Scandinavia. Report 286, Department of Economics and Statistics, Svcngcs Lantbruksuniversitet (Swedish University of Agricultural Sciences), Uppsala.Google Scholar
  49. Snedecor, G.W. (1934). Computation and Interpretation of Analysis of Variance and Covariance. Collegiate Press, Ames, Iowa.Google Scholar
  50. Tippett, L.H.C. (1935). Some applications of statistical methods to the study of varia¬tion of quality in the production of cotton yarn, J. Roy. Statist. Soc. Suppl., 2, 27–62.CrossRefGoogle Scholar
  51. Wald, A., and Wolfowitz J. (1944). Statistical tests based on permutations of the observations. Ann. Math. Statist., 15, 358–372.MathSciNetzbMATHCrossRefGoogle Scholar
  52. Welch, B.L. (1937). On the r-test in randomized blocks and Latin squares, Biometrika, 29, 21–51.zbMATHGoogle Scholar
  53. Wilkinson, G.N., Eckhart, S.R., Hancock, T.W., and Mayo, O. (1983). Nearest neighbour (NN) analysis of field experiments (with discussion), J. Roy. Statist. Soc., Ser. B. 45. 151–211.zbMATHGoogle Scholar
  54. Williams, E.R., and John. J.A. (1989). Construction of row and column designs with contiguous replicates, Appl. Statist., 38. 149–154.MathSciNetCrossRefGoogle Scholar
  55. Wishart, J. (1935). Contribution to the discussion of Tippett (1935). pp. 58–59.Google Scholar
  56. Wood, T.B., and Stratton, FJ.M. (1910). The interpretation of experimental results, J. Agric. Sci.. 3. 417–440.CrossRefGoogle Scholar
  57. Yates, F. (1939). The comparative advantages of systematic and randomized arrange¬ments in the design of agricultural and biological experiments. Biometrika, 30, 440–466.Google Scholar
  58. Yates, F. (1964). Sir Ronald Fisher and the design of experiments. Biometrics, 20, 307–321.CrossRefGoogle Scholar
  59. Yates, F. (1965-66). A fresh look at the basic principles of the design and analysis of experiments, in Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability, Vol. 4. Berkeley: University of California Press. (J. Neymanand E.L. Scott, eds.) pp. 777–790.Google Scholar
  60. Yates. F. (1975). The early history of experimental design, in A Survey of Statistical Design and Linear Models (J.N. Srivastava, ed.) North-Holland. Amsterdam: pp. 581–591Google Scholar
  61. Yates, F.. and Mather. K.. (1965). Ronald Aylmer Fisher. Biographical Memoirs of Fellows of the Roy. Soc., 9, 91–120.CrossRefGoogle Scholar
  62. Younden. W.J. (1951). The Fisherian revolution in methods of experimentation, J. Amer. Statist. Assoc., 45, 47–50.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1992

Authors and Affiliations

  • T. P. Speed
    • 1
  1. 1.University of California at BerkeleyUSA

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