同时在这段期间,他也发表了许多与生物统计相关的论文,包括《孟德尔遗传假定下的亲戚之间的相关性》(The Correlation Between Relatives on the Supposition of Mendelian Inheritance)。这篇论文在1916年完成,并在1918年发表,它同时建立了以生物统计为基础的遗传学,以及著名的统计学分法变异数分析(analysis of variance,简写为ANOVA,也称方差分析)。除了建立统计方法,这篇论文也显示,一些具有连续性变异的遗传特征,可以符合孟德尔遗传定律。在此以前,两者被科学家认为是互相违抗。他一生在统计和生物的研究兴趣与才华,已经清楚地表现出来。
科学的奠基人
1918年战争结束之后,原本皮尔森邀请他进入当时著名的高尔登实验室(Galton Laboratory),但是由于费希尔认为自己与皮尔森之间的竞争关系是一种职业障碍,因此放弃了这个机会。1919年他任职于 Rothamsted 农业实验场(Rothamsted Experimental Station)。这间农业试验所,位在英格兰赫特福德郡(Hertfordshire)的哈平登(Harpenden)。费希尔除了在其中担任一名统计员之外,所长约翰·罗素(John Russell)也让他设立了一个统计实验室。之后费希尔便开始对多年来所收集的大量资料进行深入研究,并且将成果写成一系列题为《收成变异之研究》(Studies in Crop Variation)的论文。他的全盛时期也在这时候开始。
他负责的主要工作是植物播殖实验的设计,希望透过尽量少的时间、成本与工作量,得到尽量多的有用资讯;另外是要整理该实验场60年来累积的实验资料。Fisher 在这里发展他的变异数分析理论,研究假说测试,并且提出实验设计的随机化原则,使得科学试验可以同时进行多参数之检测,并减少样本偏差。他在1925所著《研究工作者的统计方法》(Statistical Methods for Research Workers)影响力超过半世纪,遍及全世界。而他在 Rothamsted 的工作结晶,同时也表现在为达尔文演化论澄清迷雾的巨著《天择的遗传理论》(The Genetical Theory of Natural Selection)(1930)中,说明孟德尔的遗传定律与达尔文的理论并不像当时部份学者认为的互相矛盾,而是相辅相成的。并且认为演化的驱力主要来自选择的因素远重於突变的因素。这本著作将统计分析的方法带入演化论的研究。为解释现代生物学的核心理论打下坚实的基础。也因这本著作,Fisher 1933年获得伦敦大学的职位,从事 RH 血型的研究。1943至1957年他回剑桥大学任教,1952年受封爵士,1956年出版《统计方法与科学推断》(Statistical methods and scientific inference),最后三年,则在澳洲为国协科技研究组织 (CSTRO) 工作,并卒于任上。
著作
书籍
全部著作信息详见University of Adelaider网站 :
•《研究工作者的统计方法》Statistical Methods for Research Workers (1925) ISBN 0-05-002170-2.
•《天择的遗传理论》The Genetical Theory of Natural Selection (1930) ISBN 0-19-850440-3.
•《实验的设计》The Design of Experiments (1935) ISBN 0-02-844690-9
•The use of multiple measurements in taxonomic problems (in Annals of Eugenics 7/1936)
•《统计学用表》Statistical tables for biological, agricultural and medical research (1938, 与Frank Yates合著)
•《育种理论》The theory of inbreeding (1949) ISBN 0-12-257550-4, ISBN 0-05-000873-0
•Contributions to mathematical statistics, John Wiley, (1950)
•《统计方法与科学推断》Statistical methods and scientific inference (1956) ISBN 0-02-844740-9
•Collected Papers of R.A. Fisher (1971–1974). Five Volumes. University of Adelaide.
论文
•"Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population." Biometrika, 10: 507–521. (1915) doi:10.1093/biomet/10.4.507
•"The correlation between relatives on the supposition of Mendelian inheritance" Trans. Roy. Soc. Edinb., 52: 399–433. (1918). It was in this paper that the word variance was first introduced into probability theoryand statistics.
•"On the mathematical foundations of theoretical statistics" Philosophical Transactions of the Royal Society, A, 222: 309–368. (1922) doi:10.1098/rsta.1922.0009
•"On the dominance ratio". Proc. Roy. Soc. Edinb., 42: 321–341. (1922)
•"On a distribution yielding the error functions of several well known statistics" Proc. Int. Cong. Math., Toronto, 2: 805–813. (1924)
•"Theory of statistical estimation" Proceedings of the Cambridge Philosophical Society, 22: 700–725 (1925)doi:10.1017/S0305004100009580
•"Applications of Student's distribution" Metron, 5: 90–104 (1925)
•"The arrangement of field experiments" J. Min. Agric. G. Br., 33: 503–513. (1926)
•"The general sampling distribution of the multiple correlation coefficient" Proceedings of Royal Society, A,121: 654–673 (1928) doi:10.1098/rspa.1928.0224
•"Two new properties of mathematical likelihood" Proceedings of Royal Society, A, 144: 285–307 (1934)doi:10.1098/rspa.1934.0050
语录
“I believe sanity and realism can be restored to the teaching of Mathematical Statistics most easily and directly by entrusting such teaching largely to men and women who have had personal experience of research in the Natural Sciences.”
"In scientific subjects, the natural remedy for dogmatism has been found in research."
"The tendency of modern scientific teaching is to neglect the great books, to lay far too much stress upon relatively unimportant modern work, and to present masses of detail of doubtful truth and questionable weight in such a way as to obscure principles."