Örnekleme dağılımlarının tarihsel gelişimi: Ki-kare, t ve F dağılımları

Year 2023, , 96 - 109, 15.01.2023

Hakan Serin , Seyit Mehmet Taşdelen , Davut Seyhan , Tamer Çağlayan , Mehmet Emin Tekin

https://doi.org/10.33188/vetheder.1177510

Abstract

Örnekleme dağılımlarının temelini oluşturan Ki-kare, t ve F dağılımlarını sırasıyla Karl Pearson, William Sealy Gosset ve Ronald Aylmer Fisher istatistik bilimine kazandırmıştır. Karl Pearson, normal dağılım göstermeyen veriler için o dönemde yaptığı çalışmalar sonucu Ki-kare dağılımını elde etmiştir. Sonraki yıllarda Fisher, Ki-kare dağılımı üzerine yaptığı çalışmalar ile serbestlik derecesinde bir düzeltme yapmıştır. Bu durum Karl Pearson tarafından hoş karşılanmamış ancak çevresindeki bilim insanlarının etkisiyle bu modifikasyonu kabul etmek zorunda kalmıştır. Ayrıca, Fisher z dağılımının normalliği ile ilgili çalışmalar yapmış, bu konuda makale yazmış ve “Biometrika” dergisine göndermiştir. Ancak dönemin ünlü istatistik dergisi olan “Biometrika”ya başkanlık yapan Karl Pearson Fisher ile arasındaki rekabetten dolayı makalesini geri çevirmiştir. William Sealy Gosset o dönemde ünlü bir bira fabrikasında istatistikçi olarak çalışırken en iyi kalite ve verime sahip arpaları tespit etmek için yaptığı çalışmalar sonucu t dağılımını keşfetmiştir. Gosset’e mektup yazan Fisher, t dağılımında standart sapma hesaplamasında bir düzeltme tavsiye etmiştir. Bununla birlikte, Fisher makalelerinde t dağılımına değinerek t dağılımının bilim dünyasına tanıtımına katkıda bulunmuştur. Ronald Aylmer Fisher Rothamsted’ta mahsul çalışmaları yaparken mevcut yöntemlerin yetersizliği ile karşılaşmış ve t dağılımından yola çıkarak yaptığı çalışmalar sonucu F dağılımını keşfetmiştir. F dağılımının keşfi ile birlikte ileri düzey veri analizinde yeni bir dönem başlamıştır.

Keywords

İstatistik Dağılımlar, ANOVA, Örnekleme Çalışmaları, Olasılık Fonksiyonları, Yaşam öyküsü

Historical development of sampling distributions: Chi-square, t and F distributions

Abstract

Karl Pearson, William Sealy Gosset, and Ronald Aylmer Fisher introduced the Chi-square, t and F distributions, which form the basis of the sampling distributions, to the science of statistics, respectively. Karl Pearson obtained the Chi-square distribution for the data that did not show normal distribution as a result of his studies at that time. In the following years, Fisher made a correction in the degrees of freedom with his studies on the chi-square distribution. This situation was not welcomed by Karl Pearson, but he had to accept this modification under the influence of the scientists around him. In addition, Fisher conducted studies on the normality of the z distribution, wrote an article on this subject and sent it to the “Biometrika” journal. However, he rejected his article due to the rivalry between him and Karl Pearson Fisher, who was the chairman of the famous statistical journal of the time, “Biometrika”. William Sealy Gosset, while working as a statistician at a famous brewery at that time, discovered the t distribution as a result of his studies to determine the best quality and yield barley. Writing to Gosset, Fisher recommended a correction in the calculation of the standard deviation of the t distribution. However, Fisher contributed to the introduction of the t distribution to the scientific world by referring to the t distribution in his articles. Ronald Aylmer Fisher, while doing crop studies in Rothamsted, encountered the inadequacy of the existing methods and discovered the F distribution as a result of his studies based on the t distribution. With the discovery of the F distribution, a new era has begun in advanced data analysis.

Keywords

Statistical Distributions, ANOVA, Sampling Studies, Biography, Likelihood Functions

References

• Magnello ME. Karl Pearson and the establishment of mathematical statistics. international statistical review. 2009;77(1):3-29.
• Provine WB. The origins of theoretical population genetics. The origins of theoretical population genetics: University of Chicago Press; 2020.
• Norton BJ. Karl Pearson and statistics: The social origins of scientific innovation. Social studies of science. 1978;8(1):3-34.
• Pearson K. Karl Pearson: The Scientific Life in a Statistical Age. 2004.
• Pearson ES. Karl pearson. An Appreciation of Some Aspects of His Life Cambridge: Cambridge University. 1938.
• Porter TM. Karl Pearson. British mathematician. 2022;2022(20.05.2022).
• Yule GU, Filon LNG. Karl Pearson, 1857-1936. The Royal Society London; 1936.
• Magnello ME. Karl Pearson's Gresham lectures: WFR Weldon, speciation and the origins of Pearsonian statistics. The British journal for the history of science. 1996;29(1):43-63.
• Pearson K. Notes on the history of correlation. Biometrika. 1920;13(1):25-45.
• Magnello ME. Karl Pearson's mathematization of inheritance: from ancestral heredity to Mendelian genetics (1895–1909). Annals of Science. 1998;55(1):35-94.
• Öğüş E. To be Together Medicine and Biostatistics in History. Türkiye Klinikleri Biyoistatistik. 2017;9(1):74-83.
• Pearson E. Pearson, Karl. An Appreciation of some aspects of his Life and Work, Part II. 1906;1936:181-218.
• Cain J. Karl Pearson praised Hitler and Nazi Race Hygiene. 2022.
• Magnello ME. karl pearson, paper on the chi square goodness of fit test (1900). Landmark Writings in Western Mathematics 1640-1940: Elsevier; 2005. p. 724-31.
• Pearson K. b. 27 March 1857-d 27 April 1936. 1936.
• Rao CR. R. A. Fisher: The Founder of Modern Statistics. Statistical Science. 1992;7(1):34-48, 15.
• Fisher RA. The genetical theory of natural selection. Clarendon. Oxford; 1930.
• Yates F. Sir Ronald Aylmer Fisher (1890-1962). JSTOR; 1962.
• Baykul Y. İstatistik: Metodlar ve uygulamalar: Anı Yayıncılık; 1999.
• Gürsakal N. Çıkarımsal istatistik: SPSS-MINITAB uygulamalı: Dora Yayıncılık; 2009.
• Adıbelli R. Katolik-Laik Tartışması Bağlamında Ortaya Çıkan Bir Disiplin Olarak Fransa’da Dinler Tarihinin Oluşum Süreci. Çukurova Üniversitesi İlahiyat Fakültesi Dergisi (ÇÜİFD). 2011;11(2):149-92.
• Ayfer G. Onyedi Ve Onsekizinci Yüzyıl Düşünürlerinde Baskıya Karşı Direnme. Journal of Istanbul University Law Faculty. 2011;35(1-4):49-73.
• Breathnach CS. Student. Irish Journal of Psychological Medicine. 1993;10(3):164-5.
• Faraj QM. On altıncı yüzyıl Fransasında dini reformlar: Kahramanmaraş Sütçü İmam Üniversitesi, Sosyal Bilimler Enstitüsü; 2017.
• Kemp CD, Pearson ES, Plackett RL, Barnard GA, editors. Student: A Statistical Biography of William Sealy Gosset1990.
• Boland PJ. A Biographical Glimpse of William Sealy Gosset. The American Statistician. 1984;38(3):179-83.
• Mane A. From a brewer to the faraday of statistics: William Sealy Gosset. Muller Journal of Medical Sciences and Research. 2016;7:147.
• Chan M, Lai J, Kolovos E, Bibra P. Wıllıam Sealy Gosset: A Hıstory Of Beer And Statıstıcs. 2017.
• Raju TNK. William Sealy Gosset and William A. Silverman: Two “Students” of Science. Pediatrics. 2005;116(3):732-5.
• Boland PJ, editor William Sealy Gosset–An Inspiring ‘Student’. Proc 58th World Statistical Congress (Session STS028), Int Statistical Inst, Dublin; 2011.
• Pearson ESGWSPRLBGA. Student : a statistical biography of William Sealy Gosset. Oxford; New York: Clarendon Press ; Oxford University Press; 1990.
• Student. On the Error of Counting with a Haemacytometer. Biometrika. 1907;5(3):351-60.
• Mather K. “Student's” Collected Papers. Nature. 1943;152(3863):551-2.
• Vyas SA, Desai SP. The Professor and the Student, Sir Ronald Aylmer Fisher (1890–1962) and William Sealy Gosset (1876–1937): Careers of two giants in mathematical statistics. Journal of Medical Biography. 2015;23(2):98-107.
• Wojnar R. Student’s t-Distribution versus Zeldovich–Kompaneets Solution of Diffusion Problem. Integration. 2012;510(1):15.
• Box JF. Guinness, Gosset, Fisher, and small samples. Statistical science. 1987:45-52.
• Rumsey DJ. Statistics essentials for dummies: John Wiley & Sons; 2010.
• Kim TK. T test as a parametric statistic. Korean journal of anesthesiology. 2015;68(6):540-6.
• Pilling M. Handbook of Statistical Distributions with Applications 2nd edn K. Krishnamoorthy, 2016 Boca Raton, CRC Press 376 pp.£ 69.99 (hardbound);£ 66.49 (e-book) ISBN 978-1-584-88635-8. 2017.
• Zabell SL. On student's 1908 article “the probable error of a mean”. Journal of the American Statistical Association. 2008;103(481):1-7.
• Gürtan K. İstatistik ve araştırma metotları: İstanbul Üniversitesi; 1971.
• Mahalanobis P. Professor Ronald Aylmer Fisher. Biometrics. 1964;20(2):238-52.
• Rao C. Life and work of Ronald Aylmer Fisher. Journal of Statistical Theory and Practice. 2007;1(3-4):489-99.
• Fisher RA, Owen A. An Appreciation of the Life and Work of Sir Ronald Aylmer Fisher: FRS, FSS Sc. D. Journal of the Royal Statistical Society Series D (The Statistician). 1962;12(4):313-9.
• Yates F, Mather K. Ronald Aylmer Fisher, 1890-1962. The Royal Society London; 1963.
• Fisher RA. 007: Biometrika. 1916.
• Hald A. On the history of maximum likelihood in relation to inverse probability and least squares. Statistical Science. 1999;14(2):214-22.
• Fisher RA. Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population. Biometrika. 1915;10(4):507-21.
• Fisher RA. III. The influence of rainfall on the yield of wheat at Rothamsted. Philosophical Transactions of the Royal Society of London Series B, Containing Papers of a Biological Character. 1925;213(402-410):89-142.
• Fisher RA. 014: On the" Probable Error" of a Coefficient of Correlation Deduced from a Small Sample. 1921.
• Fisher RA, Mackenzie WA. Studies in crop variation. II. The manurial response of different potato varieties. The Journal of Agricultural Science. 1923;13(3):311-20.
• Williams R, Zumbo B, Zimmerman D. The scientific contributions of RA Fisher. Edgeworth Series in Quantitative Educational and Social Sciences. 2001;7:1-23.
• Zabell S. Ronald Aylmer Fisher. Statisticians of the Centuries: Springer; 2001. p. 389-97.
• Skipper Jr RA. Sir Ronald Aylmer Fisher. Philosophy of Biology: Elsevier; 2007. p. 37-48.
• Box JF. Gosset, Fisher, and the t distribution. The American Statistician. 1981;35(2):61-6.
• Gürsakal N. Bilgisayar uygulamalı istatistik: Alfa Yayınları; 2002.
• Kendall MGSAOJK. Kendall's advanced theory of statistics. Vol. 1, Vol. 1. London: Hodder Arnold; 2007.
• Gavcar E. İstatistik Yöntemler 1. Gazi Kitabevi Yayını, Muğla. 2006.
• Erbaş SO. Olasılık ve İstatistik. Ankara: Gazi. 2013.