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

Year 2023, Volume: 94 Issue: 1, 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

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