The Establishment And Early Development Of The Small Sample Statistics Theory

In the process of solving abnormal frequency curves,Karl Pearson introduced the method of moments and gave the frequency curve distribution pattern judgment rules by calculating the ratio of moment.Based on these definitions and theorem,the route-map of Pearson Curve System was constructed,which can solve almost all the problems of large sample statistics.However,there is an important premise for the application of Pearson Curve System,the sample scale of the object data needs to be large enough so that the standard deviation of sample can be regarded as that of population,and then the distribution pattern can be obtained on this basis.Therefore,when the sample scale is small,if the standard deviation of sample is still directly regarded as that of population,there will be obvious calculation error and statistical work will become unvalued.That is to say,when faced with small-scale samples,Pearson Curve System is helpless,which is a core limitation of it.It is based on Pearson's route-map that Gosset assumed the sample standard deviation s as an approximation of population standard deviation?,and he defined t transformation to build relationship between characteristics of sample and that of population,then derived t distribution,which helped Pearson Curve theorem be applied to small sample and solved the limitation problem of Pearson's route-map.However,in the process of mathematical proof of t distribution,Gosset confused different concepts between independence and incorrelation.Then Fisher found and solved this problem,and on this basis of moment method,other small sample distribution types were derived,which brought small sample statistics to prosperity.After sufficient study of original literature and research literature,this thesis reconstructs Pearson's route-map in large sample area,then under the guidance of the new paradigm for mathematical history researching proposed in A New Approach to the History of Modern Mathematics,this thesis solves problems as follow:1.Pearson's route-map for large sample statistics is reconstructed and its limitation is pointed out;2.The practical and mathematical problems Gosset faced is clarified,and the reason for setting approximation and transformation of standard deviation is introduced;3.Gosset's method and route-map based on small sample statistics for solving Pearson's legacy problems is expounded;4.Fisher's proof for the loopholes in Gosset's derivation is interpreted.