Fisher And Small-sample And "n-dimensional Geometry Method"

Learning from history makes people wiser, and the history is a mirror as the guidance for future. For any discipline, the deep research of its history is indispensable to its progress and development, thus the importance of historical research is beyond the doubt. Statistics is a discipline which has a close relationship with the development of modern scientific; it’s also a cumulative one with its theory and method have the continuity, thus we should make more efforts for the researching of its history.The first 30 years in the 20th century is a very important phase of the information of the modern statistics. In this period, British statisticians represented by Gosset and Fisher had set off the revolution of small-sample theory in the field of statistics. The background of the revolution was that with the rapid development of science and technology, the statistic data obtained in the tests under the condition of manual control were no longer applicable to the traditional large sample method based on the central-limit theorem. The "student" distribution proposed by Gosset in 1908 marks the formal foundation of the small-sample theory. After that, Fisher took the flag of the small-sample theory from Gosset, and derived the accurate distribution of a series of important statistics such as sample variance, correlation coefficient, partial and multiple correlation coefficients. These achievements not only made him the contemporary leader of the statistics without controversy, but also made the small-sample theory through the pioneering stage rapidly. Just as the famous statistician Savage said, "In the art of calculating explicit sampling distributions, Fisher led statistics out of its infancy, and he may never have been excelled in this skill." The "skill" which Savage referred to is exactly what Mr. Chen called "n-dimensional geometry method".On the basis of referring to a mount of original literatures, the paper makes detailed interpretation of Fisher’s "n-dimensional geometry method" and introduces its application in some important statistics and its influence on the following statistics with the beginning of the small-sample theory as background. The author expects to provide some help in expanding the ideas of solving problems of Statistical distribution.