Tchebycheff Inequalities as a Basis for Statistical Tests

One of the principle uses of mathematical statistics is to furnish a basis for testing the value of statistical results obtained from samples. The main purpose of this paper is to present the essential steps in the development of mathematical tests in the approximate order of their appearance. We shall see how the original theorem of Tchebycheff demonstrates the basic principle of the probability test. Some further developments of the theory are given in the last section. !3eginning in the seventeenth century we find published papers from many sources giving different test results. Presentation of the principle test results so as to bring the theory up to date should be of some use to those interested in present. practices and further developments.