Analysis of Nonparametric and Parametric Criteria for Statistical Hypotheses Testing. Chapter II. Agreement Criteria of Romanovsky, Student and Fisher

Abstract

Any assumptions or waiting for that or another distribution of random values are statistical hypotheses. The objective knowledge about hypotheses can obtain always using the spatial statistical tests that are named agreement criteria. It’s known about 100 different agreement criteria. Nonparametric tests don’t include in calculations the parameters of the probability distribution and operates with frequency only. They don’t assume that the experimental data have a specific distribution. Nonparametric criteria are widely used in analysis of the empirical data, in the checking of the hope models, the simple and complex statistical hypotheses and take a prominent place in science and practice. Parametric tests contain the distribution parameters. They are used for the samples with the normal distribution. Parametric tests permit: 1) to check the statistical hypotheses about the normal distribution characteristics of the population obtained on the base of sample processing; 2) to except the gross errors; 3) to evaluate the difference of the mathematical average values ; 4) and to distinguish the dispersions. That is why these tests are very extensively used in mathematical statistics too. The paper continues ideas of the author’s works [1; 2] devoted to advanced based tools of the mathematical statistics. The aim of the work is to generalize the well known theoretical and experimental results about the statistical tests of the hypotheses testing. Parametric criteria (Romanovsky, Student, Fisher) are discussed carefully from the uniform point of view. The peculiarities of its using for statistical hypothesis testing are highlighted. The typical tasks are suggested and solved. All this takes an opportunity to cover the main point (essence) of the problem as a whole and evaluate its actuality directly.

Keywords

• statistical hypotheses, ‎level of statistical significance, degrees of freedom, critical point, distribution laws, empirical frequency, theoretical frequency, mathematical expectation (average), variance, ‎mean square deviation, gross mistakes, parametric criteria, romanovsky criterion, student criterion, fisher criterion.