On the requirements for statistical methods of data analysis (generalizing article)

Half a century activity in consulting researchers of various specialties, reviewing articles and books, opposing dissertations provided the possibility of getting acquainted with hundreds of specific studies on the development and application of statistical methods. A variety of shortcomings in conducting research and publishing the results of studies have been revealed, which hinder the perception of the data obtained, and in some cases cast doubt on the adequacy of the conclusions. Therefore, it appeared advisable to develop natural requirements for methods of data processing and presentation of the results of statistical data analysis. This study is devoted to an initial consideration of a number of formulations of such requirements. We proceed from the modern paradigm of applied statistics, based on non-parametric and non-numerical statistics which replace the primitive paradigm of the 19th century and the paradigm of the middle of the 20th century using parametric distribution systems. When describing and discussing the procedures for analyzing statistical data, it is necessary to start with probabilistic-statistical models for generating the data under study. It is necessary to proceed from the theory of measurements, according to which the first step in the data analysis is identification of the scales in which they are measured. Statistical inference must be invariant under the allowable transformations of data measurement scales. Since almost all distributions of real data are non-normal, a preference should be given to non-parametric formulations. The possibility of using parametric families of distributions must be carefully justified. In accordance with the theory of testing statistical hypothesis, both the null and alternative hypotheses must be specified. It is necessary to study the stability of the conclusions drawn from the model with respect to acceptable changes in the initial data and assumptions of the model. A number of further publications of the author will be devoted to the problems of developing a system of requirements for statistical models and methods.