Критерії Пірсона і Крамера-Уелча в педагогічних дослідженнях

Abstract

У статті вказано найбільш вживані в навчально-методичних джерелах інформації назви критеріїв перевірки гіпотези про нормальний розподіл генеральної сукупності і гіпотези про рівність математичних сподівань генеральних сукупностей; описано умови використання цих критеріїв та можливості їх застосування в педагогічних дослідженнях; розглянуто приклад застосування. The purpose of any pedagogical research is to study the components of the pedagogical process, in particular, the justification of the research hypothesis or the validity of the theoretical results. For the objectivity of the conclusions associated with the collection and processing of statistical information, usually use statistical methods. At the same time, researchers, in the first place, from humanitarian educators, have a number of problems. We will list some of them, in particular, the use of the criteria of Pearson and Cramer-Welch. One of the problems is the difficulty of finding a statistical criterion in the sources of information in one of its names, that is, in identifying the criteria for its various names. In scientific work, the variety of names can be caused by different versions of translation, the views of different authors in relation to historical priorities, a reference to various authoritative sources, and so on. The next problem is that the use of any statistical method requires justification, that is, it requires certain conditions under which the method can be used. The absence of references to these conditions in the pedagogical study makes the conclusions obtained by the method incomplete or even incorrect. But perhaps the most complicated problem for the educator-scientist is the problem of understanding the relationship between statistical methods and methods of pedagogical research. The researcher must understand, in particular, the essence of statistical hypotheses, the content of statistical conclusions in pedagogical studies, how to interpret these conclusions from the point of view of pedagogical influence, and, therefore, apply to the introduction of new forms, methods, means of study. The name of the hypothesis, for verification of which the criterion is used, is also formulated ambiguously. For a mathematician, such a difference is not a problem, since it can quickly understand the essence of the wording from a formula or context. But the humanitarian educator needs to spend, as a rule, a lot of time and effort to understand the identity of the names and formulas. In view of the above problems, our aim is to simplify the search for and application of the Pearson and Cramer-Welch criteria according to the names of the criteria, the content of the hypotheses and the conditions of their use in the pedagogical activity of the teachers. As a result of our research, we have indicated the most used in educational and methodological sources of information titles of criteria for testing the hypothesis about the normal distribution of the general population and the hypothesis of equality of mathematical expectations of general aggregates; describes the conditions for using the criteria and the possibility of their application in pedagogical research. The prospect of our further research is the further approximation of the theory and methods of mathematical statistics to the needs of pedagogical activities in order to introduce new forms, methods and means of learning into the learning process.