«Relevant correlation» and real typology of dependences on the example of indicators of popular psychological tests

Abstract

Introduction. The analysis of statistical relation between the characteristics under study is most likely the main type of analytical tasks encountered in almost any psychological study. But as our long-term experience, including my colleagues, shows in psychological research if there is no overabundance of closely related in meaning variable, between the studied indicators dominate, first of all, dependences that are far from linear.Materials and Methods. To study statistical relation, the author's method was used in the work, which makes it possible to study, along with linear dependencies, the simplest nonlinear dependencies: with a maximum and with a minimum, far from linear, monotonic and almost monotonic. This allows not only to expand the range of revealed dependencies and get rid of numerous errors in the traditional interpretation of the correlation coefficient, but also to better understand the complex psychological subject of a particular study. To demonstrate the typology of statistical dependencies, psychological data were selected for 120 subjects using 9 popular methods. The results of diagnostics according to these methods represent 114 quantitative indicators.Results. This article is devoted to the analysis of the ratio of linear and simplest nonlinear dependencies, their features and typology, their interpretation at the intersection of different intervals of dependencies measures obtained both in the study of only linear models and in the study of the simplest nonlinear dependencies, when linear dependencies become an integral part of the entire set dependencies of research interest. For example, for 6441 pairs of psychological indicators, only 17 strong linear relationships are observed, either for the MMPI test scales or for the Leary test scales. At the same time, among the “significant”, but at the same time very weak and weak dependences in the model for quarts, 29 strong simplest non-linear dependences were found (type 2 error). And among the dependencies that did not fall into the zone of significance in the model for quarts, 37 strong simplest non-linear dependencies were found (type 1 error).Discussion and Conclusions. Basically, if we restrict ourselves to the simplest non-linear dependencies, the psychologists should be most interested in dependencies with a maximum or minimum that correspond to the essence of the mental as a subject of study.