Asymmetry of nonlinear relations as a typical case in the analysis of psychological data

   Introduction. Psychological research quite often (dissertation research is almost always) accompanied by analysis of the statistical relations between the quantitative variables being studied. At the same time, psychological variables by their nature, if we take into account only strong statistical connections but do not take into account strong statistical connections between related variables, are mainly nonlinear dependencies, even if we remain within the simplest models.

   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 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. The article quantitatively analyzed and qualitatively interpreted the dependencies for three pairs of variables: 1) “Paranoia” and “Aggressive type” (MMPI and T. Leary questionnaires) with connection strength coefficients SV = 1.256 for MMPI-5(LIR-3) and SV' = 0.089 for LIR-3(MMPI-5) with a correlation of 0.143; 2) “Egoistic type” and “Altruistic type” (T. Leary questionnaire) with connection strength coefficients SV = 0.737 for LIR-2(LIR-8) and SV' = 0.086 for LIR-8(LIR-2) with a correlation of -0.0198; 3) “Dependent type” and “Reserved – Outgoing” (R. Kattel and T. Leary questionnaires) with connection strength coefficients SV=1.1099 for LIR-6(16F-1) and SV' = 0.295 for 16F-1(LIR -6) with a correlation of 0.253. For pairs of variables “Paranoia” and “Aggressive type”, “Dependent type” and “Reserved – Outgoing ”, linear regression models, which are built on the basis of linear correlations, were also considered. And if in the first dependence the correlation is not “significant”, then in the second it is “significant”, as evidenced by the Pearson weak correlation coefficient equal to 0.25, and based on the rule widely used in the psychological community for interpreting the absolute value of the correlation coefficient for a sample of 120 subjects it indicates a relation is “significant” at the p = 0.01 level, which inevitably requires a linear interpretation. For clarity, the information discussed in the article is illustrated by graphical representations of the dependencies under consideration.

   Discussion and conclusions. The article discusses examples of asymmetrical (one-sided) strong (SV > 0.7) simplest nonlinear dependencies, which show when, when considering two inverse dependencies, one Y(X) is strong, and the other dependence X(Y) weak. This is the most typical option, especially when the variables are related by a weak or very weak correlation, which is symmetrical in nature.

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