Strong reciprocal dependencies as exceptions when correlations are weak

Abstract

The article discusses examples of strong (SV > 0.7) simplest nonlinear dependencies in a problem for 114 indicators of 9 psychodiagnostic techniques, which represent exceptions in the context of many specific problems for studying statistical relationships, when two reciprocal dependencies, Y(X) and X(Y), are strong. There were only four such dependencies in the model for quintas of the independent variable within the framework of very weak and weak correlations (a total of 180 strong simplest nonlinear dependencies). The author quantitatively analysed and qualitatively interpreted the dependencies for three pairs of variables: “16PF-E: Submissive – Assertive” of R.B. Cattell’s questionnaire and “Competition” of K.W. Thomas’s methodology (SV = 0.78 and SV’ = 0.72 at r = 0.15); “16PF-Q3: Low self-control – High self-control” and “16PF-L: Trusting – Suspicious” of R.B. Cattell’s questionnaire (SV = 1.17 and SV’ = 0.91 at r = 0.28); “Psychasthenia” of the Minnesota Multiphasic Personality Inventory and “Suspicious type” of T.F. Leary’s methodology (SV = 0.84 and SV’ = 0.73 at r = 0.19). For the pair of variables “Low self-control – High self-control” and “Trusting – Suspicious”, models of linear regression are also considered. It is built on the basis of a dependence that is far from linear, as shown by Pearson’s coefficient of weak correlation equal to 0.28. At the same time, founded on the rule for interpreting the absolute value of the correlation coefficient for a sample of 120 subjects (widely used in the psychological community), it indicates the significance of the relationship 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.