Modern Interpretations of Correlations in Sociology As a PATH to Mock-Scientific Results

In sociological science traces the exodus (intentional or subconscious) to low values of the correlation coefficient, when non-zero correlation (the hypothesis for correlation coefficient equality to zero) is sufficient to describe the statistical relations as strong.

This can be explained as a shortage of the really strong linear statistical relation with in magnitude higher 0.6 in the analysis, when studied sociological objects mostly non-linear in nature but used tools, still represented the linear models, and researchers do not want realize the synergy paradigm and non-linear models.

Let’s consider the model of exponential dependence within solving the problem of investigation of statistical relations using the author's method for 58 parameters: mathematical functions and regression lines for them, based on the correlation coefficient.

A dependency for a function with a single maximum (cut off on the right):

Y=-X^2 (left from the maximum);

Y=-0.7*X^2 (right from the maximum)

In this case, the correlation coefficient is equal to 0.25.

Dependence of the parameter Y from the parameter X as comparative weightiness of the parameter Y for quinters on a scale X:

X-1(Y=-12902); X-2(Y=-4658); X-3(Y=-742); X-4(Y=-3362); X-5(Y=-10978)

Dependence of the parameter Y’(regression line) from the parameter X:

X-1(Y’=-9616); X-2(Y’=-8328); X-3(Y’=-7196); X-4(Y’=-5730); X-5(Y’=-4866)

If we build graphics it will be apparent what a small part (21%) causation (and obviously one-sided) describes the regression line near the average value of the dependent parameter. While sociologists announce this correlation the «significant” and describe the dependence between parameters as linear.

A dependency for a function with a symmetric maximum:

Dependence of the parameter "Y=-X^2" from the parameter "X":

X-1(Y=-11944); X-2(Y=+6356); X-3(Y=+12310);

X-4(Y=+6356); X-5(Y=-11944)

Factor of the connection strength=1.65 (feedback is weak=0.00)

Coefficient of correlation=-0.00

The correlation is absent. In this case, is lost out of consideration not just the strong dependence but the dependence stronger than a linear function.