Chapter 5. The solution of the inverse problem is the restoration of projections of a certain psychological property into 16 psychotypes through known projections of this property into 8 socionic functions
First, let us remember that socionic functions do not reflect in themselves all the socionic features, but only their part - the truth, the most essential. Therefore, it is impossible in principle to restore all the complete information about the psychotype by functions, as you like combining them among themselves. To understand what proportion of the information we can recover, consider for the purpose of illustrating Table. 5.1.
Table. 5.1. Calculation of the percentage contribution to the overall variance of psychological properties associated with socionic traits. In cells, percentages of the total variance of properties are indicated, associated with this socionic trait or, in the last lines, groups of socionic traits. The calculation was carried out separately for 3 different cases.
From Table. 5.1. it can be seen that, with the immanent properties of eight socionic functions, 93% to 97% of the total variance of all possible psychological properties is associated, by any calculation. This part of the properties is determined only by the weight contribution of certain socionic functions to the psychotype and is in no way connected either with their position within the psychotype, or even more with their neighborhood within the psychotype with other socionic functions. With the peculiarities of the position of functions inside the psychotype (for example, it is program or creative, rather than actually with the size of the function), no more than 3% of the total variance is associated, and with the proximity of functions (with what functions are immediate neighbors within the TIM) 4.5% of the total dispersion of psychological properties, with the lion's share of these percentages being a sign of "aristocracy-democrats". In the order of the "lyrical digression", let us draw the reader's attention to how little dispersion in the array of the most diverse psychological properties turn out to be associated with the so-called "weak" socionic traits - they are called weak for nothing. From here you can draw a conclusion about how unreliable the type diagnosis based on the "weak" socionic traits (kvestimnost-declarations, positivism-negativism, etc.)
Thus, the overwhelming majority of the dispersion of psychological properties (93% or even higher) is associated with the individual weight content of all eight functions of the psyche in the psychotype, and more with nothing else. Only the "strength" or "power" of each function is important, or, if you like, its "dimension" - that is, something that is characterized by the numerical value of its magnitude, and does not matter at all on which position the function functions within the psychotype, with which other functions it borders and interacts. All these 93% of the variance of properties are easily modeled, obviously, by a linear additive superposition of 8 functions with weight coefficients. It is these 93% of information from that general psychological information that is contained in the properties of the original psychotype that are reflected in the 8 psychological functions, and then on these functions, knowing their individual weight contribution to each psychotype, all information about the psycho-type-related properties of the psychotype can be further restored. It follows that the maximum attainable coefficient of linear correlation between the properties of the original psychotype and the properties of the psychotype restored by the 8 functions (due to the representation of each psychotype in the form of a linear superposition of 8 functions with some weighting coefficients in front of each of them) equals the square root of 0, 9246 = 0.96 (since, according to theorems of mathematical statistics, the coefficient of linear correlation between two properties equals the square root of the fraction, which is the total variance at x properties throughout their complete dispersion). And if we consider the contribution of signs Nos. 1-7 to the total variance of properties equal to 97.16% (the case of calculating the weight contribution of features on the array of primary diagnostic correlations with type standards in a sub sample of 880 subjects), then the correlation of the "restored" the initial properties will reach a square root of 0.9716 = 0.986. Looking ahead, let's say right away that everything is exactly the way it is when we test the correlations between the properties of the "original" and the psychotypes restored by functions.