How Is the Subject’s Distance From the Psychological Center of the Population Measured

(In this post, the discussion will concern mathematical calculations, and therefore it is intended more for specialists; however, we have no right to omit it – it is scientifically important. Nevertheless, ordinary enthusiasts of socionics and psychology will also be able to derive a considerable amount of useful information from it, provided they read attentively. By contrast, the next post in the series, on the specific marker psychological properties of Mr. and Mrs. Middle, will already be entirely understandable and interesting to everyone.)

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As we have already written, the tendency to give such answers to questionnaire items as gravitate toward the responses of the “moderate center” has two different causes. We examined one of them earlier in the post vk.com/wall-168821911_13724, when we discussed socionic profiles of social normativity. It turned out that these are Judicious-Ethical-Democratic personality traits. The more strongly a person is accentuated toward these traits, the more reliably they will give “moderate responses,” avoiding any extreme excesses both in their answers and in their personal values and attitudes.

But this is only one factor!

There is another, and even more substantial, factor – namely, a person’s very location at the center of the population’s psychological space by virtue of their objectively “average” temperamental properties. In this case, their responses are moderate not at all because of their socionic Judiciousness, but - directly because of the objective “centrality” of all their psychological properties. And this, this time quite objective, psychological “centrality” will also be reflected in their responses.

In principle, an “ideally average person” should assign, in all their responses when completing a questionnaire, scores as close as possible to the intertype statistical mean of those responses. This, of course, does not happen, because in addition to temperamental differences, a person and their responses are also influenced by upbringing, education, individual experience, the situation on the current day, mood, etc. But their responses will nevertheless partly gravitate “toward the center,” and the specific ratings will also more often be “indecisive” (twos and fours instead of ones and fives). It is especially difficult for such an “average person” to compare themselves with other people in terms of whether they have more or less of particular character traits. If it is easy for a pronounced intuitive type or a pronounced sensing type to answer questions concerning the intuition-sensing balance, a person with ambiversion on intuition-sensing will inevitably encounter difficulties answering such questions. In one case, after mentally struggling a little, they will answer slightly in one direction; in another case – in the opposite direction; however, in the statistical sum of all their responses, the middle will emerge – that is, ambiversion.

HOW AN INDICATOR FOR MEASURING A PERSON’S OBJECTIVE PROXIMITY TO THE PSYCHOLOGICAL CENTER OF THE POPULATION IS CONSTRUCTED FROM THE QUESTIONNAIRE’S VARIOUS CONTROL AND CORRECTIVE “SIGMAS”

If a person is ambiverted on most of their socionic traits, their type profile will likewise be sharply smoothed and low-contrast (that is, with a low value of the reliability indicator S). And this is not because they answered the questions without sufficient thoughtfulness and care, and not because they may simply lack the life experience needed to compare themselves objectively with other people, but precisely because their life experience objectively tells them that they belong to neither clearly defined extreme.

The “sigma” indicator of their raw responses will also be reduced – that is, they will use ratings of 2, 3, and 4 (instead of the contrasting ratings 1 and 5) more often than people with pronounced trait poles.

The indicator of the social desirability of their responses will be somewhat elevated (precisely because they are located at the center of the population).

Finally, the deviations of their responses from the values averaged across all 16 types of the socion will tend to be smaller than those of other people who are not as ambiverted.

These same 4 indicators were already examined by us earlier in the post vk.com/wall-168821911_13724

(№1=sigma of raw responses;

№2=sigma of the type profile obtained from the questionnaire results;
№3=indicator of the social desirability or social normativity of responses;

№4=correlation of a person’s raw responses with the intertype mean values of those responses).

From their normalized values (that is, reduced to a common scale), we then formed a weighted sum:

F= №4-0,39*№1-0,23*№2

In that earlier post, we established that this function F is partly associated (in 40% of its variance) with purely socionic traits. Thus, Judicious traits increase the value of F, as though purely illusorily and subjectively “bringing” a person, in terms of the properties they display, closer to the center of the population, whereas Decisive traits, by contrast, decrease the value of F, purely subjectively “moving” their bearer away from the population center.

If all socionic influences are subtracted from F (mathematically, this is very easy to do), some part of F will nevertheless remain, containing 60% of the variance of the former F, but this remaining part will no longer correlate with any of the 15 socionic traits (specifically, it will have linear correlations equal to zero with all of the traits). We will denote this remaining part of F as F* (that is, F with an asterisk).

Why do we need this F*? It still contains 60% of the variance of the former, original F. And it still correlates negatively both with the range of the subject’s raw responses and with the height of the type profile they obtain, while at the same time correlating positively with social dissimulation and the tendency to bring one’s responses closer to the average position of the majority. (See Fig. 4.)

But now these correlations can no longer be attributed to socionic causes (that is, purely to the DIRECTION of the subject’s deviation from the center of the population). This means that only one factor of importance to us remains in F*, and this factor is the objective distance itself, in psychological space, between the subject and the center of the population (let us recall that it is in no way associated with sociotypes – sociotypes indicate only the direction of the vector in which the subject deviates from the center in multidimensional psychological space, but they say nothing about the distance of this deviation from the center). If the subject is located directly at the center itself (“Mr. Middle”), then their F* will be maximal. If, by contrast, they are located very far from the center of the population in terms of their psychological properties (regardless of the direction), then their F* will be very low.

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We calculated F* values for all subjects on several of our questionnaires with large accumulated datasets (specifically, questionnaire forms 059, 060, 061, 062, 063).

If all socionic traits were perfectly orthogonal to one another, then the task of removing all correlations of F with socionic traits and transitioning to the already purified indicator F* could be solved in a single step, purely analytically. But the socionic traits among questionnaire respondents are, although weakly, still partially correlated with one another (that is, the correlations among the 15 traits are not exactly zero). Therefore, in order, for each individual questionnaire, to free the subjects’ F indicator from all its correlations with socionic profiles, making it perfectly free of linear correlations with socionic traits, we needed neural networks. Fortunately, the EXCEL program has a built-in neural network that handles this task perfectly. As a result, F* at the “output” is indeed completely free of any nonzero correlations both with all 15 socionic traits and with the 16 sociotypes of the type profile.

Thus, F is calculated easily, using the indicators known for each subject (F= №4-0,39*№1-0,23*№2).

F* is also calculated for each subject without any particular difficulty; however, each individual questionnaire yields its own formula (more precisely, the formula is the same in all cases, namely a simple linear formula for removing correlations with socionic traits, but its weighting coefficients may differ slightly across questionnaires). Another disadvantage here is that until sufficiently large statistics have been accumulated for a particular questionnaire, the formula for calculating F* for all its subjects can be written only with a fairly large degree of approximation, by averaging formulas previously obtained from other questionnaires. But the worst thing about F*, if one intends to use it as a marker of the subject’s distance from the psychological center of the population, is nevertheless that F* depends not only on this distance, but also on the subject’s diligence while working on the questionnaire, as well as on a number of other minor situational factors. Therefore, F* can serve as an indicator of the subject’s distance from the psychological center of the population, but only as a somewhat coarse, approximate reference point.

Unfortunately, the issue here is that the value of F* contains, in addition to the role of distance from the center of psychological space, a purely random, situational component.

After all, we calculate F* through F, while F, in turn, was calculated through various sigmas. And these sigmas - for example, the sigma (standard deviation) of the subject’s resulting raw type profile - also depend on how carefully the subject works on the questionnaire and on response-style characteristics of their responses. That is, F (and, consequently, F*) depends not only on the sociotype and the subject’s distance from the psychological center of the population, but also on certain nuisance factors that are of no interest to us at all.

ALTERNATIVE MEASUREMENT OF THE DISTANCE BETWEEN THE SUBJECT AND THE CENTER OF THE POPULATION DIRECTLY USING A SPECIALIZED QUESTIONNAIRE SCALE, BASED ON THE SPECIFIC PSYCHOLOGICAL CHARACTERISTICS OF THIS CENTER

Can any completely different indicators of the subject’s distance from the psychological center of the population (apart from F*) be obtained that would be free of the listed disadvantages of F*?

They can, if one relies on psychological characteristics that are markers only of the center of the population.

In this connection, let us look at the attached Figures 1, 2, and 3.

Unfortunately, when determining a person’s distance from the center of the population, we cannot rely on the degree of ambiversion of the socionic traits in their profile. Why? Because the height of the profile, and hence the actual “scale” of all the traits on the profile, depends not only on actual ambiversion, but also on how carefully the subject works on the questionnaire. Otherwise, the S indicator itself (the range of the subject’s resulting “raw” type profile) would already be a final and fully sufficient indicator of a person’s distance from the center of the population, and at very low values of S it would be possible to assert that the person is almost completely ambiverted and is located at the very center of the population. Unfortunately, this is not the case – S depends both on the subject’s experience and carefulness when working on the questionnaire, and S also depends on Judiciousness-Decisiveness, Logic-Ethics, etc. (in the post vk.com/wall-168821911_13724, we established that S is usually somewhat smaller among Judicious types and somewhat larger among Decisive types, and we even determined what causes this).

Thus, indicators that can be extracted from socionic profiles will not be useful to us for determining the subject’s distance from the center of the population (from them, we cannot disentangle the roles of the very different factors affecting the calculation of distance, which may reflect either the distance itself or various kinds of noise that are detrimental to us).

But, as it turns out, fundamentally different indicators are also possible!

In order to selectively diagnose, by questionnaire, precisely the middle zone of the population (middle in psychological properties, that is, ambiverted on socionic traits), it would ideally be useful to have questionnaire items with a clear parabolic dependence – so that at the center of the population people would more often answer “YES” to the item, while at all edges of the population – in any directions of those edges – they would more often answer “NO.” Or vice versa – at the center they would more often answer NO, while at any edges – YES. This type of dependence is shown in Figure 3D.

Unfortunately, psychological questionnaire items of this kind in pure form practically do not exist in reality. There is always also a component of linear dependence on some psychological factors. But if, when moving along the axis of a trait, the probability of answering “YES” to an item increases not strictly linearly (that is, not along an inclined straight line), but along a convex or concave curve (as shown in Figures 1 and 2), then this is already something, and such items can quite well be used for selective diagnosis of the psychological center of the population. How this occurs is shown in Figure 3.

For an item to be usable for diagnosing proximity to the center of the population, the dependence of “YES” responses to that item on socionic traits must not be straight, but convex or concave, and the stronger this “convexity,” the better.

HOW TO IDENTIFY AND SELECT THESE ITEMS THAT WE NEED?

For this purpose, as a selection criterion, we have the F* indicator previously obtained for each subject in all questionnaires, which, albeit somewhat coarsely (that is, with an admixture of various situational noise), nevertheless reflects the subject’s proximity to the center of the population. Most importantly, F* has absolutely no linear correlations with any socionic trait. Therefore, if “YES” responses to some questionnaire item correlate positively with this F* indicator, this unambiguously demonstrates that the dependencies of answering “yes” to that item have a CONVEX form for the majority of socionic traits (as in Figure 1). And if the correlation is negative, then the majority of the dependencies on the traits are concave (that is, with their humps directed downward – as shown in Figure 2).

Very well, suppose that by measuring their correlations with F* we have selected an array of such items – with convex and concave dependencies. But all the selected items still retain linear dependencies on socionic traits!

How can a scale be constructed from these items to measure purely the distance from the center of the population, while this scale DOES NOT CORRELATE with any socionic trait or type, that is, does not correlate with the direction in which the subject’s point deviates from the center of the population? In other words, so that there are correlations with the distance of deviation, but no correlations at all with the angle of deviation?

Well, this is quite simple. We take an array of items, composing it so that it contains exactly as many items with “concave” dependencies as with “convex” ones. As the coefficients of association with distance from the center of the population, for each item we take the correlation that it showed with the F* indicator. Next (over the array of all selected items), we measure the correlations of these coefficients with all 15 socionic traits (after all, each questionnaire item has its own ready-made socionic trait profile, where coefficients of association with the traits are also available). It turns out that the correlations with the traits are very small (this is because we balanced the number of “convex” items with an equal number of “concave” ones, so that their linear correlations cancel one another out), but some linear correlations with the traits nevertheless remain. We then begin shortening the list of items – when rejecting them, adhering to the criterion that each reduction in their number should simultaneously reduce the sum of squares of the correlations with socionic traits that are “parasitic” for us. If, at the end of a series of reductions, some residual correlations with the traits nevertheless remain, we finally solve the problem of eliminating them completely by varying the weighting coefficients before the items, - these small variations either slightly increase or selectively slightly decrease the diagnostic coefficients of the items used to calculate distance from the center. The Excel neural network handles this task perfectly.

The final result is the questionnaire that we presented to you yesterday. It has only one scale – for measuring distance to the center of the population. At the same time, the diagnostic coefficients of the items on this scale no longer linearly CORRELATE with anything else (neither with types, nor with functions, nor with traits). Only - with the distance to “Mr. Middle.”

To be continued.

Fig. 4

Intercorrelations of indicators associated with the subject’s distance in psychological space from the central (neutral, average) point of that space (5000 respondents)