On the Reliability of Determining Intertype Relations Using Questionnaires
(This is an excerpt from an article in preparation by V. L. Talanov – for enthusiasts of the “serious”)
The agreement between two independent methods for determining a sociotype diagnosis is equal to:
Сх(1;2)=P1*P2 + (1-P1)*(1-P2)*0,111 ; - see www.sociotoday.narod.ru/validnost.htm
Where P1 and P2 are the probabilities of arriving at the true type for the first and second diagnostic methods, respectively.
Let P1 be the probability of correctly identifying the type through self-typing, and P2 the probability of correctly identifying the leading sociotype with a questionnaire (for different questionnaires consisting of approximately the same number of diagnostic questions and constructed according to the same methodological procedure, we quite justifiably equate this probability, considering it equal to P2 in all cases).
We will now use the part of our sample of subjects in which they reported their self-assessed psychotypes, - there are 252 such data points. In this subsample, the average agreement between sociotype diagnoses from self-typing and from the questionnaire (any of the three forms used) was 0,567. In this same part of the sample, the average retest agreement between diagnoses of the leading sociotype obtained with two different (independent) diagnostic questionnaires was 0,627.
Thus, to find P1 and P2, we have two equations with two unknowns:
0,567=P1*P2 + (1-P1)*(1-P2)*0,111
0,627=P2*P2 + (1-P2)*(1-P2)*0,111
From the second equation, P2= (0,222+sqrt(0,222^2+4*1,111*0,516)/2,222 = 0,7887
(Note that if we had calculated the agreement in the second equation using the simplified formula Сх=P2*P2, then for P2 we would have obtained a value only very slightly higher, namely 0,7918).
Now, knowing P2, we can also find P1 from the first equation, that is, the accuracy of self-typing:
P1=0,7103
(again, if approximate formulas were used, that is, Сх=P1*P2, the accuracy of self-typing would have been only slightly higher, 0,716).
Thus, in this sample (which, incidentally, matches very well in its parameters the overall sample on which we study intertype relations), the average accuracy of questionnaire-based sociotype diagnoses (that is, correctly identifying the one standard type out of 16 to which the subject is closest in their characteristics) is 0,7918=0,79. In the same sample, the average accuracy of self-typing (that is, the probability of a correct diagnosis based on a person’s self-assessment) is 0,7103=0,71.
Now let us turn to intertype relations, to assessing the accuracy of their determination in the experiment.
The average probability of correctly determining the intertype relations between two people using questionnaires is again 0,627, because it is calculated using the same formula: P2*P2 + (1-P2)*(1-P2)*0,111
Accordingly, when determining ITR from self-typing, the ITR is correctly determined in only approximately 50% of cases (0,71*0,71).
But all of this applies only to the case where we calculate intertype relations not from the type profile as a whole, but only from the single leading peak of the profile. However, relying on the single highest peak is a major coarsening. When ITR is calculated from complete type profiles (we will show below how this is done), what “makes the difference” in correctly determining ITR is not agreement in identifying the highest peaks of the two profiles, but their variance commonality (the proportion of common overlapping variance) across the two complete type profiles. This is easy to understand using the example of a single ITR, Identity. An ideally identical relation between two people is one in which the shapes of their type profiles fully coincide, that is, in which the variances of these two profiles fully coincide. The proportion of coinciding variance between two profiles is a direct analogue (but a considerably more accurate one) of the retest agreement of the highest peaks of the type profile in the same person. At the same time, according to the laws of mathematical statistics, the proportion of coinciding variance is calculated as the square of the coefficient of linear correlation between the profiles. Consequently, for ideally identical relations (now between two different people), the profiles must likewise be identical, and the correlation between these two type profiles must likewise be equal to one.
In the general case, the reliability of determining ANY intertype relation between two complete type profiles is, on average, equal to the square of the retest correlation coefficient between the two profiles.
The median retest correlation between two type profiles of the same person, measured using different questionnaires in the same sample of 252 people on which we perform all the calculations here, is 0,927, and its square is 0,859.
This value of 0,859 is the sought average accuracy of determining ITR using the Talanov questionnaires employed in the project studying the statistics of intertype relations. The probability of an erroneous determination of ITR in this case is, as we can see, only 14% - not 37%, as when ITR is determined by relying only on the leading peaks of the profiles, and certainly not 50%, as in the case of relying on respondents’ self-typing.
Let us now see how intertype relations are calculated between two complete type profiles.
The point is that each intertype relation between any pair of the 16 sociotypes corresponds to a quite definite set of pluses and minuses across the 15 Reinin traits. A plus sign – if the pole of the given Reinin trait must be the same for the two people connected by this particular ITR. A minus sign – if the polarity of this trait within the given ITR must be opposite between the two people.
See this table in the attached figure!
2nd respondent:
| 1st rational | 1st irrational | Extraversion | Irrationality | Static | Intuition | Judiciousness (Peripheral) | Tactics | Carelessness | Logic | Merry (Ascending) | Constructivism | Yielding | Questimity | Democracy | Positivism | Process (Right) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Identity | Identity | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| Mirror | Mirror | -1 | -1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 |
| Duality | Duality | -1 | 1 | -1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 |
| Activation | Activation | 1 | -1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 |
| Kindred | Business | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 |
| Supervisor | Supervisee | -1 | -1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 |
| Semi-duality | Mirage | -1 | 1 | -1 | 1 | -1 | 1 | -1 | -1 | 1 | -1 | 1 | 1 | -1 | 1 | -1 |
| Benefactor | Beneficiary | 1 | -1 | -1 | 1 | -1 | -1 | 1 | -1 | 1 | 1 | -1 | 1 | -1 | -1 | 1 |
| Super-ego | Super-ego | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 |
| Conflict | Conflict | -1 | -1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 |
| Extinguishment | Extinguishment | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | -1 | 1 | -1 | 1 |
| Quasi-identity | Quasi-identity | 1 | -1 | -1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | -1 | 1 | 1 | -1 |
| Business | Kindred | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 |
| Supervisee | Supervisor | -1 | -1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 |
| Mirage | Semi-duality | -1 | 1 | -1 | -1 | 1 | -1 | 1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 |
| Beneficiary | Benefactor | 1 | -1 | -1 | -1 | 1 | 1 | -1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 |
The more strongly a given trait is expressed in terms of its modulus (that is, its absolute value), the greater the influence it exerts on the given ITR. Clearly, a pronounced rational LII and an equally “pronounced” irrational SEE, both with strongly expressed Nality moduli that are opposite in sign, are one thing – here the relations will be sharply conflictual. A completely different case is an LII that is ambiverted in Nality and is therefore close in its characteristics to ILI, and an equally ambiverted individual close in their characteristics to the ESE “Napoleon”. In this case, the modulus of their Nality is close to zero, and the conflictuality should weaken noticeably, approaching duality.
Therefore, when we consider ITR in a pair of two profiles, what matters to us is not only the sign (polarity) of each Reinin trait (PR) in the pair, but also the absolute value of that PR.
And because a relation is constructed not on one person but on a pair of people, it proves convenient (and correct), in all calculations of the influence of this PR on the relation, to average the moduli of this PR for the members of the pair. The best way to do this is through averaging products. That is, the optimal function for estimating the influence of a given PR in a pair on any intertype relation is the product of the signs of this PR in the two people multiplied by the square root of the product of the moduli of this same PR in those people. Thus, the influence of each PR on any possible ITR in the pair is estimated by the formula: sign(PR1)*sign(PR2)*sqrt(abs(PR1*PR2)). If a particular ITR requires opposite signs of this PR in the members of the pair, then the more strongly negative this number is, the better. Conversely, if it is positive, it will work in favor of those intertype relations for which the polarity of this PR must be the same in the two members of the pair. And the greater the modulus of the resulting number, the stronger its effect will be.
Next, for the pair of our two subjects, we only need to calculate all these within-pair values for each of the 15 PRs and obtain a final vector of 15 numbers, each of which characterizes its own PR in the pair. The scalar product of this vector is then, in turn, taken with the row in the table attached to the post that corresponds to the ITR of interest to us. When we perform this scalar multiplication for all 16 ITRs, we obtain 16 ultimate numbers - for the quantitative characterization of all 16 possible intertype relations. The intertype relation closest to the given specific pair will be the one for which the scalar product is largest.
An example of such a calculation-comparison is shown in the lower part of the same figure.
| Extraversion | Irrationality | Static | Intuition | Judiciousness (Peripheral) | Tactics | Carelessness | Logic | Merry (Ascending) | Constructivism | Yielding | Questimity | Democracy | Positivism | Process (Right) | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1st respondent (PR1) - IEE | 0,062 | 0,041 | 0,005 | 0,070 | 0,042 | -0,006 | 0,011 | -0,206 | -0,019 | -0,018 | 0,005 | -0,006 | -0,003 | -0,006 | -0,016 |
| 2nd respondent (PR2) - SLE | 0,062 | 0,038 | 0,021 | -0,098 | -0,063 | -0,009 | 0,001 | 0,120 | 0,015 | 0,002 | -0,002 | 0,004 | -0,002 | -0,020 | 0,001 |
№1*№2 100*sign(PR1)*sign(PR2)*sqrt(abs(PR1*PR2)).
| Extraversion | Irrationality | Static | Intuition | Judiciousness (Peripheral) | Tactics | Carelessness | Logic | Merry (Ascending) | Constructivism | Yielding | Questimity | Democracy | Positivism | Process (Right) | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| №1*№2 | 6,193 | 3,950 | 0,971 | -8,273 | -5,151 | 0,749 | 0,391 | -15,706 | -1,657 | -0,598 | -0,298 | -0,512 | 0,241 | 1,132 | -0,439 |
Scalar products of vector №1*№2 with the vectors of trait-wise coefficients of intertype relations:
| Identity | -19,0 |
| Mirror | -41,2 |
| Duality | 13,1 |
| Activation | 20,8 |
| Business | 4,7 |
| Supervisee | -10,1 |
| Mirage | 9,2 |
| Beneficiary | 9,2 |
| Super-ego | 42,1 |
| Conflict | 20,9 |
| Extinguishment | -21,1 |
| Quasi-identity | -13,6 |
| Kindred | 16,7 |
| Supervisor | -6,3 |
| Semi-duality | -14,0 |
| Benefactor | -11,3 |
CONCLUSION: the largest indicator is for super-ego relations.
Incidentally, the remaining errors in the accuracy of determining ITR using questionnaires can also be statistically corrected quite reliably. That is, the effect of diagnostic error, which reduces the contrast in the experimental statistics of the frequency distribution of ITR, can be mathematically eliminated. This calculation is laborious, but it is sufficient to perform it only once, obtaining constant correction coefficients for all ITRs for all subsequent use; these coefficients can perform their task quite well, restoring the true expected form of the frequency distribution of intertype relations. We will discuss how this is done later. Not today.