**N – 1**

where: P (A) is the probability of a random event (A) of a sociometric choice;

N is the number of group members. The P(A) value was selected according to Table No. 1 (Appendix 8).

Thus, we determined that with the number of students in the class N = 27, P (A) should be located in the interval 0.22-0.19. This means that the “limit of elections” for a teenager when performing a sociometric procedure according to the given parameters can be approximately equal to six. According to the standard, we suggested that adolescents make three positive choices and three negative ones, that is, three rejections.

The introduction of a “sociometric constraint” significantly increases the reliability of sociometric data compared to a non-parametric procedure and facilitates the statistical processing of the material. From a psychological point of view, sociometric restriction makes adolescents more attentive to their answers. The selection limit significantly reduces the chance of random responses and allows for standardization of election conditions in groups of different sizes in the same sample. This makes it possible to compare material across different groups.

Then, for the mathematical processing of the obtained sociometric data, tabular and indexological methods of quantitative analysis of the material were used. First of all, for tabular analysis, we built the simplest sociomatrix, into which we entered the results of the elections using generally accepted symbols.

There are various classifications of sociometric status based on the analysis of the results of sociometric studies. So, J. Moreno distinguishes the following groups: “stars” who are most popular in the group; “outcasts” who received more negative choices than positive ones; “isolated”, not noticed by other members of the group, either positively or negatively; “social proletariat”, the vast majority of members enjoying a fairly positive attitude of the group.

Ya.L. Kolominsky built his classification based only on positive choices by members of each other’s group: “stars”, “preferred”, “accepted”, “isolated”. Sometimes they singled out a group of “outcasts”, those who received negative elections.

We believe that the division of the group into 4-5 categories does not fully reflect the structure of interpersonal relationships. For a more detailed analysis of interpersonal relations in the group, we used a classification based on both positive and negative choices of adolescents (V.G. Bazhenov, L.A. Bayserkeev, 1998).

Based on the chosen approach to sociometric research, we identified seven categories of groups of teenagers in the classroom. The basis for the inclusion of a teenager in one or another microgroup was the number of positive and negative choices similar to other members of the microgroup, which he received from classmates. The following levels were designated: I – “stars”. Adolescents who received at least 5 positive choices and no more than 1 negative. II – “preferred”, scored 3-4 positive and no more than 2 negative. III – “tolerant”. Adolescents received 1-2 positive and no more than 2 negative choices. At the same time, the total number of choices received by a teenager is not less than 2. IV – “ambiguous” – teenagers who received the number of positive and the number of negative choices almost equal to each other. Moreover, the number of negative ones is not less than 2; V – “invisible”, received no more than 1 vote. VI – “isolated” – a microgroup of teenagers who received more negative votes than positive ones. Moreover, the difference between the numbers of positive and negative choices is not less than 2. VII are the “persecuted” who received at least 10 negative choices.

This classification was used in the study of the levels of sociometric status of a teenager. As the results of a study of 27 seventh grade students showed, the largest number of adolescents were included in the group that was at the first level of sociometric status – 22% of adolescents from the entire class stood out in the “star” group. This result turned out to be quite unexpected, since the average group of “star” status is usually 10–11% [14], that is, two times less than our result. Next come the groups of teenagers who were called “preferred”, “tolerant”, as well as “isolated” and “persecuted”, they turned out to be quantitatively equal and each made up 15% of the total number of students in the class. A smaller number of students were included in the “ambiguous” (11%) and “inconspicuous” (7%) groups.

Analysis of the sociomatrix showed that in each group, except for the group of “ambiguous”, unruly adolescents are represented. It was also unexpected that in the status group “stars” along with disciplined, well-performing adolescents actively participating in the life of the class, there were also undisciplined adolescents. Two undisciplined teenagers in the status of a “star” were “bosom” friends – they spent all their free extracurricular time together, they were the “ringleaders” of noisy companies, they could “break” the lesson; being popular, they “exploited” their more obedient and academically successful friends — they forced them to do written homework assignments for themselves, tests in some educational “unloved” subjects. Vladimir B. and Astik G. did not hide the fact that they were proud of their position as “undisciplined”. Statements: “We are not suckers …, Just think, we were late for five minutes … etc.” showed open bravado of teenagers by violations of elementary norms and rules of school life. Two other teenagers in the status of “stars” were Elena V. and Elena G. Both seventh-graders are successful in their studies from the first grade, friendly to classmates, and outwardly attractive. Classmates are not friends with each other. In general, there are no friends in the class, they say that there is no time to be friends. And going to school discos is not interesting. In the classroom, the main thing for them is educational work. Classmates do not participate in noisy fun, they do not express condemnation of violators of school discipline. They are respected by their classmates. These teenagers, opposite in terms of discipline, ended up in the same status group. They equally received more than five elections, but teenagers of different disciplines grouped around them. The other two girls in the status group “stars” – Angela K. and Karina E., are very friendly with each other, are included in the selected class asset, speak out against violators of school discipline in the class, and carry out teachers’ instructions.

The levels of sociometric status that we are studying reflect the different nature of schoolchildren’s involvement in interpersonal relationships. There is no doubt that the first three types of status (“stars”, “preferred”, “tolerant”) indicate successful inclusion in interpersonal relationships in the study group, and it is better to be “preferred” than “tolerant”, and it is better to be a “star”. ” than “preferred”). For all adolescents of these statuses, the number of choices exceeds the number of deviations.

In all status subgroups, except for “ambiguous”, there are unruly teenagers: in II, III, V, VI – one teenager each. The name of the status – “imperceptible” – does not fit at all for Ashot B. In the sociometric experiment, he received one choice and one deviation. As a result, the sociometric status of CC=0, therefore the status of “inconspicuous” was determined for the teenager. However, the undisciplined behavior of a teenager makes him very noticeable and memorable: not completing school assignments, he constantly argues with teachers and classmates about unfair treatment of himself, shouts out in class, draws attention to funny (from his point of view) facts and situations. Acting in the classroom as a jester, a teenager interferes with both classmates and teachers. Ashot B. really wants to be in the spotlight, to be elected even with a minus sign. Classmates treat the teenager’s “original” violations of discipline without malice and say that he “does not stand for the truth, but to show himself.” Apparently, because of this, Ashot B. found himself in the status of a member of the group, with whom they do not want to be friends or hostile, that is, in the status of “inconspicuous”. Another teen in “inconspicuous” status received three selections and three rejections. Thus, he also has CC=0. Andrey B. is a classic “inconspicuous”: even “troeshnik”, passive silent and compromising. It can also be considered indisputable that the last two types (“isolated” and “persecuted”) indicate an unsuccessful degree of inclusion in a group where the situation of teenagers of the seventh type (“persecuted”) is the worst. As for the comparison of the fourth and fifth types (“ambiguous” and “imperceptible”), it is no longer so easy to determine their place in the system of interpersonal relations. It is also difficult to say what is better, to be “ambiguous” i.e. cause conflicting feelings among peers, or be “inconspicuous” when no one from the group shows an emotionally charged relationship with a teenager. In the “ambiguous” status, adolescents have a negative sociometric status, that is, the number of deviations begins to prevail over the number of choices. This subgroup did not include unruly teenagers. This gave us reason to believe that the undisciplined behavior of a teenager cannot cause an ambiguous attitude towards him. Along with a negative attitude towards him, a positive one is also manifested among adolescents. Sociometrics showed that at least as many classmates wanted to be friends with the undisciplined (and were friends with them) than the number of teenagers who sought to interact with the disciplined.

Thus, our classification of the sociometric statuses of adolescents in the system of interpersonal relations in the study group made it possible to single out seven levels. Each of them makes it possible for the school psychologist and class teacher to conduct a quantitative and qualitative analysis of the status of a teenager, depending on the characteristic features of the student’s unruly behavior.

To study the leading internal factors influencing the characteristics of the sociometric status of a teenager, we analyzed the sociometric status indices, which were determined by the formula:

**i –** n

**E (Ri ^{+} + Ri ^{–} )**

**Ci = (2),**

**Nl**

where: Ci— sociometric status,

i – group member number,

Ri are the choices received by the i-th member of the group,

E is the sign of the algebraic summation of the numbers of the received choices of the i-ro member,

N is the number of group members.

We interpreted sociometric status as a subjective measure of the influence of an individual on a group. Depending on the predominance of the received choices or received deviations, the sociometric status received a positive or negative sign (Table No. 3). We assumed that in this way it would be possible to judge the positive or negative influence of a teenager on others, on his classmates.

However, as a qualitative analysis of the obtained quantitative indicators showed, in reality, in school life, a positive sign of the sociometric index is not a guarantee that a teenager in the “star” status is a leader. Indeed, the sociometric status measured a person’s potential ability to lead. But depending on direction of behavior, the ability to lead can lead to “anti-leadership” – bossiness.This occurs inevitably in undisciplined adolescents with the status of a “star”.

The results of the sociometric study of undisciplined behavior partially confirmed the hypothesis of the thesis work – the features of the sociometric status of a teenager depend on his unruly behavior. Initially, we assumed that this would be expressed in the inability to take the status of a “star” for an undisciplined teenager. But the hypothesis found not quantitative, but qualitative confirmation of the dependence of sociometric status characteristics on the personality characteristics of the adolescent’s behavior.

In the status of “isolated” Viktor R. received the lowest index. His CC=-0.27. An analysis of observations showed that his undisciplined behavior is characterized by an extremely pronounced hostile attitude towards classmates and teachers. The sociometric status of adolescents is even lower at the level of “persecuted”. Their behavior in the classroom leads to the fact that many classmates, and not they, actually fall into the position of being persecuted. For example, Olesya R. arranged in the class periodically repeated “showdowns” of conflicts with classmates. Skillfully created unbearable conditions of scandal around them. By the seventh grade, not only peers, but also teachers became “victims” of the persecuted.

Thus, the classification of the sociometric status of adolescents in the study group made it possible to reveal that the adolescent’s deliberate violation of the rules of school disciplined behavior, the deliberate creation of risk situations, influenced his position in the problem of peer interpersonal relations, depending on his personal characteristics.

3.7. Quantitative-qualitative methods for analyzing the results of psychodiagnostics

Psychodiagnostics of deviant behavior within the framework of a comprehensive program for studying the socio-pedagogical situation of the life of schoolchildren made it possible to collect diverse data characteristic of the personality and behavior of pedagogically neglected schoolchildren. In order for the obtained material to be used conclusively in substantiating the solution of scientific and methodological problems of one’s own research and teaching activities, its statistical processing is necessary.

For example, the data obtained on the Dembo-Rubinstein self-assessment scale must be summarized in a common protocol for their primary statistical processing. The calculation of the sample mean is recommended. The sample mean value as a statistical indicator is the average assessment of the psychological property studied in the diagnostic experiment. This assessment generally characterizes the degree of its severity in general in the entire group of subjects, which was subjected to a psychodiagnostic examination. In this case, the level of claims was diagnosed by self-assessment of various manifestations: intelligence, abilities, authority among comrades, skillful hands, appearance and self-confidence. To find a general indicator of the level of claims (UP), it is necessary to add up all the indicators for these manifestations and divide the resulting amount by the number of indicators. Comparison of the obtained sample mean with individual indicators of the studied manifestations makes it possible * to judge the severity of UP for each of them. For the same purpose, it is sometimes proposed to find the median. The median is the value of the studied attribute, which divides the sample, ordered by the value of this attribute, in half. Consider, for example, a part of the protocol, which summarizes the indicators of the signs of the level of aspiration and the level of self-esteem, obtained as a result of psychodiagnostics of schoolchildren using the Dembo-Rubinstein scale in trainee practice at school.

Consider the first data array, placing it in order: 73, 86, 91, 95, 96, 97. There are six indicators in total. The middle one, which divides this sample in half,

must be between 91 and 95. To find the median, you need (91+95):2=93. This is the median, it is equal to 93. If the number of indicators is odd, then the median is the indicator that symmetrically divides the entire sample. What does knowing the median give? First of all, in our case, the median is a general indicator of the level of claims. Comparison of individual indicators of BP with the median makes it possible to judge the level of their formation. For example, the subject under No. 1 UP has three points higher than the median in his assessment of his appearance, and seven of the same units lower in his assessment of his authority among his peers. Knowing the median makes it possible to compare different indicators with a median value – the median, and not just among themselves. Medians were calculated: 93, 94.5, 75.5, 92.5, 82.

To compare the AP of different subjects diagnosed using the same technique, it is necessary to calculate the sample mean. It becomes possible to compare the levels of claims of different subjects according to the obtained average values: 90, 94.5, 75.2, 88.3, 82.3. At the level of arithmetic comparison, it is obvious that subject No. 3 has the lowest level of claims, and this gives reason to assert some personal characteristics. I would like to warn novice researchers against hasty conclusions only on the basis of the results of primary statistical analysis and note the need for further secondary statistical processing of the results of psychodiagnostics.

Knowing the median and the sample mean is useful in order to establish whether the resulting distribution of particular values of the trait under study (in our case, SP) is symmetrical and approaches the so-called normal distribution. The mean and median for a normal distribution are usually the same or differ very little from each other. In our case, such a coincidence is observed in the indicators of the subjects numbered 2, 3 and 5, and under the numbers

1 and 4, the difference between the median and mean values is significant. Thus, we have established that the resulting distribution is not normal. If the sample distribution of features is normal, then secondary statistical calculation methods based on the normal distribution of data can be applied to it. Otherwise, this cannot be done, since serious errors can creep into the calculations, warns R.S. S.33-34].

Usually in mathematical statistics, when describing the method of secondary statistical processing, there are or are no indications that it can be applied only to a normal or close to it distribution. If there is such an indication, then it is necessary to strictly follow it and check the obtained empirical data for the normality of the distribution. If there is no such indication, then the statistics is applicable to any distribution of the trait’s scores.

Among the methods of secondary statistical processing of the results of psychodiagnostics, methods that make it possible to establish:

1. Statistically significant difference between the two samples. For example, whether the expected changes actually occurred as a result of the corrective action (experiment). In this case, it is recommended to calculate the Student’s t-test to accurately establish the presence or absence of statistically significant differences between the mean values before and after the experiment. Only in the case of a significant difference will it be possible to draw a definite conclusion that the experiment was a success. Sometimes such a conclusion is asserted on the basis of an arithmetic comparison of averages or comparison of percentages. For greater importance, diagrams are built (fortunately, on a computer, you can now colorfully apply the methods of tabular and graphical presentation of the results of the experiment), which outwardly seem to confirm the conclusions of psychodiagnostics, but are absolutely unreliable.

2. If there is a special task of comparing before and after the experiment the frequency distributions of quantities expressed as a percentage, then it is recommended to use x2 – criterion.

3. To compare the variance (it characterizes how much the particular values deviate from the average value in a given sample) of two arrays of received data, in order to establish whether they differ, it is recommended to use the Fisher test. For example, it is possible to compare the effectiveness of correctional programs or methods of work with pedagogically neglected schoolchildren according to the individual range of assessments of schoolchildren’s behavior.

4. Correlation method – a method of secondary statistical processing, through which the connection or direct relationship between two series of experimental data is clarified. Its application makes it possible to establish the measure of the influence of one phenomenon on another or the relationship between the indicators of two different manifestations. For example, to identify a measure of the relationship between the index of sociometric status and indicators of unruly behavior of adolescents.

We considered it possible to use the rank correlation coefficient, since the indicators obtained during the psychodiagnostics of the sociometric status of adolescents and their personal characteristics refer to ordinal, and not to interval scales. For example, to assess the personality characteristics of adolescents, answers such as “yes”, “no” were used. The scores were then converted into points. The linear correlation coefficient is not applicable to the results obtained in this way. In this case, in order to identify the degree of closeness of the rank series, a statistical technique is used to calculate the rank correlation coefficients.

We used the correlation coefficients to find out whether there is a relationship between the variables: the characteristics of the socio-psychological status and the personal characteristics of unruly adolescents. It was also necessary to establish its degree, i.e., the tightness of the relationship. Thus, in our version, to establish the relationship between the sociometric status and personal characteristics of unruly adolescents, it was most correct to use Ch. Spearman’s rank correlation coefficient, which is determined by the formula:

**R u003d 1 – 6 E d ^{2} / n (n ^{2} – 1) (1),**

where: R is the correlation coefficient;

d is the difference between the ranks of the compared objects;

n is the number of subjects or ranks in the correlated series.

The value of the correlation coefficient varied from -1 to +1. The values lying within these limits reflected the maximum possible relationship between the compared variables. If the correlation coefficient were equal to zero, then this would mean that there is no relationship. A positive correlation indicated a directly proportional relationship between the two variables, and a negative correlation indicated an inversely proportional relationship. The greater the absolute value of the correlation coefficient, the closer the relationship between the studied variables. When the values of the coefficients + 1, we can talk about the relation of identity between the variables. With a positive value of +1, the identity is direct, and with a negative value, the opposite is observed.

To start the calculation, a summary table of all indicators of the socio-psychological status of unruly adolescents obtained as a result of psychodiagnostics was compiled. Then the calculated rank correlation coefficients between the sociometric status index and the level of claims, between the sociometric status index and the level of self-esteem, as well as between the sociometric status index and resentment, vindictiveness and hostility were entered into the table.

To calculate the coefficient according to formula (1), a number of operations had to be done. First of all, it was necessary to tabulate all the primary results to determine the ranks. We started by establishing a rank correlation between sociometric status indices (variable X) and the level of aspirations of unruly adolescents (variable Y1). The data of these variables were summarized in table No. 2. In table No. 2, to tabulate these primary results, in line 1, the numbers of the test subjects in the class journal were written out, in the 2nd and 3rd lines – the scores they received according to the first method (variable X ) and the second one (variable U1). Y1 – these are indicators of the variable – “the level of claims.”

Each primary outcome was then assigned a rank in the following way.

Table number 1.

**The relationship of sociometric status and personality traits**

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