The article proposes consider the application of visual analysis of psychological testing results through the use of directed graph representations. It is proposed to consider the method of visual analysis by means of various representations based on the analysis of the number of connections between the elements of the system, considered as the basis for the formation of a directed graph. In the example considered in the article, it is proposed to consider the scales of the integrated test technique used as the vertices of the graph. As the main views, the application of calculating centrality properties based on the number of links, the topological structure of links, and the Page Rank parameter is demonstrated. It is proposed to use the method of visual analysis of the graph as an additional to the classical method of correlation analysis used in processing the results of the application of psychodiagnostic methods. The possibility of using visual analysis to form hypotheses about the possible optimization of the structure of the scales used in the design of psychodiagnostic techniques (test batteries) is shown. In parallel, the results of the analysis of the leadership qualities of such a category of specialists as software developers (members of development teams) are presented.
Over the past few years, there has been a growing interest in developing professional leadership
skills. This is due to many reasons, however, one of the main ones is that business, technology,
communications, human values today function in an era of continuous change. The sphere of
professional project management is no exception. Organizations such as the International Project
Management Association (IPMA) [
Today, a wide range of approaches to the development of professional leadership qualities are
being formed. Each organization, human resources specialists, consultants have their own preferred
approach to leadership. But, unfortunately, there are not enough studies, the results of which could
demonstrate which of the approaches is the most effective [
A serious problem in solving such a problem is the professional choice of the concept of
"leadership" among many modern approaches - in modern psychology there are at least several dozen
such approaches. The presence of such a large number of theories hinders progress in practice and
research, in which case it becomes necessary to consolidate leadership theories. Emmanuel Mango,
author of the article "Rethinking Leadership Theories" [
The existing methods of assessing and profiling personality traits are based both on standard tests and on the creation of our own "test batteries", collection of primary data, their processing (including using statistical methods) and interpretation of the results. This is not to say that the current state of affairs is at the "initial" stage - rather, we can talk about many years of established practice. Nevertheless, today more and more attention in the field of direct data analysis is paid to visualization. There was even such a thing as "visual data analysis". One of the most effective ways to represent data in complex integrated systems is to represent it in the form of graphs, which is extremely rare in the field of data analysis in the field of engineering psychology.
An important problem, according to the authors, is that it is extremely rare to find in practice attempts to create programs for the development of professional competencies based on the relationship between the leader's character and personal characteristics, making it as individual as possible, thereby increasing the rather low efficiency of personnel development programs, often based on the idea of "development of all" in "all directions", regardless of the account of personal characteristics.
As a possible approach to the construction of models of complex organizational, technical,
socioeconomic and other systems, it is proposed to use the graph theory toolkit, which is a constituent
element of the general theory of systems in the representation of L. Bertalanffy [
This article proposes to consider the use of tools from another, theoretical block of the Bertalanffy structure - the toolkit of graph theory in relation to classical methods of data processing of research carried out in the field of practical psychology.
The transformation of the classical correlation matrix into an adjacency matrix is proposed for the analysis of the structure of the factors underlying some test methods, using the example of the analysis of some results that were obtained in a real study.
The main methods used were the following:
1. Analysis of leadership theories and construction of a system of "scales" for the development
of test methods
2. Psychological testing
3. Methods of statistical data processing in the program IBM SPSS 23.0 [
5. Visualization of the obtained adjacency matrix in the form of a directed graph in the yEd
environment [
The review and analysis of leadership theories in the work of E. Mango, as well as a broad
analysis of scientific literature on leadership, was carried out in terms of the presence of six
fundamental areas of leadership: the character of a leader as a whole (based on morality and ethics),
special individual characteristics (mental abilities , level of extraversion, emotional intelligence,
perseverance, courage, striving to achieve success) [
In the modern "managerial" approach (in particular, in the competency models of project
managers), "skill theory" and "behavioral theory" are very common. Behavioral theory is based on a
leader demonstrating certain behaviors to achieve desired goals. In behavioral practice, leaders are
people-oriented in the first place, create and maintain optimal conditions for the activities and
development of followers. In an organizational context, the behavior of a leader is aimed at tasks, the
effectiveness of processes in the organization, in this case, leaders rely on current research and
innovation [
In our opinion, the most effective approaches to the study of leadership are still transactional and transformational theory. These theories are well developed and relevant today. In addition, there are techniques for diagnosing the character of a leader in terms of transactional and transformational leadership, the use of which is the standard for leadership research.
Transactional leadership involves the use of transactions, rewards, and punishment to motivate
followers to achieve organizational goals. In this approach, there are several ways: accompanying
reward, deviation management (search for violations of agreements and contracts, the leader suggests
punishment or fines), passive deviation management (the leader only takes steps to punish followers
in case of failure to achieve goals) [
Transformational leadership refers to situations in which followers are producing more results than
expected. A leader motivates followers beyond expectations. Within this theory, both the leader and
the followers work together to increase the level of productivity. The behavior of leaders is
characterized by ideological influence, inspiring motivation, intellectual stimulation, and an
individual approach to their followers [
This opinion is caused, in a practical sense, by the study by the authors of the combination of such
qualities as "controlling" and "leadership". The behavior of individuals with a high level of control is
characterized by a high level of organization, persistence, purposefulness, and a low level of
impulsivity [
The "controlling" (synonym: “conscientiousness”) component includes a high level of
selfdiscipline, productivity, ethical behavior, and striving for achievements [
Accordingly, despite the use of a number of techniques by the authors in their psychodiagnostic projects, it is proposed to consider in this article the results of using the Eight-Factor Leadership Questionnaire, which includes both the scale for assessing the factors of the "Big Five" and the scale for assessing leadership qualities, including limited, transactional and transformational leadership styles.
As already mentioned in the Methods section, of particular interest is the analysis of the results obtained in a sample of 58 specialists of an IT companies using the Eight-Factor Leadership Questionnaire, which includes scales for assessing the Big Five factors and for assessing the limited , transactional and transformational leadership.
Table 1 shows the mean values on the Big Five scales of the eight-factor leadership questionnaire.
Based on the data obtained on the main scales of the "Big Five" of the eight-factor leadership questionnaire, described in Table 2.4, it should be noted that the lowest level on the Emotionality (N) scale was 3.96. The highest score belongs to the scale of Originality (O), 5.32.
Indicators on the scales of Emotionality (3.96), Energy (E) (4.74), Cooperation (A) (4.68), Controlling (C) (4.87) are in the range of average values. It can be concluded that study participants are able to control their impulses, cope with stress and negative emotions. In addition, the research participants have the characteristic that they do not strive to constantly be in a team, they are not very sociable individuals, however, being in a group of people, they do not experience much discomfort. If it is possible to avoid making unpopular decisions in the group, research participants tend to act in this way. In their work, research participants strive to follow the rules and requirements, but do not attach much importance to them. They tend to feel uncomfortable in an environment where there are strict rules and at the same time in an environment where there are no rules. The results of the study on the Originality scale (5.32) are in the high range. This means that the subjects practice new methods and approaches in their work, even when there are established standards, they feel comfortable in a creative environment where there is freedom of decision-making.
It should be noted that the results of the study on the eight-factor leadership questionnaire coincide with the results of the study on the NEO-PI-R questionnaire.
Table 2 presents the mean values for the leadership style scales of the eight-factor leadership questionnaire.
Based on the data obtained on the scales of styles and consequences of leadership of the eightfactor leadership questionnaire, described in Table 2.5, it should be noted that the lowest level on the Laissez-Faire scale was 2.90. The highest score belongs to the Idealized Influence (behavior) scale, 5.54.
Indicators on the Limited Leadership (3.09), Passive Management-by-Exception (3.35) and Laissez-Faire (2.90) scales fall within the range of medium and low values. This means that subjects are less likely to resort to these leadership styles than to transactional and transformational ones. Rarely does their behavior show aloofness from communication with followers, unwillingness and lack of desire to understand the needs of followers, as well as a lack of assistance to satisfy them. The subjects are not inclined to use a system of penalties and sanctions against followers. Indicators on the scales Transactional Leadership (4.95), Proactive Management-by-Exception (4.67) are in the range of average values, it can be concluded that the subjects tend to control the performance of tasks by their followers, as well as take proactive actions when problems arise, another indicator of transactional Leadership, Contingent Reward (5.23), Scale scores are in the high range, which means that subjects tend to reward followers for successful tasks and other expected results. Most often, subjects use styles related to Transformational Leadership (5,13), among them, an Individualized Consideration (5.50), Idealized Influence (5.10) and in particular Behavioral Influence (5.54), this means that the behavior of the subjects, characterized by a trusting attitude towards followers, understanding of their intellectual needs and the ability to satisfy them, purposefulness, perseverance, is a reference and arouses respect from followers. Inspirational Motivation (4.98), Intellectual Stimulation (4.97), and Idealized Influence (attributed) (4.67) are somewhat less common, however, the indicators of these factors border on high. This means that the subjects are able to predict the future of joint activities with followers from a positive side, as well as effectively broadcast this point of view. It should be noted that the results of the 8FLQ Eight-Factor Leadership Questionnaire are similar to the results on the Multifactor Leadership Questionnaire in that subjects rarely resort to hands-off and tend to resort to transactional leadership styles more often when communicating with followers. As a result of the correlation analysis of the data, relationships were found between the personality traits of the Big Five NEO-PI-R and the leadership qualities of the eight-factor leadership questionnaire, the personality characteristics of the Big Five and the leadership styles of the eightfactor leadership questionnaire. The variables were tested for normal distribution, since a number of variables had a distribution that differed from the normal one; later, a nonparametric method of statistical analysis, the Spearman method, was chosen. So, Figure 1 shows a table with the results of the correlation analysis of the Big Five data of the NEO-PI-R questionnaire and the leadership qualities of the eight-factor leadership questionnaire. Negative correlations are indicated in red, positive correlations are in green. The cells contain Spearman's correlation coefficient and the significance level below the coefficient. The sign * marks the presence of the significance of correlation (bilateral) at the level of 0.05, and ** - at the level of 0.01. can be displayed using the adjacency matrix
[сij]S = [i, j], (3)
each line of which shows the connections of one vertex with other vertices of the graph [
For the analysis of such structures use the adjacency matrix, which has specific properties [
To formalize the adjacency matrix obtained by the method described above, it is proposed to use
the Microsoft Excel [
Correlations between the selected factors F01-F19, noted in Tables 1 and 2, based on a sample of the relevant data from the full correlation matrix (Figure 2), using the above rules, can be represented as the following adjacency matrix (Figure 3).
An adjacency matrix can serve as the basis for constructing a directed graph for subsequent analysis. For further visual analysis of the resulting graph, it is proposed to use such well-known and open-source software as yEd, which allows modeling various kinds of complex structures, in particular, using a wide range of different graph representations. Figure 4 shows the structure of a graph created in the yEd environment using the standard Shape Nodes template of structural e Figure 4: Directed graph for FL01-FL19 subsystem model implemented in yEd (screenshot fragment)
As you can see from the presented figure 4, yEd allows you to visualize the links (edges) between the elements of the model (the vertices of the graph), including the direction of these links. Nodes FL in this graph correspond to the elements F from adjacency matrix for F01-F19 elements
Unfortunately, such a basic view does not allow making any analytical conclusions. It is worth using other representations to analyze the graph. In particular, the simplest next step can also be a "circular representation", but with the visualization of the weights of the vertices based on the number of their connections with other vertices of the graph, as shown in Figure 5 (normalized with respect to the element FL02 with the maximum number of connections).
As can be seen in the presented figure 5, yEd allows visualizing the weights of vertices (model elements) based on information about the number of edges (links), which makes such a representation much more information-rich than the primary representation of the model in the form of a graph presented in Figure 4. Nevertheless, such a representation, although it already allows you to form some hypothesis based on the visualization of the parameters of the system of links, in particular, to allow ranking the vertices by the number of links, but any spreadsheet editor in which you can sum up values in rows and columns of the original adjacency matrix (Figure 3) or primary corellation matrix (Figure 2). In graph analysis, one of the key concepts is centrality. Accordingly, visualization of representations of such a parameter as "centrality" will be of undoubted interest. At the same time, "centrality" can be considered both "structural" and "weighted". In particular, thanks to such a representation as "Weighted Centrality" (Figure 6), it is possible to assess the importance for the entire structure as a whole, for FL02 element. This representation allows one to form a number of hypotheses regarding the role of elements FL01 and F04 presented in the "far orbit" in the system under consideration, in addition to other assumptions that can be formed on the basis of the visualization presented in Figure 5. In any case , it is obvious that the information content of such a representation is much higher than that of Figure 4 or Figure 5. The visualization capabilities allow you to assess "centrality" directly from a structural point of view as shown in Figure 7. In particular, such a representation allows us to develop the previous hypothesis - the absence of significant relationships of the FL01 element in the structure of the fragment under consideration is visible, which suggests the possibility of excluding this element from consideration (accordingly, to further optimize the set of scales for further use of the already initially optimized method). Moreover, judging by the visual representation of the links of the FL04 element, such an exception for this element may not be worth making.
The approach proposed in the article significantly expands the previously described [
In our opinion, the use of such powerful tools for versatile visualization of the graphs of the
studied models allows us to look somewhat differently at the systems under study than only through
the prism of analytical indicators presented in a matrix (tabular) form. Based on the information
presented graphically, it becomes possible not only to propose new hypotheses regarding the
structural relationships of the systems under study, but also to “quickly test” them by visual means.
The presented visualizations certainly provide a lot of information, at least for the formation of
hypotheses. it is obvious that some of these hypotheses, in principle, could not have appeared without
visualization, similar to the one shown in the screenshots of the model views made in the yEd
environment. It is of interest to consider other possible representations that are possible for
visualization in the yEd environment. In particular, when calculating the weight characteristics, taking
into account not only the presence of the number of links, but also their structure, as suggested by the
Page Rank method [
The presented approach to the use of graphical representations, according to the authors, can be used in the analysis of any other complex systems, where a sufficiently large number of mutually influencing elements can be identified. In order for the analysis of such systems to be as effective as possible, it is necessary to use the appropriate systems that automate the work on the primary processing and visual presentation of information. Such an effective tool for an analyst's work can be software with functionality similar to the example of using the yEd product presented in the article. Perhaps this approach will allow a more “instrumental” approach to assessing the importance of individual elements, incl. by modeling situations such as “excluding” a number of nodes or edges (elements of the studied systems or connections between them), and “adding” (predicting the need for a real but previously unidentified element or a connection between identified elements), which will allow a more professional and objectively approach the assessment of complex systems.
I would like to express my gratitude to the developers of the yEd software, thanks to which today any computer user has the opportunity to perform a visual analysis of complex systems, which can be converted into a graph form. I would also like to express my gratitude to prof. V.D. Gogunsky (ONPU), thanks to whom the topic of using methods of graph theory appeared in the works of the authors.