Exploration of Determinants of Verbal Aggressiveness and Leadership through Network Analysis and Conventional Statistics : Using School Class as an Illustration

The purpose of this study is to detect structures of verbal aggressiveness and leadership using social networks analysis. Standardized questionnaires including network and non-network variables have been distributed to 128 students and 43 teachers at secondary schools. We performed complete analysis of social networks and further processing by applying principal component analysis. According to the results, a complex structure of verbal aggressiveness occurred in the classes (networks) and the structure was necessary to be explored with several network indicators (Katz, pagerank etc.). Structures of verbal aggressiveness and leadership appeared to converge. The following types of verbal aggressors were proposed: a) the “mocker”, b) the “scorner”, c) the “insulter”, d) the “teaser” and e) the “ridiculer”. As for the leadership, two types of leaders have been revealed: a) the “ideologist leader”, b) the “realist” leader. It is noticeable that both leader types appear in the occasional (indegree) as well as in the accumulative (Katz) structure. This means a rigid character of these leadership profiles.


Leadership
Research on leadership mainly focuses on transformational leaders who could change deep structures, major procedures or the overall organisation (Van Wart, 2003).Bass (1985) model examines the relationship between transactional and transformational leadership.Transactional leadership based on a relation transaction between directors and members/employees, promoting them with rewards (Burns, 1978;Pashiardis, 2004).It consists in an administration of minimal interventions (laissez-faire), based on the exceptions management (management by exception) and contingent reward (Robbins & Judge, 2012).In contrast, transformational leadership is a special leadership style applied by superiors to motivate subordinates to operate at a higher level, offering spiritual challenges and paying attention to their individual needs by creating a supportive environment (Belias & Koustelios, 2014;Gkolia, Belias, & Koustelios, 2014b).
Transformational leadership is based on trust and respect, engaging a parallel commitment to a vision creating incentives for employees (Eliophotou-Menon, 2011).The transformational leadership is grounded on the following characteristics: idealized influence, inspirational motivation, intellectual stimulation and personalized care (individualized consideration) (Bass, 1991(Bass, , 1999;;Bass & Stogdill, 1990;Robbins & Judge, 2012).According to the afore-mentioned assumptions, leadership can be regarded as process influencing thought, emotions, attitudes, and behaviours of a group of people from the leader.In this process, the led members are supposed to willingly and appropriately cooperate in order to achieve their best performance (Bouradas, 2005).
Aim of this research is to suggest determinants and effects of verbal aggressiveness and leadership, measured in term of its effect, leadership, as well as to analyze relations between leadership and verbal aggressiveness.The expected innovation lies in the implementation of complete network analysis which is expected to depict more objectively the structures of leadership and verbal aggressiveness.

Network Analysis
Complete network analysis focuses on the interaction of participants and uses a set of metrics for the analysis of their relationships (Scott, 2000;Wasserman & Faust, 1994).The following network analysis metrics have been calculated by Visone software: 1) In-degree is defined as the percentage of edges which ends in a node.It can be interpreted as an occasional hierarchy position.
2) Katz status expresses chains of successive relations using power series.Thus, it can be interpreted as an accumulative hierarchy position.It signifies situations much deeper than indegree.
3) Pagerank is based on the transferred value from one node to others and interpreted as distributive hierarchy position.It is similar to Katz status but it restricts outliers.Furthermore, it prevents hierarchy deformations induced by Katz status.
4) Authority indicates the nodes who attracting most links from other nodes, among those ones who intensively seek to maintain links.

Sampling
Classes of public secondary schools (Gymnasium and Lyceum) in Trikala have been surveyed as network samples.Each class consisted a network, where the pupils were the nodes and the links among them were their relations (trust, company, conflicts etc).In other words, such a network sampling is a cluster sampling including the survey of links among the population (Farmakis, 2000).The set was calculated to be composed by 171 individuals.There were 128 pupils (class A: 20 pupils, female: 5 male: 15, class B: 21 pupils, female: 10 male: 11, class C: 22 pupils, female: 8, male: 14, class D: 21 pupils, female: 10 male: 11, class E: 21 pupils, female: 8 male: 13, class F: 24 pupils, female: 15 male: 9).Their age varied from 13 to 17. Also, there were 43 teachers (female: 22, male: 21).Their age varied from 32 to 62. Precondition to participate a teacher was to teach over two hours per week in the class involved in the research.

Questionnaire
The questionnaire consisted of two parts: a) non-network variables (e.g.gender, birth year, teaching years etc.), and b) network variables (power dimensions, verbal aggressiveness and leadership).
The part b of the questionnaire was based on the Verbal Aggressiveness Scale (Bekiari & Digelidis, 2015) in order to measure verbal aggressiveness.Preliminary examination Scale (Bekiari & Digelidis, 2015) supported the psychometric properties of the instrument.In particular, confirmatory factor analysis indicated satisfactory fit indices (CFI: .97,SRMR: .02),and internal consistency of the scale (α = .96).The scale consisted of eight items (e.g., "insults students or teachers," "makes negative judgments of ability").
The part b of the questionnaire was based on the Principal Leadership Questionnaire which consisted of twenty four items (Gkolia, Belias, & Koustelios, 2014a) in order to measure transformational leadership.Preliminary examination supported the psychometric properties of the instrument.In particular, confirmatory factor analysis indicated satisfactory fit indices (CFI = .97,RMSEA = .06),and internal consistency of the scale (α: from .60 to .81).The scale consisted of four factors (leader models behavior, fosters commitment, provides individual support, and holds high expectations) (e.g."treats me as an individual with unique needs", "leads by 'doing' rather than simply by 'telling')".

Statistical Analysis
The network data were processed by Visone 2.16 software.Several indicators were computed (indegree, status, pagerank, authority, density).Also, different networks structure was depicted.
Thereafter, both the network and non-network data were entered into SPSS 21.Spearman bivariate correlation (to avoid outlier effect) and principal components analysis (for formulating typology) were conducted.

Examples of Structures in Verbal Aggressiveness and Leadership
In actual connections (Sparrowe, Liden, Wayne, & Kraimer, 2001).The observed conclusion can be confirmed and as shown in the Table 1, the average density of verbal aggression was .030while leadership has average density .090and the proposed as president was .091.Additionally, the average indegree-outdegree of leadership networks was bigger than verbal aggression one as shown in Table 2.
Additionally, differences can be observed in the networks observing various indicators (pagerank, status, authority etc.).These differences were expected because various indicators reveal no identical properties and meanings.So, it is useful to apply several indicators in social network analysis and not only one (Bekiari & Hasanagas, 2015).

Relationship between Verbal Aggressiveness, Leadership Characteristics and Preferred Class President
In Table 3  All leadership variables were significant correlated with the property of being preferred for president.The results showed a positive correlation between this property and the various characteristics of leadership (leader acts, leader is an example, does not believe in mediocrity, personal approach and communication).No significant correlation had been found between the property of being preferred president and "have high expectations of a leader".This can be explained by the nature of the position of the class president.It is sure that anyone of classmates expects the president to be the most capable but also knows the limitation of the position, so they don't have high expectation from him.Also, all other characteristics of power were significant correlated with the preferred class president.The cooperation, the socialization, possible future business cooperation, advisory on social matters or technical themes is positive correlated with the preference of pupils for the class president.Also, the property of being preferred for class president is positive correlated with some verbal aggression variables.If someone has threatened a classmate or keeps him out of his social surrounding he creates a profile of detached person.This profile can be enforced if the person believes that the other one use negative comments for him in his surroundings.Additionally, the use of verbal aggression in run around situations is positive correlated with the preference of class president.This can be explained as a result of the fact that pupils use verbal aggression as a technique for choosing someone from their friends as a president.

Typology of Verbal Aggressiveness Based on Indegree Indicator
Table 4 shows the factor loadings after rotation.The same components suggest that the type "mocker" represents verbal aggressive pupils that making negative comments and mock with their classmates.The "insulter" type depicts pupils who do not simply mock or comment other pupils but threaten and exclude their classmates from their social milieu.The "insulter" could be regarded as an aggressive type stronger and more threatening than "mocker".Both types are based on indegree.Thus, they express an occasional situation.

Typology of Verbal Aggressiveness Based on Pagerank Indicator
Table 5 shows the factor loadings after rotation.The types appearing in this table are quite similar with these revealed in Table 4. "Mockers" want to cause  repeated emotional pain, distress, or annoyance to theirs' classmate using any type of comment.The "scorner" type describes schoolchildren who the victim describes them as pupils who have lack of approval for them."Mockers" use verbal aggressiveness because they don't want someone to be to their surroundings."Scorners" seem to be more decided to exclude others, as they do not even spend time for commenting them.

Typology of Verbal Aggressiveness Based on Kantz
Status Indicator Table 6 shows the factor loadings after rotation.The items that cluster on the same components suggest represents mockers and the second component "scorners".This could be explained because status and pagerank have quite similar structural meaning.

Typology of Verbal Aggressiveness Based on Authority Indicator
Table 7 shows the factor loadings after rotation.The items that cluster on the same components suggest that first type represents verbal aggressive students named "teaser".They act cruel and criticizing their classmates with unkind way.The second type describes verbal aggressiveness students proposed to named "ridiculer".They were making harsh comments, making fun in cruel way.This typology is authority based.Thus, these two types reveal a much more persistent structure created by a respectively fanatical activity.The "teaser" behavior simply consists in commenting while the "ridiculer" is much more active than just commenting.

Typology of Leadership Based on Indegree Indicator
Table 8 shows the factor loadings after rotation.The first factor had four parameters with high loads that denote a leader behaviour pattern but also with high  expectations.This factor was named "ideologue" leader.The second factor had the remaining two parameters that indicate providing personalised support from the leader.This factor was called "realist leader," after trying to take account of real possibilities and the degree of acceptance of decisions.These two leadership profiles seem to be exclusive to each other, as they do not present any common parameter.Thus, they are two absolutely different alternatives.

Typology of Leadership Based on Kantz Status Indicator
Table 9 shows the factor loadings after rotation.The factors are the same just with those of the indegree (see Table 8) and, therefore, are named similarly,  "ideologue" and "realist" leader respectively.This means that they both are equally implemented in incidental as well as in deep-rooted leadership tactics.

Conclusion
Results of present study, regarding structures in verbal aggressiveness and leadership, indicate that pupils choose for their leader as a person which comes from their surroundings, especially those they trust and have the most of the characteristics of a transformational leader.The networks of leadership were more cohere than ones of verbal aggressiveness.
As for the verbal aggressiveness is present to our classes and the structure seems to be complicated so it is useful to apply several indicators (Katz, pagerank etc.) and not only one.Different indicators reveal different properties and meanings.The following types were proposed: a) the "mocker", b) the "scorner", c) the "insulter", d) the "teaser", and e) the "ridiculer".The using of a wide range of network metrics (indegree, Katz, pagerank, authority) reveals a re-spectively meticulous range of types depicting distinct structures and behaviors.
As for the leadership types ("ideologue" and "realist"), it is noticeable that they both appear in the occasional (indegree) as well as in the accumulative (Katz) structure.This means a rigid character of these profiles.

Table 2 .
Average in-out degree of six networks (computed by Visone 2.16).

Table 3 .
Table of correlations.
Verbal Aggressiveness (do you believe that you express negative comments) .220.824Verbal Aggressiveness (don't want you in his social surrounding) .186.454Extraction Method: Principal Component Analysis.Rotation Method: Varimax with Kaiser Normalization. a Rotation converged in 3 iterations.
a Rotation converged in 3 iterations.

Table 6 .
Katz status typology of verbal aggressiveness.
a Rotation converged in 3 iterations.
a Rotation converged in 3 iterations.
a Rotation converged in 3 iterations.

Table 9 .
Status typology of leadership.
Extraction Method: Principal Component Analysis.Rotation Method: Varimax with Kaiser Normalization. a Rotation converged in 3 iterations.