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This is to certify that the
dissertation entitled

THE ONTOLOGICAL STATUS OF BULLIES AND VICTIMS

presented by

RONALD D. DERRER

has been accepted towards fulﬁllment
of the requirements for the

Ph.D. degree in School Pchhology

 

 

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2/05 p:/ClRC/DaleDue.indd-p.1

THE ONTOLOGICAL STATUS OF BULLIES AND VICTIMS
By

Ronald D. Derrer

A DISSERTATION

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Counseling, Educational Psychology and Special Education

2005

ABSTRACT
THE ONTOLOGICAL STATUS OF BULLIES AND VICTIMS
By
Ronald D. Derrer
This study utilized an empirical approach to explore whether or not unique groups of
students exist in a population based on involvement with bullying and victimization
experiences. Nearly 90% of upper elementary students (N=268) in an urban elementary
school located in the American Southeast completed the bullying and victimization
questionnaires used for analysis. Each addressed six types of bullying behavior and asked
for rates of involvement over the past week. Split-sample hierarchical cluster analyses did
not identify consistently discemable groups, including those that might be labeled bullies
or victims. This failure to ﬁnd unique clusters of children based on bullying and
victimization levels was accompanied by a ﬁnding that 63% of the students said they had
committed at least one act of bullying during the past week while 81% reported being
victimized. The results of this study challenge the prevailing view that small numbers of
children are involved with bullying and raise concerns with several standard practices of

bullying research.

ACKNOWLEDGEMENTS

I wish to sincerely thank my advisor, Dr. Jean Baker, for continual encouragement and
support in this dissertation process. She has modeled scholarship as a shared endeavor
and allowed learning situations that made this work possible. I am also grateful to Dr.
Eugene Pemell for the teaching opportunities he provided and the example he set in
shaping the ideas of others with laughter. Finally, I am thankful to Drs. John Carlson,

Christopher Dunbar and Matthew Mayer for serving on my doctoral committee.

iii

TABLE OF CONTENTS

LIST OF TABLES .............................................................................. v

LIST OF FIGURES ........................................................................... vi
CHAPTER

I INTRODUCTION ............................................................. 1

11 REVIEW OF THE LITERATURE .......................................... 3

III METHOD ....................................................................... 26

Sample ................................................................... 26

Procedure ................................................................ 27

Measures ................................................................ 27

Bullying .......................................................... 27

Victimization .................................................... 3O

Cluster Analysis Techniques .......................................... 31

Cluster Analysis Procedure ............................................ 32

Variable requirements .......................................... 33

Treatment of cases .............................................. 34

Similarity measures ............................................. 34

Clustering algorithms ........................................... 35

Cluster solutions ................................................. 38

Cluster validation ............................................... 39

Demographic Analysis Procedure ..................................... 40

IV RESULTS 41

Demographic Findings ................................................. 41

Grade level ....................................................... 41

Gender ............................................................. 41

Race / ethnicity ................................................... 41

Informal Assessment of Distributions ............................... 43

Cluster Analysis Results .............................................. 51

V DISCUSSION ............................................................... 58

Limitations of the Study ............................................... 63

Directions for Future Research ....................................... 66

Summary ................................................................ 68

REFERENCES ................................................................................. 70

iv

LIST OF TABLES

Utilized Bullying and Victimization Questions ....................................... 28
Unused Aggression and Victimization Questions .................................... 29
Descriptive Statistics: Medians, Means, and Standard Deviations on

Bullying and Victimization Scores Based on Grade Level, Gender and

Ethnicity .................................................................................... 42
Cluster Analysis Results for Subsample A: Agglomeration Schedule ............. 51
Descriptive Statistics: Medians, Means, and Standard Deviations on

Bullying and Victimization Scores for the Three Clusters identiﬁed in

Subsample A ................................................................................ 53
Cluster Analysis Results for Subsample B: Agglomeration Schedule ............. 54

Cluster Analysis Results for Subsample B2(one case removed):
Agglomeration Schedule ................................................................. 55

Descriptive Statistics: Medians, Means, and Standard Deviations on
Bullying and Victimization Scores for the Three Clusters identiﬁed in
Subsample BZ .............................................................................. 57

LIST OF FIGURES

Bar plot of composite bullying score distribution in subsample A ............... 44
Bar plot of composite victimization score distribution in subsample A ......... 45
Bar plot of composite bullying score distribution in subsample B ............... 46
Bar plot of composite victimization score distribution in subsample B ......... 47
Scatter plot with bullying and victimization scores for subsample A ............ 49
Scatter plot with bullying and victimization scores for subsample B ............ 50

Scatter plot of bullying and victimization scores for subsample A with
individual cases labeled by cluster group membership ............................. 52

Scatter plot of bullying and victimization scores for subsample B with
individual cases labeled by cluster group membership ............................. 56

vi

CHAPTER I

INTRODUCTION

By deﬁnition, bullying results in physical or emotional suffering for victims and
can exist in any social group where afﬁliation is not self-selected. Adults will encounter
bullying in the workplace, making it a focal topic for Industrial and Organizational
Psychologists in some parts of the world (Schuster, 1996). Children, will encounter
bullying in their educational settings, making it an obvious area of interest for School
Psychologists. This profession’s expertise working with children and the educational
system provide a unique position from which to address bullying concerns.

With involvement by School Psychologists, a ﬁeld of research has developed over
the past three decades in attempts to identify the individuals who perpetrate or are
victimized by childhood bullying and to learn more about them. Answers have been
sought to the questions of why bullies bully and why victims are victimized. Family
backgrounds, parenting styles, physical traits and psychological characteristics have all
been explored as potential answers for why children are involved in these antagonistic
behaviors. Trends for bullying involvement related to gender, age, and culture have been
investigated multiple times. Attempts have even been made to identify the long term
impacts of bullying involvement during childhood. However, conclusions reached from
these research efforts have ﬁequently been inconsistent and have sometimes been
contradictory. When the variations in ﬁndings have been acknowledged, the explanations
for discrepancies have themselves diverged. Yet, in spite of differing opinions regarding

the ﬁeld’s current understanding of bullying, at least one unifying idea has been present

throughout the research. It has encompassed a belief that bullies and victims are unique
populations who distinctly differ from their peers in their bullying behaviors and
experiences.

While no one has claimed the labels bully and victim should be considered
clinical diagnoses, these terms have largely been treated as though representing unique
forms of psychopathology. Identity as bully or victim becomes the deﬁning feature of
individuals, allowing etiological and functional commonalities to be explored. Yet, no
studies published in English were located that explicitly began without a priori
assumptions regarding the existence of unique bully and victim groups within a larger
population. In other words, the ontological status of bullies and victims has not been a
strict target of research.

In defense of this void in bullying research, the ﬁeld’s history makes the absence
of focused exploration into the ontological status of bullies and victims understandable. It
is also the case that limitations in current statistical techniques do not allow for absolute
answers when asking whether- or not distinct groups exist within a sample or p0pulation.
However, numerous methods are available to indicate patterns of characteristic dispersion
and strongly inform theoretical classiﬁcations of human beings. Such techniques are
commonly used in the investigation of clinical deﬁnitions of psychopathology but have
not previously been employed in the study of bullying. This study attempted to place
current assumptions about the nature of bullying and victimization in historical context

and initiated empirical exploration of the ontological status of bullying and victimization

in children.

CHAPTER II

REVIEW OF THE LITERATURE

The deﬁnition of bullying used in most research has changed little since it was
ﬁrst delineated nearly 30 years ago (Olweus, 1978). In sum, bullying involves acts of
aggression that are (a) intentional, (b) repeated, and (c) perpetrated within a relationship
of imbalanced power. Though succinct, this deﬁnition encompasses a wide range of
behaviors. Under the ﬁrst criterion, bullying may include acts of aggression ranging from
direct physical confrontation and assault to the manipulation of social situations toward a
goal of embarrassing or rejecting others. Similar actions done with playful intent are not
considered bullying regardless of any ensuing psychological or physical injury. The
requirement of repetition means even severe isolated acts of aggression do not constitute
bullying. Singular hostile behaviors may be components of bullying, but the concept
itself refers to the commission of such behaviors over time. As further clariﬁcation, the
criterion of repetition refers to a series of actions united in their aggressive intent and not
a need for multiple displays of one speciﬁc behavior. The ﬁnal standard in the Olweus
deﬁnition of bullying requires disparate levels of power between the involved parties.
Bullying exploits this differential. Aggression between children of equal physical or
social stature is explicitly excluded. The nature of behaviors and interactions within this
deﬁnition of bullying has led some to suggest the term peer abuse as an alternative label
(Hodges & Perry, 1996).

Around the world, bullying research has typically begun with the pragmatic goal

of using ﬁndings to reduce peer victimization. As a ﬁeld, it has sometimes struggled to

balance a desire to intervene with the need to systematically acquire new knowledge. In
the United States, additional awareness of bullying and a greater impetus to eradicate it
followed a series of school shootings, including those at Columbine High School. State
legislatures have begun passing laws mandating that schools implement programs to
address the problem of bullying (Limber & Small, 2003). Underlying these laws is a
perceived connection between the actions of shooters and reports of their longstanding
victimization by peers. This association has been evidenced by the fact that states
implementing anti-bullying laws were more likely to have had notable school shooting
incidents than others (Furlong, Morrison & Greif, 2003). In countries where bullying
research has been most active, similarly tragic events have commonly provided a societal
level impetus to understand children’s experiences with it (OIWeus, 1993). The
heightened public awareness and calls for intervention following these events strains the
ever-present tension between investigation and response demands.

Though the victims of bullying initially come to mind when considering its
effects, the immediate and long term consequences for the perpetrators have been of
interest as well. Early work in the ﬁeld led researchers to question whether the aggressive
behavior patterns typifying bullying persisted into adulthood. Findings at the time
suggested a high level of stability in these aggressive tendencies (F arrington, 1993;
Olweus, 1979). Without intervention, bullies were believed more likely to engage in
future behaviors harmful to themselves, others and the community. Thus, identifying and
modifying harmful interpersonal behaviors in childhood has been viewed with the
potential to provide signiﬁcant and long lasting beneﬁts at both the individual and

societal level.

The practical goals of bullying research have taken precedence over the
formulation of a unifying developmental theory. A tendency to emphasize correlational
studies while avoiding a theoretical incorporation of ﬁndings has drawn criticism
(Schuster, 1996). However, cognitive behavioral frameworks were sometimes implied in
early studies and have been more explicitly stated recently (Ma, 2002; Pellegrini 1998).
Researchers working from a cognitive behavioral perspective posit that bullying, like any
repeated social experience, inﬂuences a child’s perceptions of self and others. Thus,
experiences shape future thoughts and actions.

Generally speaking, researchers working from a cognitive behavioral perspective
have conceptualized bullying in one of two ways (Arsenio & Lemerise, 2001; Espelage &
Swearer, 2003). One group emphasizing information procession models has envisioned
the use of bullying behaviors as a result of skill deﬁcits. In other words, the child bullies
others because they do not possess more appropriate skills to attain social and material
goals (Crick & Dodge, 1994). An alternative perspective has held that bullying stems
from conscious decisions by children to utilize aggressive behaviors even though
alternative approaches and skills may be possessed. One of the better examples of the
latter view has most recently been espoused in Dominance Theory, which asserts
bullying behaviors are used to help establish a social hierarchy among children (Long &
Pellegrini, 2003).

Other theoretical models have focused less on the cognitions and behaviors of
individuals than on the systemic inﬂuences on bullies and victims. A handful of scholars
have clearly utilized an ecological perspective to help frame their discussions (e. g.

Rodkins & Hodges, 2003; Swearer & Doll, 2001). They emphasize the nested systems

within which bullying occurs. From an ecological understanding, it makes little sense to
focus on individual characteristics of bullies and victims in isolation ﬁ'om their social
settings. However, researchers working from this model have been a minority in the ﬁeld.

Whether espousing an atheoretical or cognitive behavioral framework for
bullying, reliance on a medical model of pathology has been remarkably consistent in this
ﬁeld of research. In other words, involvement with bullying and victimization has been
framed as an identiﬁable marker of atypical individuals, the bullies and victims. Even
scholars emphasizing systemic understanding have begun with research questions asking
how bullies and victims ﬁt into their peer ecolologies (Rodkin & Hodges, 2003).
Bullying and victimization are regarded as intrinsic traits for a relatively small number of
children. Consequently, the majority of research efforts in the ﬁeld have begun with
efforts to determine which children are the bullies and victims. This accomplished,
researchers have sought to identify demographic and psychological characteristics for
these groups toward the goal of informing intervention (Batsche & Knoff, 1994). In light
of the desire to understand and comprehensively describe the children involved with
bullying, correlational studies have been a favored, if sometimes criticized technique. In
sum, the assumption that bullies and victims ﬁrndamentally differ from other children has
guided the preponderance of research.

A second characteristic of bullying research has been its self-contained quality. It
has rarely integrated work from other areas. Authors who have attempted to place
bullying behaviors within a larger research paradigm have generally considered them a
sub-category of aggression or violence (Ma, 2001; Smorti, Menesini, & Smith, 2003).

Certainly, the lack of reference to related ﬁelds has not been unidirectional, with bullying

often missing from discussions, articles and books focusing on other forms of childhood
aggression until recently. Relevant areas of research may include general aggression,
youth violence and conduct disorders. Fortunately, a recent summary of bullying research
in America asserted that the incorporation of such parallel lines has begun (Espelage &
Swearer, 2003). Several authors have been making efforts to directly tie bullying to
related areas of study. For example, ongoing research efforts in reactive and proactive
aggression have been explored with attention given to contributions this may make in
understanding bullying (Camodeca, Goossens, Meerum—Terwogt, & Schuengel, 2002;
Salmivalli & Nieminen, 2002). Similarly, researchers studying attributional tendencies
have also made forays into the ﬁeld (Pellegrini, 1998). However, such work remains in
its early stages and is not yet standard practice.

In contrast to research on bullies, studies solely focusing on victims have been
less hindered by topical boundaries. To an extent, the higher ﬂuidity in victimization
research may be the result of vocabulary in the English language. Few other terms refer
to a person who is adversely impacted by an external entity or force. A victim will be
labeled so, regardless of whether experiencing bullying, harassment, abuse, violence, or
other forms of hostility.

The history of bullying research holds some clues as to its present status as a self-
contained and primarily atheoretical ﬁeld of study. While contemporary authors noted a
British paper on teasing and bullying was published in 1897 (Karatzias, Power &
Swanson, 2002), little scholarly attention was given to the topic in the ﬁrst half of the
twentieth century. According to several accounts, modern bullying research emerged

from a chance observation by a Swedish medical doctor walking past a neighborhood

playground. Peter Heinemann saw a group of boys chasing one child. The observation
prompted Heinemann, who recalled similar events from his own youth, to study this type
of hostility in human beings (Munthe, 1989; Schuster, 1996). He labeled the phenomenon
mobbing, a term that came from an English language version of animal research and
aggression theory written by Konrad Lorenz (1966). In line with the ethological origins
of the word, mobbing was viewed as group aggression against an individual who deviated
from the others in some way (Munthe, 1989). While neither fully intending to blame the
victim nor excuse those involved with the attacks, this early conceptualization did portray
mobbing as having a degree of inevitability in human interactions.

Shortly after the work of Heineman appeared, Dan Olweus, a Swedish
psychology professor working in Norway, published a work on the phenomenon of
mobbing (Olweus, 1973). The multilingual Olweus has used the terms mobbing and
bullying interchangeably in the majority of his writings, referring to the former for his
Scandinavian audiences and using the latter in English. Condensing the more individually
perpetrated implications of bullying with the group action implied by mobbing was a
conscious decision on his part. He reasoned the two were closely related phenomena
whose inﬂiction of suffering on an individual provided more justiﬁcation to join them in
study than pursue them in separate lines of research (Olweus, 1993). In 1982, an event
occurred that catapulted the topic of bullying into the Norwegian national spotlight.
Three young males committed suicide, apparently in relation to the repeated hostilities
they were subjected to by peers (Olweus, 1993). In response, the government
commissioned a nationwide study to explore the extent of bullying in Norwegian schools.

Olweus, already working in the ﬁeld, was charged with leading the investigation. From

this context, deﬁnitions, methodologies and empirical information about school bullying
began to emerge. Olweus would play a major role in similar large scale studies in Sweden
and heavily inﬂuence most work done at national levels around the world. The early
entry, immense sample sizes from which Olweus and colleagues framed their
understandings of bullying, and cogent descriptions of their conclusions lifted their work
to forefront of the ﬁeld. A framework that assumed bullies and victims were
characteristically identiﬁable became the model for research that would follow.
Certainly, acceptance of the Olweus’ conceptualization of bullying has not been
universal and critics of his theory have made themselves known. Some researchers have
insisted that bullying behaviors by groups, implied with Olweus’ native term of mobbing,
should be differentiated from the acts committed by one individual (Salmivalli,
Lagerspetz, Bjorkqvist, Osterrnan, & Kaukianinen, 1996; Schuster,l996). Others have
sought to distinguish direct bullying from indirect bullying. The former is characterized
by interactions between the perpetrator and victim, while the latter includes aggression
directed through social channels (Pellegrini, Bartini, & Brooks, 1999; Wolke, Woods,
Bloomﬁeld, & Karstadt, 2000). Indirect bullying has also been referred to as relational
aggression (Bjorkqvist, 2001). However, the majority of researchers explicitly examining
bullying has been comfortable using concepts very similar to those utilized by Olweus.
More often than concerns with the prevailing concept of bullying, criticisms have
been directed at its operational deﬁnition in research (e. g. Pellegrini, 1998;
Schuster,l996). Many mentioned weaknesses stem from the signiﬁcant challenges facing
researchers attempting to apply the three-faceted conceptualization of bullying. For

example, unless self-report techniques are utilized, any measures of intent must be

implied. In a school cafeteria, one child walking past another already sitting alone may or
may not result from a conscious effort to exclude or reject that student. In this example,
properly identifying bullying behavior hinges on correctly identifying intent. While some
forms of bullying would often provide less ambiguous interpretations in direct behavioral
observation, such as a series of verbal insults or physical abuse, they would not represent
the wide spectrum of potential bullying behaviors under a typical deﬁnition. A second
operational difﬁculty comes in establishing power differentials between students.
Techniques exist to allow estimates of social status among peers. However, the
assumption that social hierarchies ﬁ‘orn a large group directly map on to individual or
small group interactions may be problematic. Further, the majority of utilized status
measures have emphasized likeability while paying less attention to actual levels of social
inﬂuence (Rodkin & Hodges, 2003). Finally, determination of repetitive hostility evokes
further methodological difﬁculties. Either observation must occur over a considerable
period of time or self-report measures must have their validity accepted. Moreover, once
multiple occurrences of bullying type behaviors have been recorded, decisions must be
made regarding the frequency that is indicative of repetition or pattern. Such
considerations shape the methodological decisions made by researchers in the ﬁeld.

Pragrnatically, the use of self-report measures of bullying has been an attractive
choice in research efforts. The operational and stafﬁng difﬁculties found in observational
techniques have made self-reports a more feasible approach. While behavioral report
measures may also be obtained from teachers and some parents, a reasonable assumption
holds that much bullying among children occurs without adult knowledge or

identiﬁcation. Recent studies have provided support for this belief (Kumpulainen et

10

al.,1998; Pellegrini & Bartini, 2000). Thus, study methodologies have tended to center
around answers children provide themselves about their involvement with bullying
behaviors at either the initiating or receiving end. A straightforward approach has also
been taken with questions about bullying’s frequency. Often, a general deﬁnition and
speciﬁc examples of the term bully have been provided, with students asked how often
they performed or experienced such actions. Olweus began using such a procedure,
hereafter referred to as the Olweus technique, and multiple researchers have followed suit
(e. g., Borg, 1997; Boulton & Underwood, 1992).
As an example of the Olweus technique, one study in England gave the following
deﬁnition to students (Whitney & Smith, 1993):
We say a child is being bullied, or picked on when another child or young person,
or group of children or young people, say nasty or unpleasant things to him or her.
It is also bullying when a child or young person is hit, kicked, threatened, locked
inside a room, sent nasty notes, when no one ever talks to them and things like
that. These things can happen frequently and it is difﬁcult for the child or the
young person being bullied to defend himself or herself. It is also bullying when a
child or the young person is teased repeatedly in a nasty way. But it is not
bullying when two children or young people of about the same strength have the
odd ﬁght or quarrel. (p. 7)
After receiving this deﬁnition, children were asked to indicate how often they were
involved at both the bullying and victimization ends of these behaviors during the current
term of school. Answer options included; never, once or twice, sometimes (or now and
then), once or twice a week, almost daily, and more than once per day. With slight
variations, this technique has been the most common method for assessing involvement
with bullying.

Other questionnaire based studies have obtained information about the frequency

of involvement with speciﬁc behaviors believed typical of bullying. For example,

11

students may be asked to report how many times they teased someone, hit another child,
were threatened by somebody, and so on (Bosworth, Espelage, & Simon, 1999). A
variation of this speciﬁc behavior approach has asked students to rate the involvement of
other students in bullying activities (Schwartz, Dodge, Petit, & Bates, 1997). Compiling
and analyzing these data has provided another way for researchers to assess involvement
with bullying.

While only a handful of broad approaches to measuring involvement with
bullying exist, criteria for denoting levels of substantial concern have been more
numerous. No gold standard has been established for the identiﬁcation of bullies and
victims. Studies following the Olweus technique often use a commission rate of
sometimes or more often during the school term as marker on problematic functioning
(e. g. Menesini et al. 1997; Whitney & Smith, 1993). However, others using identical
questions have asked respondents to report involvement based on incidents per week
rather than the school term and developed different cutoff criteria (Rigby, 1997; Yates &
Smith, 1989). Researchers who develop composite bullying and victimization scores
typically choose some standardized distance above or below the sample mean to denote
involved groups but the distance chosen varies from study to study. Some studies have
used cutoffs as low as 0.50 SD above the mean (Schwartz, 2000). In other places, some
groups have been denoted by scores showing more than 1.25 SD of elevation (Carnodeca
et al., 2002).

Though the methods used to identify critical levels of bullying involvement have
varied, it should again be noted that few challenges have been raised to the assumption

that children with the highest participation rates comprise unique groups deserving the

12

focus of bullying research. Involvement with bullying has repeatedly been considered a
trait or characteristic of a child and not just a pattern of aggressive behavior. Nearly all
studies have divided their samples into at least three groups: (a) bullies, (b) victims, and
(c) not involved students. A fourth group of students who meet criteria as both bullies and
victims, have been less likely to be included in analyses. When present, they may be
given one of several names. Bully-victims (e. g. Haynie et al., 2001), aggressive victims
(e. g. Schwartz, 2000), and proactive victims (e. g. Smith, 1991), are among the terms
commonly used.

The current literature on bullying reveals inconsistent ﬁndings across most of the
key variables and demographics on which researchers have focused for the three or four
groups. Nowhere, has the variability of ﬁndings been more noticeable than in the
prevalence estimates obtained for children considered bullies, victims, and bully-victims.
Near the low end of frequency ﬁndings for children committing repeated acts of
aggression, one study of middle school students in the United States found only 3% of the
students sampled to be bullies (Haynie et al. 2001). Nearer the high end, roughly 28% of
American middle school students from the rural South were considered bullies (Duncan,
1999). Studies from Europe and North America commonly have suggested prevalence
rates for bullies somewhere between 5% and 15%.

The frequency estimates of victimization have been more widely scattered than
for bullies. A large study of upper elementary Finnish students identiﬁed slightly over 6%
as victims (Salmivalli & Nieminen, 2002). Yet, a study of similarly aged students in
England identiﬁed nearly 45% as victims of bullying (Wolke, Woods, Stanford, &

Schulz, 2001). A commonly cited prevalence estimate has asserted 15% to 20% of

13

children are victims of bullying at some point in their school career (Batsche & Knoff,
1994)

Bully-victims have typically been identiﬁed as the smallest portion of students in
studies. Estimates have ranged ﬁ'om less than 2% (Solberg & Olweus, 2003) to over 14%
(O’Moore, Kirkham & Smith, 1997). The former study was done in Norway, while the
latter ﬁgure emerged from data collected from Irish elementary school students.

One of the more consistent ﬁndings in bullying studies has been the relationship
between gender and identiﬁcation as an aggressor. A majority of studies have shown
boys are more likely than girls to be identiﬁed as both bullies and bully-victims
(Kumpulainen et al.,1998; Wolke et al., 2001). Yet, this ﬁnding has not gone
unchallenged, with some researchers arguing that reported gender differences in bully
identiﬁcation have resulted from an over-emphasis on physical forms of aggression.
When considering both direct (i.e. physical) and indirect (i.e. relational) aggression
several studies suggested more equivalent numbers of boys and girls are bullies (Crick,
1997; Haynie et al., 2001). However, studies showing low levels of relationship between
gender and bully identiﬁcation have been fewer than those suggesting a marked
difference between boys and girls.

Findings regarding the impact of gender on the likelihood of being a victim have
been less clear. Some research has identiﬁed minimal or no difference between the
number of boys and girls identiﬁed as victims (Bond, Carlin, Thomas, Rubin, & Patton,
2001; Kochenderfer-Ladd & Skinner, 2002). Still, the more common ﬁnding has been
that boys again and up being more prevalent in this group (N ansel et al., 2001; Osterrnan

et al., 1994).

14

Relationships between age and bullying involvement have been construed several
different ways. Some American researchers have asserted that bullying is most prevalent
during elementary school years and gradually declines through secondary school
(Pellegrini & Long, 2002). In a recent review of bullying research, other authors from the
United States asserted bullying peaks in early adolescence then declines through the high
school years (Espelage & Sweater, 2003). Yet another large study done in Norway found
involvement with bullying to increase all the way through the middle teen years, though
younger students were more likely to report victimization (Solberg & Olweus, 2003).
Though no research ﬁndings have suggesed older adolescents have the highest rates of
involvement with bullying, an argument has been made that this group simply
participates in more subtle forms of bullying and is less likely to report involvement on
self—report measures (Salmivalli, 2002).

Two other demographic characteristics have also shown inconsistent relationships
with bullying. Some studies indicated a higher likelihood for bullies to come from
families of lower socio economic status (Schwartz et al., 1997 ; Siann, Callaghan,
Glissove, Lockhart, & Rawson, 1994) while others saw little evidence of this pattern
(Bosworth et al., 1999; Wolke et al., 2001). Correlations between ethnicity and bullying
have been examined less often than other characteristics. Since much of the
groundbreaking work in this area occurred in Scandanavia, an ethnically homogenous
region, it was not a variable examined in many studies (F arrington, 1993). Researchers
who have explored this factor have had differing results. In general, European studies
have not tended to ﬁnd a substantial connection between ethnicity and bullying

involvement (Whitney & Smith, 1993; Moran et al., 1993). The few American studies

15

including this variable have been mixed in their ﬁndings, with an analysis of the largest
sample indicating very slight differences between ethnic groups (N ansel et al., 2001).
Smaller projects did indicate signiﬁcant relationships between ethnicity and rates of
involvement, with African-American children self-reporting higher levels of bullying and
lower levels of victimization than other groups (Graham & J uvonen, 2002; Leff,
Kupersmidt, & Patterson, 1999).

Beyond demographic correlates, considerable effort has been exerted in attempts
to identify physical, psychological and behavioral characteristics of children who bully.
One criticism of these studies should be mentioned in preface to this discussion. Nearly
all studies exploring these potential characteristics of children have focused on
statistically signiﬁcant mean differences between groups on utilized measures while
failing to comment on the clinical signiﬁcance of such ﬁndings (Wolke et al., 2000).
Even so, after 30 years of research, the general functioning of those identiﬁed as bullies
without concurrent victimization has not been found to be as problematic or extreme as
might be expected. The most consistent ﬁndings have indicated bullies exhibit higher
levels of externalizing behavior problems and hyperactivity than children not involved
with bullying (Kumpulainen et al., 1998; Schwartz, 2000). Assertions that bullies are
excessively depressed, anxious, suffering from low self-esteem, lacking in empathy or
socially rejected have not been repeatedly supported (Austin & Joseph, 1996; Duncan,
1999)

Higher levels of consistency have been seen in ﬁndings regarding psychological
and behavioral correlates for victims than in ﬁndings for bullies. Multiple studies have

suggested this group displays more symptoms of depression, anxiety and low self esteem

16

than do uninvolved children (Bernstein & Watson, 1997; Hawker & Boulton, 2000).
They have also been more likely to report physical health problems (Dake, Price, &
Telljohan, 2003; Espelage & Swearer, 2003). Contrary to popular belief, little evidence
has been gathered to support the notion that victims have unique physical characteristics
that contribute to their targeting by peers, especially beyond early school years (Ma,
2002). In the absence of this traditional explanation for victimization, many discussions
have implied the heightened internalizing tendencies of victims in some way open them
up for persecution (Bernstein & Watson, 1997). This perspective has been countered with
multiple regression techniques suggesting the interaction of internalizing tendencies and
the experience of victimization is cyclical (Hodges and Perry, 1999). Others have gone
further, claiming victimization is the causal agent for the symptoms identiﬁed in research
(Bond et al., 2001). In sum, many questions remain unanswered regarding speciﬁc traits
or characteristics of victims that warrant their consideration as a unique population aside
from the fact that they end up suffering high amounts of abuse from peers.

Bully-victims have not always been considered a third type of involved child in
bullying research. When they have appeared, more psychological and behavioral
difﬁculties have typically been identiﬁed than for any of the other groups considered
(Haynie et al., 2001; Schwartz, 2000). Bully-victims have been assessed with higher
levels of aggression than those who are bullies alone (Sahnivalli & Nieminen, 2002).
They have also been found to have the highest degrees of psychopathology of any group
and have been the most likely to be referred for a psychiatric evaluation (Kumpulainen et
al., 1998). Bully-victims have also been rated by teachers with the highest levels of

anxiety and depression (Ladd & Kochenderfer-Ladd, 2002). Yet again, even these results

17

have not been universal, with some studies not identifying any differences on measures of
emotional symptoms for bully-victims when compared to other groups (Wolke et al.,
2000)

One possible explanation for the different ﬁndings regarding behavioral,
psychological, and demographic proﬁles of bullies, victims and bully-victims resides in
the variety of techniques used to identify these groups in the ﬁrst place. Because no
consensus exists on how to best distinguish these groups, researchers have utilized
multiple approaches. As mentioned previously, techniques for identifying parties
involved in bullying have varied in many ways, including their choice of informants. A
majority have used self-reports while others collected data from peers, teachers or
observations. Measures of bullying have also differed; with some researchers choosing to
ﬁrst describe bullying then ask about involvement directly while others utilize composite
scores derived from speciﬁc behavioral examples. Further, cutoff points for those
considered a bully or victim have been considerably different, even within studies similar
in their use of criterion referenced or statistically based measures. Consequences of the
considerable methodological variation within the ﬁeld were recently addressed by its
foremost member. Mona Solberg and Dan Olweus (2003) emphasized that the issue of
choosing a suitable cutoff point for denoting involvement has not received adequate
attention in the bullying literature. They further asserted this oversight, along with other
methodological variations, has been largely responsible for the wide ranging prevalence
estimates. To the extent that nearly all information on bullies and victims has been
derived following the identiﬁcation of these groups in research samples, the implications

of methodological variations reach beyond frequency estimates.

18

After raising concerns with methodological variations within the ﬁeld of bullying
research, Solberg and Olweus (2003) conceptually defended the latter’s longstanding
approach to bully and victim identiﬁcation with supportive analyses provided from a
large sample of adolescents in Bergan, Norway. That study’s focus on the difﬁculties
posed by variable methodologies and the provision of recommendations for a plausible
standard was an important addition the ﬁeld. However, the possibility remains that
increased methodological consistency in the identiﬁcation of bullies and victims will not
eliminate the differences seen in prevalence rates and characteristics across studies. One
extensive review of epidemiological studies from multiple countries, which included
Olweus as a co-author, showed wide variations between nations even though the same
technique for bully and victim identiﬁcation had been used (Smith et al., 1999).

Researchers interested in these differences between countries have begun
exploring the impact of culture and language on ﬁndings. These factors may offer another
explanation for the signiﬁcant variations and occasional inconsistencies seen in bullying
research. Because there are no equivalent terms to bullying in many languages, words
chosen by researchers to replace it are inﬂuenced by their native meaning, regardless of
the deﬁnition read to respondents (Smorti et al., 2003). This same study also suggested
cultures differ in their sensitivity levels to the various aspects of bullying. For example,
children and parents in some countries may readily note any acts of physical aggression
while being less attuned to social exclusion, or vice versa. A concern with the potential
inﬂuence of cultural differences on bullying research has led the ﬁeld’s founder to
caution against comparison of results from different countries until extensive statistical

analysis has been done (Solberg & Olweus, 2003). The need to cautiously borrow

l9

ﬁndings from international research poses challenges for scholars in the United States
already ﬁ'ustrated by the dearth of bullying research ﬁom this country (Espelage &
Swearer, 2003; Nansel, 2001).

Both methodological concerns and cultural differences potentially offer some
explanation for inconsistencies found the overall body of bullying research to this point.
Yet, a third possible reason for the variations in prevalence rates and characteristics of
bullies and victims rests at the conceptual level. Since its inception, bullying research has
assumed that unique and identiﬁable groups of children exist. The ﬁeld has presented
involvement in bullying as dichotomous phenomena where subjects either are a bully,
victim, perhaps a bully-victim, or they are simply not involved. Teasing the groups apart
becomes the necessary ﬁrst step before further understanding can occur. An alternative
perspective would conceptualize involvement in bullying as a matter of degree rather
than absolutes. Bullying and victimization may occur along a continuum, or dimension,
rather than as discrete phenomena classiﬁable by dichotomies and categories. To the
extent that boundaries and cutoff points deﬁning the groups may be arbitrary and
artiﬁcial, inconsistencies in results emphasizing those dichotorrries could be expected.
Recently, respected members in the ﬁeld of bullying research expressed support for a
transition to an increasingly dimensional view of bullying involvement they perceived as
occurring (Espelage & Swearer, 2003). However, little explicit study of the
appropriateness of this conceptual shift has been done and most published research
continues to utilize a categorical approach.

Concerns with how to best conceptualize problematic behaviors are not new to

psychology. Debates pairing dimensional models of psychopathology versus discrete

20

models have a long history. A categorical classiﬁcation system similar to that used within
the ﬁeld of medicine has largely been the assumed framework for psychological
classiﬁcation (Widiger, 1997). Yet, concerns with the appropriateness of this model,
especially when working with children, have been clearly voiced by researchers for at
least the last 50 years (Cantwell, 1996). Computerized searches of the literature suggest
an ebb and ﬂow to publications on this topic, with a new wave of papers being put out
recently (e. g. Beauchaine, 2003; Mandara, 2003; Pickles & Angold, 2003).

Beyond its traditional hold on psychology, a categorical model of pathology has
reasons for support with multiple authors typically creating similar lists (e. g. Cantwell,
1996; Mandara, 2003). First, categorical models allow high amounts of information to be
held within a single label or construct. Classiﬁcation helps organize and condense the
vast amounts of knowledge and theory about the human condition and maladaptive
possibilities. By compressing information on symptoms or behaviors, communication
between professionals is greatly facilitated. Categorical models also clearly denote who is
frmctioning normally or healthily and who is not. In this way, those persons in need of
treatment can be readily identiﬁed. Recognizable diagnoses then guide research on the
disorder along with interventions and decisions regarding treatment. Once the category of
pathology has been identiﬁed, the best practices for treating that particular problem can
be followed.

In spite of intuitive appeal and a parallel with medical models found in a
categorical perspective of psychopathology, many criticisms have been leveled against it.
Several of them surface repeatedly in the literature (e. g. Karnphaus, DiStefano, & Lease,

2003; Pickles & Angold, 2003). As one point of concern, categorical models tend to

21

place the locus of problems within an individual. Like a disease, psychological or
behavioral dysfunction is perceived as a condition of the person, with environmental
settings largely ignored. This tendency of categorical models to ignore environmental
settings carries over into a minimization of cultural differences on behavioral and
emotional norms. Moreover, as categorical models focus on similarities of dysfunction,
heterogeneity within groups can be ignored. The efﬁciency introduced by allowing
assumptions based on classiﬁcation or label poses the risk that complexities and
uniqueness will be oversimpliﬁed. In addition to overlooking uniqueness in areas outside
of a classiﬁcation’s focus, differences in the etiologies of similar symptoms are largely
ignored. The dichotomous perspectives of categorical models have difﬁculty accounting
for developmental differences in cognitions and behaviors apparent under the umbrella of
a speciﬁc pathology. Finally, categorical perspectives ignore the potential impact of
subthreshold conditions.

The concerns with categorical models of pathology have led some to promote
dimensional models. In psychology, one branch of the dimensional movement has sought
to identify core characteristics of personality whose variations potentially explain
numerous disorders (e. g. Cloninger & Svarkic, 1994). A second branch has felt
comfortable maintaining existing areas of problematic or adaptive functioning but
envisioned their presence of absence along a continuum (Clark, 1999). Supporters of the
second position mention a dimensional model’s ability to address many of the
shortcomings found in a categorical perspective. They readily incorporate subsyndromal
levels of impairment rather than forcing decisions about whether impairment is present or

not (Kamphaus et al., 1999). This quality can make handling cases of comorbidity or

22

multiple symptom patterns less problematic (Cantwell, 1996). By emphasizing the
presence of given symptoms in many people, rather than just a few extreme cases,
dimensional models more easily incorporate environmental inﬂuence into understandings
of dysfunction. Researchers examining the continuous nature of depression noted that
dimensional perspectives of disorder often result in group level or systerrric interventions
(Pickles & Angold, 2003). Finally, dimensional explorations of psychological and
behavioral functioning typically provide more statistical strength and evidence greater
reliability in research studies than categorical models (Cantwell, 1996). They increase the
possibility that subtle relationships with other factors might be uncovered.

The debate between supporters of categorical and dimensional models of
psychopathology has no clear resolution in sight. Theodore Beachaine (2003) has stated
neither camp will ever claim complete victory because neither holds true all of time. He
reviewed adult psychopathology literature, since little taxometric work has been done
with children, and suggested at least some traits and disorders are distributed as discrete
classes while others appear better conceptualized as dimensional phenomena. In his
article, Beachaine noted that the majority of arguments historically used in the debate
between dimensional and discrete views of psychopathology have been based on
methodological or pragmatic grounds but few discussions have actually focused on the
ontological status of behavioral traits. Beauchaine argued that identifying the discrete or
dimensional distribution of behavioral characteristics is best considered a topic for
empirical inquiry, which can and should be explored through theory-driven taxometrics

research.

23

Returning to the existing body of bullying research, several supports for the
relevance of a dimensional perspective are identiﬁable at both the empirical and
theoretical level. In the large study intended to evidence the validity of Olweus’s
traditional cutoff scores for bullies and victims, clear linear trends were seen between
bullying and externalizing problems and between victimization and internalizing
problems (Solberg & Olweus, 2003). Though the authors explicitly mentioned these
trends, their potential support of a dimensional model of bullying involvement was not
discussed. Second, a recent meta-analysis of research suggested the stability of general
aggression in individuals is far lower than the early work of Dan Olweus had suggested
(Derzon, 2001). In other words, aggression did not emerge as a static personality
characteristic but was widely distributed within individuals and the general population.
Though the analysis was not limited to aggression deﬁned as bullying, it included work
ﬁom the ﬁeld. Finally, at least one aspect of the typical deﬁnition of bullying readily ﬁts
a dimensional perspective of its occurrence. The requirement that aggression be repeated
slides easily into a continuous model. Peer abuse occurring 20 times within a speciﬁed
time frame can be seen as more severe than the same behaviors occurring three times in
the same window.

The vast majority of research exploring bullying and victimization in children has
assumed both to be discrete rather than dimensional entities. This consensus at the
conceptual level has not led to similar unity in ﬁndings. While methodological and
cultural differences may account for some of the ﬁeld’s inconsistent ﬁndings, an
improperly imposed categorical framework may have also hindered attempts to

understand these behaviors. Prior to this study, no research had explored the distributive

24

nature of bullying perpetration or victimization without a priori hypotheses. Utilizing
empirical methods with a sample of upper elementary students, this study asked whether
or not naturally distinct clusters of children were identiﬁable based on their bullying and
victimization experiences. Framed another way, the study utilized taxometric research

methods to explore the ontological status of bullies and victims.

25

CHAPTER III

METHOD
Sample

The sample for this study came ﬂom archival data made available by the public
elementary school where it had been collected. The midsize city where the school was
located was in the Southeastern region of United States. All 268 study subjects (139 girls,
129 boys) attended this school during the spring of 1998. They were enrolled in the third
(11 = 89), fourth (n = 96), or ﬁfth grade (n = 93) at that time. Ages ranged between 8 and
12 years. The school collected the data as part of its educational programming, so a
participation rate of approximately 90% was obtained. The sample was 44% Aﬁican-
American, 44% White, 3% Asian, 3% Native-American, and 6% other. This compared
favorably with the racial composition of the entire school district, where 48% of the
children were Aﬂican-American and 38% White. Students attending the school were
transported ﬂom a large geographic region within the district. The dispersion of
children’s homes was due to a limited school choice plan as well as an enrollment system
designed to maintain balanced racial compositions within district schools. The school
reported a 58% participation rate in the ﬂee and reduced cost lunch program, indicating
signiﬁcant poverty among the students. Race and SES were crossed in the school, with
poverty over-represented among African-American students. Descriptions of the entire
school stated 74% of African-American students received ﬂee or reduced lunch

assistance while only 5% of White children participated.

26

Procedure

Survey information was collected ﬂom students by the elementary school to
establish a baseline for ﬁxture evaluation of a school wide violence prevention plan.
While information was gathered at each grade level, students below the third grade
completed less extensive questionnaires that could not be utilized for the purposes of this
study. Because the surveys were administered in conjunction with a school-wide
curricular initiative, individual parental consent was not required or obtained. The
elementary school and the Michigan State University Committee for Research Involving
Human Subjects approved the use of this archival data for research purposes. Surveys
were administered in students’ classrooms by consulting faculty and students ﬂom a
nearby university with classroom teachers present and assisting as needed. The measures
were presented visually, using an overhead projector, and read aloud to control for

reading differences among the students.
Measures

Bullying. Involvement with the commission of bullying behaviors was gauged by
self-reported acts of aggression performed during the week prior to the survey. The
Aggression Scale (Orpinas & Frankowski, 2001) had been incorporated into the
questionnaires completed by third through ﬁfth grade students. It was composed of 11
items and was intended by the authors to measure physical and verbal aggression, along
with information about anger. While The Aggression Scale was not designed as a speciﬁc
measure of bullying behavior, it has been used for this purpose (Bosworth et al., 1999). A
factor analysis done during the study by Bosworth and colleagues suggested two distinct

features were actually being measured by the scale: one bullying and the other anger.

27

Differences between the two types of aggression were not apparent. Replication of The
Aggression Scale factors could not be attempted during this study, as the cluster analysis
techniques eventually used were not compatible with conduction of a preliminary factor
analysis on the aggression measure (see Aldenderfer & Blashﬁeld, 1984; Hair et al.,
1998). Hence, ﬁndings ﬂom the Bosworth group provided empirical reason to selectively
incorporate items ﬂom The Aggression Scale into a measure of bullying behavior.
Theoretically, the concepts of verbal and physical aggression targeted by the survey
authors were common to the deﬁnition of bullying while the inclusion of anger was not.
Regarding bullying and anger, one does not necessitate the other. Undoubtedly, bullying
Behaviors and feelings of anger can coexist. However, a child need not feel angry to
commit acts of bullying, and feeling angry without any aggressive action does not

constitute bullying.

Table 1

Utilized Bullying and Victimization Questions

 

Bullying Victimization
l. I teased students to make them angry. I. A student teased me to make me angry.
2. I said things about other kids (made fun 2. A student said things about me to make
of them) to make other students laugh. other students laugh (made fun of me).

3. I pushed or shoved other students. 3. A student pushed or shoved me.

4. I slapped or kicked someone. 4. A student slapped or kicked me.

5. I called other students bad names. 5. A student called me (or my family) bad

names.
6. I threatened to hurt or to hit someone. 6. A student threatened to hurt or to hit me.

 

 

28

Table 1 indicates items retained, while Table 2 displays those withheld from use.
Three of the rejected questions speciﬁcally referred to the perpetrator’s anger. Another
implied anger, or at least reactive aggression, by asking how often the student hit
someone after being hit ﬁrst. While possible to imagine situations where an afﬁrmative
response to that question would be indicative of bullying, scenarios missing the
premeditated quality of bullying or directionally appropriate power differential more
readily come to mind. Similarly, a ﬁfth question was not included because of its own
ambiguous standing in relation to bullying. Encouraging other students to ﬁght certainly
could have bullying qualities in some situations while not meeting the three part

deﬁnition in others.

Table 2

Unused Aggression and Victimization Questions

 

 

Aggression Victimization
l. I got angry very easily with someone I. A student beat me up.
2. I hit back when someone hit me ﬁrst. 2. Other students encouraged me to ﬁght.
3. I encouraged other students to ﬁght. 3. A student asked me to ﬁght.
4. I was angry most of the day. 4. A student tried to hurt my feelings.
5. I got into a physical ﬁght because I was 5. Other students did not want to spend
angry (ﬁst ﬁght, pull hair, bite, etc.). recess with me and I ended up alone.

 

 

The six questions retained as markers of bullying ﬂom The Aggression Scale were
consistent with the common conceptual deﬁnition of bullying, though an imbalance in
power could not be explicitly addressed. Intentionality was clear in each. Repetition was

considered by assessing ﬂequency of commission.

29

For each of the bullying questions, students were asked how often they had
displayed such behavior during the past week. Possible responses were 0 times, 1 time, 2-
3 times, 4-5 times, 6-7 times, and 8+ times. The six potential answers for each question
were coded as interval responses ranging ﬂom O to 5. The alpha reliability coefﬁcient for
the resulting bullying scale was .88 across the entire sample. Consistent with previous
bullying research using a portion of The Aggression Scale (Bosworth et al., 1999), item
responses were summed, forming a composite score. The raw composite measure of

bullying involvement during one week potentially ranged ﬂom 0 to 30.

Victimization. To measure victimization, questions directly parallel to the bullying
measure were selected (see Table 1). These six questions were again pulled ﬂom a larger
selection found in the victimization scale that had been utilized by the school. Response
options were also the same. Unlike the situation with the archived aggression scale, the
original victimization scale had additional items that ﬁt within a deﬁnition of bullying
experiences. However, the overall design of this study favored the use of parallel
questions and composite scores rather than unlike forms. Rejected questions have been
listed in Table 2. By keeping the formation of bullying and victimization scores identical,
raw scores were utilizable in the analysis and discrepancies of scale were avoided.
Further, parallel scales eliminated the potential confound of sampling different behaviors
under the assumption they were part of the same construct. The alpha reliability
coefﬁcient for the victimization scale was .83 across the sample. Mirroring treatment of
the bullying scale, victimization questions were also summed in the formation of a
composite score. The raw composite measure of victimization during one week

potentially ranged ﬂom 0 to 30.

30

Cluster Analysis Techniques

Reviews of empirical approaches in the exploration of categories or dimensions
within an area of behavior revealed that a variety of techniques have been utilized.
Coherent cut kinetics, mixture analysis, latent class analysis and latent growth trajectories
have all received endorsement ﬂom some scholars in the ﬁelds of psychology and
psychiatry as best suited for identifying homogenous groups within larger populations
(see Beauchaine, 2003). However, the most popular technique has been a collection of
algorithms collectively known as cluster analysis. Its ﬂequency and history of use as an
exploratory technique in classiﬁcation studies led to its selection as the methodology of
choice for the current study.

Cluster analysis is a general term used for a variety of techniques whose primary
purpose is to identify groups of similar objects within a collection of cases. It is most
often used in psychology and psychiatry with the aim of inferring the number and nature
of distinct populations within a sample described by multiple variables (Tonidandel &
Overall, 2004). For this reason, other names used for cluster analysis techniques have
included typology construction, classiﬁcation analysis and numerical taxonomy.
Typically utilized as an exploratory technique without a priori hypotheses, the results
ﬂom cluster analysis may also be compared to existing theoretical models of
classiﬁcation (Aldenderfer & Blashﬁeld, 1984; Everitt et al., 2001; Hair et al., 1998).

Studies utilizing cluster analysis continue to appear in journals published by the
American Psychological Association. Distinct subgroups were identiﬁed when examining
adjustment patterns of 228 children whose mothers had been battered (Grych, Jouriles,

Swank, McDonald, & Norwood, 2000). Levels of educational expertise were recently

31

classiﬁed in a sample of only 81adults (Alexander, Sperl, Buehl, Fives, & Chiu, 2004).
At the other end of a sample size continuum, cluster analysis was used to explore
typologies of behavioral adjustment in young children based on self-reports of 4,981
participants between the ages of 8 and 11 years (Kamphaus, DiStefano, & Lease, 2003).
These recent examples of use point to the ongoing utility and ﬂexibility of cluster
analysis within the ﬁeld of psychological research.
Cluster Analysis Procedure

While cluster analysis holds the potential to help uncover naturally distinct groups
of objects or individuals, correct application requires an understanding of its limitations.
By design, cluster analysis imposes structure on nearly any form of multivariate data. The
uncovered differences may be artiﬁcial, inconsequential, or meaningless. Further,
clustering techniques vary enough in the aspects of variables and similarities emphasized
to the extent that they can produce different results while using the same data. These two
features, along with an absence of statistically reliable tools to evaluate possible
classiﬁcation structures, comprise the bulk of criticisms raised toward cluster analysis.
However, with an awareness of these limitations, researchers continue to advance their
ﬁelds through the use of cluster analysis. To be effective, the technique requires
particular care and intentionality in decision making throughout the procedure (Hair et
al., 1998). J udgrnents that must be made include gauging the completeness and
characteristics of utilized variables, selecting the measure of similarity between cases,
choosing the most appropriate clustering algorithm, determining the best ﬁtting cluster
solution, and implementing sufﬁcient validation techniques. Over the past two decades,

leaders in the use of cluster analysis have provided guidelines to assist in the decision

32

making process (see Aldenderfer & Blashﬁeld, 1984; Everitt, Landau, & Lease, 2001).
The following sections were intended to provide a brief overview of that process and
justify the procedures used in this research.

Variable requirements. Once the objective of the cluster analysis was determined,
the potential variables available in the archival data were examined. Following universal
guidelines for cluster analysis, the variables created for bullying and victimization were
based on theoretical rationale and prior research ﬁndings. Details supporting their use
were previously described. The statistical characteristics of the variables were then
considered. Few traits would have eliminated the possibility of variables being used in
cluster analysis, but later procedural decisions were inﬂuenced by their characteristics.
Since measures with an interval or continuous quality were used, more potential analytic
techniques were available than would have been the case otherwise. Though assumptions
of normality, linearity and homoscedasticity are not mandatory in cluster analysis (Hair et
al., 1998) the common practice of standardizing or transforming variables was still
considered. Such adjustments would have been performed if unwanted scaling
differences were present in the selected variables or need had arisen to compensate for
vastly different distributive characteristics (Aldenderfer & Blashﬁeld, 1984). However,
since the variables came ﬂom identical scales and had shared a positively skewed
distribution, raw composite scores were maintained to maximize clustering technique
options. Finally, collinearity between variables was explored, with a correlation of .41
present between the bullying and victimization measures. This degree of relationship
between the measures was regarded as meriting attention at the stage where a clustering

algorithm was to be selected.

33

Treatment of cases. After attaining theoretical and statistical comfort with the
variables, two more decisions were made about them at the individual case level. For one,
treatment of incomplete data was determined. Cases missing two or more responses ﬂom
either the bullying or victimization scale were dropped ﬂom the sample. Examination of
all records found two instances where the victimization questionnaires had not been
satisfactorily completed and one case where two bullying questions had been left blank.
Additionally, one case contained no demographic information and was dropped ﬂom
ﬁrrther analysis. Thus, 4 cases were dropped ﬂom an original sample of 272 children,
resulting in the ﬁnal total of 268 students. In cases where only one question response was
missing ﬂom the data, the subject’s mean bullying or victimization score across
remaining responses was used as a replacement for the respective missing response. This
was done for a total of 12 students, 6 because of a missing bullying response and 6
because of a missing answer on victimization questions. While extreme cases can exert
signiﬁcant inﬂuence on the results of cluster analysis, they were desirable in this effort to
identify naturally occurring groups of children based on their involvement with bullying
and victimization. No student obtained maximum scores on both measures and no reason
to question the validity of responses was identiﬁed for any subject. Thus, no cases were
viewed as outliers requiring exclusion ﬂom study.

Similarity measures. With decisions about the variables and cases made, attention
was given to type of cluster analysis that would be done. Choosing the similarity
measure, or the statistic that would quantify the resemblance of cases, came ﬁrst. This
choice was signiﬁcant since different similarity measures could have resulted in the

formation of different cluster formations. At a broad level, two families of similarity

34

measures were available for this metric data. Correlation based measures would have
explored patterns of relationship between variables while ignoring magnitudes of
difference. Since bullying and victimization have always been measured by level of
involvement with ascribed behaviors, a similarity measure insensitive to magnitude
would not have been appropriate. Thus, this study needed to utilize a distance measure,
also referred to as a proximity measure, to indicate the likeness of cases. From the list of
possibilities, a squared Euclidean distance was chosen. It simply measured the squared
distance between objects when their bullying and victimization scores were
conceptualized dimensionally. Unlike many of the alternatives, a squared Euclidean
distance did not require a priori predictions about cluster size variations or reﬂect a need
to inﬂuence weighting of the variables. It was also appropriate for use with raw data. The
squared Euclidean distance has been the most widely used and recommended proximity
measure (Hair et al., 1998) and came as the default distance measure for exploratory
cluster analysis procedures in the Statistical Package for the Social Sciences (SPSS
version 10.0), which was utilized for all data analysis in this study.

Clustering algorithms. When the similarity measure had been chosen, the actual
clustering algorithm was then targeted for selection. Again, two broad choices were
available: hierarchical and nonhierarchical techniques. In nonhierarchical approaches, the
number of clusters generated by the analysis would have been speciﬁed. In other words,
the cases would have been formed into a predetermined number of groups in a manner
that maximized their similarity with other group members while emphasizing differences
with cases in other groups. The initial cluster centers for those groups, or seed points,

could have been intentionally chosen or randomly selected, with individual cases then

35

assigned to clusters based on proximity to them. One advantage the nonhierarchical
algorithms offered was an iterative capacity, allowing cases to be repeatedly reorganized
to produce the best possible ﬁt as cluster characteristics changed.However, the
generation of speciﬁc solutions without empirical or theoretical defensibility has not been
recommended as a useful technique for exploratory purposes. Not only are any strengths
of nonhierarchical clustering techniques eliminated through the use of random cluster
seeds, they become markedly inferior to other methods (Hair et al., 1998). In line with
best practice suggestions, nonhierarchical techniques were considered as part of a
potential follow-up, or second stage, procedure but were not utilized for preliminary
exploration (Aldenderfer & Blashﬁeld, 1984). Instead, a hierarchical clustering procedure
was utilized. In this approach, each case was considered a unique cluster at some point of
the analysis. Divisive hierarchical techniques would have started with the entire sample
considered a single cluster and sequentially ungrouped the cases until each stood as its
own cluster. Conversely, agglomerative hierarchical techniques began with the
assumption that each case was a unique cluster and combined them one at a time until all
were melded into a single cluster. For both, the researcher explores the clusters present at
different stages and determines which, if any, solution best ﬁts the data. Divisive and
agglomerative hierarchical techniques act very similarly and computer packages
emphasize the latter (Hair et al., 1998). For these reasons, the general category of
agglomerative hierarchical techniques was selected as the preferred clustering approach
in this exploratory study.

From within the agglomerative category, a speciﬁc clustering algorithm had to be

chosen. Once again, this decision was made with awareness that it would inﬂuence the

36

cluster solutions generated (Aldenderfer & Blashﬁeld, 1984). Simply put, agglomerative
techniques differ in their criteria for joining clusters. For example, the most basic
algorithm, known as single linkage, joins the two clusters having the smallest distance
between any objects within them. More complex techniques consider a wide range of
statistical properties within and between groups to determine which should be joined at a
given stage. All of the algorithms have characteristics that make them more desirable in
some situations than others. For exploratory purposes, two techniques have repeatedly
received the strongest recommendations. One, known as Ward’s method, has been
praised for its efﬁciency and ability to recover known structures (Aldenderfer &
Blashﬁeld, 1984). It has been the preferred algorithm in the important work done by
Randy Kamphaus and colleagues in classifying the behaviors of school-aged children
(e.g., Kampaus at al., 1997, 1999, 2003). Ward’s method joins clusters based on the sum
of squares between the two clusters across all the variables. However, this makes it
heavily inﬂuenced by outliers and forms a bias toward the production of clusters with
approximately the same number of observations. Because of the latter quality, this
technique is not recommended when roughly equal numbers of cases are not suspected in
a ﬁnal solution (Everitt et al., 2001). This study of bullying and victimization intended to
reﬂain ﬂom a priori assumptions about the nature of groups involved. This, combined
with the prevailing sense in the literature that highly involved groups were far smaller in
size than the number of children not involved with these behaviors, led to the decision to
reject Ward’s method for use as an agglomerative procedure. There was not reason to
suspect uncovered groups would be roughly equal in size. A method referred to as

average linkage then emerged as the most feasible choice for an exploration of bullying

37

and victimization experiences. Multiple scholars have summarized research suggesting
average linkage equals or supercedes Ward’s method in the identiﬁcation of naturally
occurring clusters (Everitt et al., 2001; Aldenderfer & Blashﬁeld, 1984; Hair et al., 1998).
As the name suggests, average linkage joins clusters based on the average distance
between all pairs of objects in them. It has also been referred to as unweighted pair-group
method using arithmetic averages (UPGMA). It performs equally well when clusters
form distinct clumps in the data or when they are spread out in a chain-like manner
(Statsoft, n.d.). The sensitivity to elongated groups was regarded as beneﬁcial, given the
moderate degree of correlation found between the bullying and victimization measures.
With the nearly consensus opinion that either Ward’s method or an average linkage
method should be used for exploratory analyses such as this study, average linkage was
determined to be the better choice given the characteristics of the question asked and
utilized data

Cluster solutions. Once conducted, the hierarchical cluster analysis using a
squared Euclidean distance measure and average linkage agglomerative method formed
groups in the sample. A determination of the most meaningful solution, also known as the
stopping rule, then had to be made. No consensus on formal procedures for this purpose
has been reached in the ﬁeld. In large part, this difﬁculty has been due to the fact that
appropriate statistical tests for solutions are not readily obtainable. A null hypothesis
holding that no meaningful structures exist within the data suffers ﬂom irnplausibility.
Other rules with more defensible assertions have not provided notable improvements
over much simpler approaches (Hair et al., 1998). Thus, determining the most appropriate

cluster solutions within an analysis has essentially remained a heuristic process. The most

38

common stopping heuristics for agglomerative algorithms have involved some method of
looking for signiﬁcant changes in within-cluster distances as they are formed. By
performing simple computations with the squared Euclidean distance between clusters,
the actual changes ﬂom one step of a cluster solution to the next were computed. The
additional step of computing a ratio of change was then done. Using the ratio of change
approach, the steps where the largest percentage jump occurred in between cluster
distance were explored. Identifying large jumps was important because they indicated
highly unlike groups had been combined in the agglomerative process. To the degree that
one ratio of change in squared Euclidean distances substantially differed ﬂom the others,
an indication of the optimal cluster solution had been found in the step immediately prior
to the largest change. This simple ratio of change approach has been a heuristic stopping
rule shown to provide satisfactory results (Everitt et al., 2001; Hair et al., 1998).

Cluster validation. Determining the validity of cluster solutions has been an
ongoing challenge for researchers. Though often done, performing a MANOVA or
similar statistical analysis of the groups on the cluster variables has been described as
inappropriate (Aldenderfer & Blashﬁeld, 1984). Since cluster analysis seeks to emphasize
the difference within data, the presence of variation should not be a surprise once the
groups have been formed. However, utilizing independent but theoretically relevant
variables to explore the utility of new typologies has been recommended. At the
exploratory stage of analysis, this form of validation is difﬁcult. It is often unclear what
types of relationships should be found with factors not deemed essential to the
identiﬁcation of groups. In the case of bullying and victimization, previous research had

not established clear connections between involvement and external measures. Another

39

approach to establishing the validity of cluster solutions comes in displays of reliability.
Replicability is cited as an important, though insufﬁcient marker of validity (Everitt et al.,
2001). Failed attempts to display reliability provide reason to reject solutions
(Aldenderfer & Blashﬁeld, 1984). While replicating cluster solutions on unique samples
is optimal, the utilization of split sample analysis is far more commonly done (Hair et al.,
1998). A split sample approach informs validity decisions and assures that cluster
solutions are not merely the result of different similarity measures or clustering
algorithms (Kamphaus et al., 2003). Thus, a split sample technique was incorporated into
this study. A random assignment ﬁrnction of SPSS was used to divide cases equally into
two groups (N = 134). The sample size compared favorably to those in the split sample
work of Grych and colleagues (2000) published in an APA journal. Parallel analyses
were done and the results compared.
Demographic Analysis Procedure

Because few other American studies have examined bullying in an urban
elementary school environment, a brief exploration of relationships between demographic
variables and bullying experiences was performed. AN OVA procedures were used to
examine possible differences related to grade, gender and ethnicity. Moderate differences
in group size and heterogeneity of variances led to the use of a Games-Howell method in

the post-hoc analysis (Toothacker, 1993).

40

CHAPTER IV

RESULTS

In the entire sample, 63% of the students reported they had committed at least one
act of bullying during the week the survey was given. The median bullying score was 1.0
with a mean of 3.9. Nearly 83% said they were the victim of at least one bullying act
during the same time period. The median victimization score was 5.0, with a mean of 6.7.
Demographic Findings.

Grade level. No signiﬁcant differences were seen between grade level and scores
for bullying or victimization. This held true for composite scores as well as for
percentages of students committing or experiencing at least one act of bullying during the
week prior to the questionnaire’s administration.

Gender. Boys and girls did not report signiﬁcantly different levels of
victimization. However, gender differences were apparent on the measure of bullying.
Boys (M = 4.83, SD = 6.21) had higher composite scores for bullying than girls (M =
3.04, SD = 5.35), F(1, 266) = 6.44, p < .05. Boys (M = 0.75, SD = 0.43) were also more
likely to have committed at least one act of bullying behavior during the week than girls
(M = 0.53, SD = 0.50), F(1, 266) = 15.58, p < .01. Examining these latter ﬁndings
another way, 75% of boys reported committing at least one bullying behavior during the
previous week while 53% of girls said the same.

Race / ethnicity. In the archival data used for this study, the stimulus question for
this category read, “What would you say you are?” Respondents may have provided

responses for either racial or ethnic self-identity. Three groups were formed for analysis

41

in this project, African-American, White, and “Other.” There were signiﬁcant differences
between them on bullying composite scores, F(2, 263) = 14.71, p < .01. Similarly, the
groups differed in percentages of students claiming to have committed at least one act of
bullying during the week, F (2, 263) = 23.27, p < .01. Of the three demographic variables
analyzed in this study, ethnicity was the only one linked to signiﬁcant differences in
overall victimization scores, F (2, 263) = 5.33, p < .05. An even stronger trend emerged
when examining the numbers of children reporting at least one instance of victimization
during the week, F(2, 263) = 10.40, p < .01. Group scores can be seen in Table 3. Post-
hoc analysis suggested most signiﬁcant differences between the groups were found
between Aﬂican-American and White students. In comparisons of these two groups,
African-American students had higher scores in both total bullying and victimization.
Students who identiﬁed themselves as African-American were also more likely to have
both committed and been subject to an act of bullying during the week.

Table 3

Descriptive Statistics: Medians, Means, and Standard Deviations on Bullying and
Victimization Scores Based on Grade Level, Gender and Ethnicity

 

 

 

Bullying Scores Victimization Scores
Sample Group n mdn M SD mdn M SD
Total Sample 268 1 3.90 5.84 5 6.70 7.01
Grade 3 89 2 4.12 5.39 5 6.52 6.75
Grade 4 96 1 3.05 4.89 4 6.42 7.43
Grade 5 83 2 4.65 7.11 5 7.24 6.79
Boys 129 3 4.83 6.21 5 7.17 6.79
Girls 139 l 3.04 5.35 4 6.28 7.18
Aﬁican-American 117 4 5.80 6.34 6 8.18 7.13
White 116 0 1.86 4.56 3 5.23 6.83
Other Ethnicity 35 2 4.24 5.76 7 6.90 6.24

 

42

Informal Assessment of Distributions.

The exploration for the presence of groups began with a visual inspection of the
distributions for bullying and victimization in the two subsamples created by random
assignment of cases in SPSS. Signs of multirnodality would have been potential
indicators of naturally distinct groups while continuous distributive characteristics would
be more indicative of a dimensional status (Everitt, Landau, & Leese, 2001). Bar pots
(see Figures 1-4) evidenced a positive skew in each instance. In other words, students
reporting no experiences with bullying or victimization experiences over the past week
were the most ﬂequently appearing group. Across the four distributions, low levels of
involvement were more often reported than were high levels. A continually smooth
decrease in frequencies at the higher ranges was not clearly apparent, but neither were
overt signs of multimodality. Thus, the visual exploration of bullying and victimization
experiences in isolation across the sample provided no conclusive evidence regarding the

status of unique groups of children within them.

43

60

 

Frequency of Cases in Subsample A

 

 

 

0 2 4 6 8 10 12 15 18 25 30

Composite Bullying Score

Figure 1. Bar plot of composite bullying score distribution in subsample A.

 

40

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Frequency of Cases in Subsample A

 

 

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Composite Victimization Score

Figure 2. Bar plot of composite victimization score distribution in subsample A.

45

 

 

 

 

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Figure 3. Bar plot of composite bullying score distributi

46

 

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Figure 4. Bar plot of composite victimization score distribution in subsample B.

47

 

A second visual inspection was done with the experiences combined graphically.
Scatter plots were formed with the bullying and victimization scores to portray combined
experiential proﬁles. The plot ﬂom subsample A (see Figure 5) suggested a unique
cluster of students was identiﬁable with high rates of bullying behavior while
experiencing only moderate to low levels of victimization based on their self reports. In
the same sample, a less clear, but potentially distinct group was identiﬁable that
experiences high levels of victimization while committing low to moderate levels of
bullying behaviors toward other children.

However, in subsample B, no groups were readily apparent in the scatter plot
portrayal (see Figure 6). There, the combined scores appeared evenly distributed around a
general correlation between bullying involvement and victimization experiences. While
the scatter plot ﬂom subsample A suggested ﬁndings possibly ﬁtting with the
classiﬁcation of some children as bullies and victims, the plot ﬂom subsample B did not

show similar characteristics.

48

Victimization Score for Subsample A

 

 

 

 

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13 5 7 911 13 15 17 19 21 23 25 27 29 31

Bullying Scores for Subsample A

Figure 5. Scatter plot with bullying and victimization scores for subsample A.

49

Victimization Scores for Subsample B

 

 

 

 

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Bullying Scores for Subsample B

Figure 6. Scatter plot with bullying and victimization scores for subsample B.

50

Cluster Analysis Results

With informal appraisals of the presence or absence of unique groups in the
subsamples leading to few conclusions, the results of cluster analysis were examined. For
subsample A, the ratio changes in the squared Euclidean distance suggested an optimal
solution of either two or three clusters (see Table 4). In such cases, it has been
recommended the higher number be utilized (Everitt et al., 2001). For this reason, case
membership was retained for a three group solution.
Table 4

Cluster Analysis Results for Subsample A: Agglomeration Schedule

 

 

Number of Fusion Stage Cluster 1 Stage Cluster 2 Ratio
Clusters Coefﬁcient Appears Appears of change
6 74.83 125 0
5 105.57 127 124 0.41
4 124.98 121 128 0.18
3 187.76 129 130 0.50
2 285.98 131 123 0.52
1 686.52 132 126 1.40

 

For visual comparison, the cluster identiﬁcations were noted on a second scatter
plot of the bullying and victimization scores for subsample A (see Figure 7). Descriptive
statistics were computed for the three groups (see Table 5), with median scores used for
interpretive purposes because of the skewed distributions for both bullying and
victimization (Dreger, 1995). The groups appeared to loosely ﬁt within the traditional
descriptors of bully, victim and uninvolved children. The latter group was represented by

over 69% of the children in the ﬁrst randomly assigned subsample who reported minimal

51

 

 

 

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Bullying Scores for Subsample A

Figure 7. Scatter plot of bullying and victimization scores for subsample A with

individual cases labeled by cluster group membership.

52

involvement with bullying or victimization. Their median score for bullying was 0
incidents during the week and a median score on the victimization scale was 2 during
that time. On the other hand, the ﬁve students clustered together at the high end of the
bullying scale had a median score near the maximum possible. In other words, this small
group of children said they repeatedly committed multiple forms of aggression during the
week.

Table 5

Descriptive Statistics: Medians, Means, and Standard Deviations on Bullying and
Victimization Scoresfor the Three Clusters identiﬁed in Subsample A.

 

 

 

 

Group 1 (n = 93) Group 2 (n = 36) Group 3 (n = 5)
Bullying Victimization Bullying Victimization Bullying Victimization
mdn 0 2 7 15 . 29 6
M 1.45 2.61 7.06 16.00 27.60 6.60
SD 2.10 2.68 5.80 5.64 2.41 3.36

 

Victimization scores were higher for the bully group than for the uninvolved, but did not
suggest nearly the same level of involvement as seen in their hostile actions. The ﬁnal
group was the least clearly deﬁned. It was formed by all of the students between the bully
group and the uninvolved. Some of its members reported extremely high victimization
scores while committing few acts of bullying. These ﬁt the traditional victim category.
On the other end were children who reported slightly more acts of bullying than
victimization experiences. This proﬁle more closely resembled the group referred to as
bully-victims.

With results ﬂom subsample A examined, an identical cluster analysis was
performed on the second group. The results were quite different. Examination of the

agglomeration schedule revealed that an individual case was not assigned to a cluster

53

until the next to last step (see Table 6). In other words, at the point on the agglomeration
schedule indicating two clusters were present, the reality was that a cluster of 133 cases
existed alongside a cluster of 1 case. Until all cases have been incorporated, a ﬁnal
solution has not been formed. The speciﬁc case left out of the grouping for so long had a
maximum bullying score and near maximum victimization score.

Table 6

Cluster Analysis Results for Subsample B: Agglomeration Schedule

 

Number of Fusion Stage Cluster 1 Stage Cluster 2 Ratio
Clusters Coefﬁcient Appears Appears of change
5 147.86 127 0 0.68
4 246.99 125 128 0.67
3 267.73 130 129 0.08
2 289.98 126 0 0.08
1 724.57 131 132 1.499

 

While initial inspection had not supplied reason to regard any of the cases as
outliers, the focal case in this situation was the most extreme of any in the entire sample.
The overall score patterns of that speciﬁc case were re-examined. Again, reasons to
question the validity or reliability of those scores were not seen. Since the utilized
questions for this study were part of a larger questionnaire, response patterns could be
examined. The student with extreme bullying and victimization scores reported very low
incidences of other behaviors within the same section of the questionnaire (e. g. feeling
angry most of the day, getting into ﬁghts). The decision to maintain the case as part of the
study was afﬁrrned. It was supported by an absence of rationale to remove the student

ﬂom consideration and an understanding that the average linkage agglomeration method

54

used for this cluster analysis was less susceptible to the inﬂuence of outliers than the
other considered option, Ward’s method, would have been. Given these factors, the
results of the cluster analysis performed on subsample B failed to indicate the presence of
any unique clusters.

The forthcoming discussion of the study results has been based on the broad
ﬁnding that parallel cluster analyses failed to identify similar groups of students based on
their involvement with bullying and victimization. While that ﬁnding needed to be
emphasized, given the speciﬁc designs of the study, the exploratory intentions of this
research were also served by repeating an analysis of subsample B with the extreme case
removed. That modiﬁed sample was referred to as subsample BZ. With this change, the
identiﬁcation of three clusters again seemed to form the best solution (see Table 7).

Table 7

Cluster Analysis Results for Subsample 82(one case removed): Agglomeration Schedule

 

Number of Fusion Stage Cluster 1 Stage Cluster 2 Ratio
Clusters Coefﬁcient Appears Appears of chagge
4 147 .86 127 O
3 246.99 125 128 0.67
2 267.73 130 129 0.08
1 613.63 131 126 1.29

 

However, they did not match the three clusters seen in subsample A (see Table 8 and
Figure 8). In subsample B2, the majority group again contained students who typically
have been referred to as uninvolved. However, the largest cluster also contained students
who clearly would have been considered victims in traditional typologies. In other words,

students with extremely high levels of victimization experience and few bullying

55

 

—L-I
4‘

4.3.3.:
‘3
N

Victimization Scores for Subsample 82
a

 

 

 

-1135791113151719212325272931

Bullying Scores for Subsample 82

Figure 8. Scatter plot of bullying and victimization scores for subsample B2 with

individual cases labeled by cluster group membership.

56

behaviors were not differentiated by the cluster analysis ﬂom the students who had no
involvement with either. The next largest cluster formed in the subsample BZ contained
students who reported roughly equal levels of involvement in bullying and victimization.
The smallest cluster was comprised of ﬁve students who displayed moderately high
levels of bullying and extremely high levels of victimization. While both the second and
third groups could be considered representative of the bully-victim typology seen in the
literature, two more commonly discussed groups did not emerge. No group in the
analysis of subsample B2 neared a proﬁle indicative of non-victirnized bullies seen in the
literature and hinted at in the cluster analysis of subsample A. Not only did traditionally
deﬁned bullies not emerge in the modiﬁed subsample, but a cluster of non-bullying
victims only was also not seen. Even with an extreme case removed ﬂom analysis, the
results ﬂom subsample B were not consistent with those ﬂom the ﬁrst.

Table 8

Descriptive Statistics: Medians, Means, and Standard Deviations on Bullying and
Victimization Scores for the Three Clusters identiﬁed in Subsample BZ

 

 

 

 

Group 1 (n = 118) Group 2 (n = 10) Group 3 (n = 5)
Bullying Victimization Bullying Victimization Bullying Victimization
mdn 1 4 14 12 13 27
M 2.30 5.59 14.84 12.12 13.68 26.96
SD 2.75 5.39 4.20 4.19 3.93 3.15

 

The failure to replicate cluster solutions across a split sample provided reason to
reject the validity of any groups assigned to the sample population based on the measures
of bullying and victimization utilized. In sum, support for the traditional typologies in
bullying was not found. Further, no evidence for a competing model of naturally

occurring groups was located.

57

CHAPTER V

DISCUSSION

The purpose of the present study was to identify naturally distinct groups of
children based on their involvement with bullying and victimization experiences. This
was the ﬁrst study in the ﬁeld to begin without a priori assumptions about the existence
of clearly differentiated categories of children. The most signiﬁcant ﬁnding came in a
failure to uncover any unique clusters of elementary school students based on self-
reported involvement with bullying behaviors and victimization experiences. In other
words, the results did not support the widely held notion that distinct groups of bullies
and victims exist within a larger population. While childrendisplayed a range of
involvement in their experiences perpetrating or being victimized by bullying behaviors,
the study failed to locate clusters that were signiﬁcantly alike in their patterns of
involvement while being substantially different ﬂom any other groups.

The failure to identify naturally distinct clusters of bullies, victims or any other
group in this study has potentially signiﬁcant ramiﬁcations for the ﬁeld of bullying
research at the theoretical and practical level. Conceptually, the ﬁndings provided reason
to question the widely made categorical distinctions between involved and uninvolved
parties in bullying. Nearly two thirds of the students involved in this study said they had
committed at least one behavior during the past week that could potentially have been
considered an act of bullying. Further, eight out of every ten students claimed to have
been the victim of an aggressive act during the week. When considered along with other

recent research ﬁndings indicating a high percentage of children have some degree of

58

involvement with bullying experiences (N ishina & Juvonen, 2005), the current results
challenge a pathological model that regards bullying and victimization as akin to illnesses
affecting relatively small numbers of children. Rather than conceptualizing these
behaviors as primarily unique to select groups of bullies and victims, models may need to
shift toward an understanding of many children as involved with these experiences.
Separations in bullying experiences may be better represented as a matter of degree than
as absolutes. In this sense, the study provided empirical reason to support a shift away
ﬂom a categorical perspective of bullying and victimization toward a dimensional view,
as has been called for by some leaders in the ﬁeld (Espelage & Swearer, 2003).

While the ﬁndings of this study do not provide grounds to reject any existing
theoretical explanations of bullying, they are more readily incorporated into some
perspectives than others. To the extent that individual experiences with bullying become
conceptualized along a continuum rather than as a dichotomous trait, emphasizing
individual skill deﬁcits as causal factors becomes more difﬁcult. Authors writing ﬂom an
information processing perspective have typically ﬂamed the problem of bullying as a
matter of missing or faulty social skills for a small group of children and assumed they
are present for the majority. The higher the number of affected parties, the more difﬁcult
it becomes to consider them in possession of atypical skills. In this way, variations of
theories within the cognitive behavioral ﬂamework that emphasize the functional aspects
of bullying behaviors may more seamlessly incorporate dimensional views of
involvement. For example, the ideas in Dominance Theory put forth by Pellegrini (2002)
emphasize the utility and purpose in aggressive acts such as bullying. Reminiscent of the

ethological perspectives present at the ﬁeld’s inception, bullying becomes viewed as one

59

means of establishing a social hierarchy. While not condoning bullying behaviors,
dominance models emphasize normative aspects of these experiences.

While a core function of bullying behaviors may rest in the establishment and
maintenance of a social hierarchy, other factors inﬂuencing these behaviors must be
understood as well. At least two demographic ﬁndings ﬂom this study supported
consideration of cultures and subcultures in understanding childhood bullying
experiences. While methodological differences prohibit direct comparison with most
existing research, results suggested considerably higher levels of involvement with
bullying for this American sample of students than in the Scandinavian studies that
comprise a large portion of the existing body of knowledge in the ﬁeld. If the
extrapolation of involvement rates ﬂom the once per week level to the several times per
month or term proved even close to accurate, ﬁndings ﬂom this study suggested the
percentage of students involved with bullying at traditional levels of concern was three to
four times higher than in most European studies. As a second endorsement of cultural
inﬂuence, the presence of bullying and victimization differences across ethnic groups in
this study, though hindered by an inability to account for socio economic status, added to
several other small studies of bullying in the United States suggesting cultural inﬂuence
does not stop at the national level (Graham & Juvonen, 2002; Leff, Kupersmidt, &
Patterson, 1999). Students who identiﬁed themselves as African-American were
signiﬁcantly more likely than their White counterparts to report having both bullied and
been bullied during the previous week. The mean and median bullying and victimization
scores for Aﬂican-American children were also higher than those for White students.

Information was not available in this archival data to help understand why differences in

60

bullying involvement appeared at the level of self-reported ethnicity but ﬁndings
suggested this cultural trend was present.

Though only a handﬁrl of other studies have documented self-reported bullying
and victimization differences related to ethnic identity, existing research has suggested
the need to explore systemic factors related to bullying well below the levels typically
addressed. Bullying involvement can vary considerably within environments having
seemingly similar populations and characteristics. Levels of bullying not only differ
between countries and communities, but also between schools within the same
community (Olweus, 1993). Further, research has shown considerable variation between
classrooms within the same school (Kellam et al., 1998; Leadbeater, Hoglund, & Woods,
2003). A thorough understanding of bullying may not be conﬁned to the individual
characteristics of the children who are involved or fully ascribed to social stratiﬁcation in
one peer or social group. The ecological systems within which these factors operate may
have more inﬂuence on bullying activity than has been assumed by the vast majority of
research to this point. The emerging body of work incorporating systems theory holds
promise for ﬁrrthering an understanding of children’s bullying experiences.

At a practical level, the existing emphasis on categorizing children as bullies or
victims may be limiting the effectiveness of research and help explain the inconsistent
ﬁndings seen across the ﬁeld. Given the current study’s inability to identify the presence
of any naturally occurring groups within a sample of elementary school children, the
standard practice of imposing categories in early steps of data analysis may misrepresent
the distributive nature of bullying experiences and contribute to high levels of variability

in ﬁndings ﬂom one study to the next. If groups display heterogeneity on the very criteria

61

by which they are deﬁned, consistency of ﬁndings in other areas should not be expected.
More directly, if children classiﬁed as bullies or victims do not actually have qualitatively
unique bullying experiences, there would be little reason to expect distinct patterns in
their psychological, behavioral or demographic proﬁles. An alternative to research
looking for clear descriptors of groups whose boundaries may be artiﬁcial would come in
exploration of trends between all children’s bullying involvement and factors of interest.
The use of continuous measures allows greater statistical power in the examination of
relationships between variables (Cantwell, 1996). In addition to improved statistical
sensitivity, utilization of a dimensional model of bullying would be consistent with
conceptualization of many dependent variables commonly explored in bullying research.
For example, the psychological and behavioral proﬁles of bullies and victims have often
been explored through the use of behavior rating scales which portray items such as
anxiety, depression and inattention as dimensional constructs.

The ramiﬁcations of this study may be greater for bullying theory and research
practices than for current intervention efforts, which have increasingly incorporated
universal prevention and intervention perspectives (Leff et al., 2001). If bullies and
victims are not clearly distinct populations of children, attempts to identify these groups
before conducting a targeted intervention makes little sense. Whole school approaches to
bullying intervention also allow incorporation of ecological perspectives and strategies.
The focal point for change can move away ﬂom the characteristics or behaviors of
individual children to the systems within which they are involved. Efforts to ﬁnd
common ground between attempts to understand bullying in children and attempts to

intervene will continue to be a crucial task for scholars in the ﬁeld.

62

Limitations of the study. The ﬁndings of this study raised questions about one of
the basic assumptions held in 30 years of bullying research. By ﬁnding no evidence to
support the existence of bullies and victims as unique groups of children, the
classiﬁcation systems so widely used in the ﬁeld were brought into question. Given the
potentially signiﬁcant ramiﬁcations of this position, the limitations of this study must be
recognized and suggestions for further research provided. To begin with, the data was
collected ﬂom elementary school children in the spring of 1998, one full year before the
tragedy at Columbine High School thrust bullying into the national spotlight. Altered
sensitivities to bullying and increased intervention efforts by schools since then increase
the importance of recognizing this data came ﬂom one school at a speciﬁc point in time.
Another uniqueness of this study’s sample came in demographic characteristics, which
differed ﬂom those in the vast majority of bullying studies. While an important addition
to ﬁeld in this sense, there was little information available to inform the relevance of
these ﬁndings ﬂom one urban school in the American Southeast for other communities.
Though typically unheeded, the founder of bullying research has cautioned against
generalization of ﬁndings across wide cultural spreads (Solberg & Olweus, 2003).
Incorporating an ecological perspective of bullying, which appears warranted by current
and previous ﬁndings, heightens the importance of recognizing the roles of cultures and
systems on bullying experiences for children.

In addition to the uniqueness of the study sample, its relatively small size provides
another reason for caution in interpreting results. While cluster analyses have commonly
been done with sample populations of similar magnitude, repetition of similar exploratory

techniques should be conducted with larger groups of participants. The elucidation of

63

psychological and behavioral characteristics of children so effectively done by Kamphaus
and colleagues (1999, 2003) incorporated thousands of children into cluster analytic
procedures.

While sample size numbers impact most quantitative research models, limitations
unique to cluster analytic techniques must also be acknowledged in discussion of the
results. Cluster analysis is primarily an exploratory technique and does not have the
statistical ability to determine how likely or unlikely a given solution may be. Decisions
regarding solution structures remain largely heuristic and the possibility that different
conclusions may have been suggested by other clustering methods exists. At the same
time, a common critique of cluster analysis actually lends credibility to the ﬁndings of
this study. Authors ﬂequently caution that cluster analysis will always impose structure
on data and will typically suggest the presence of subgroups (Aldenderfer & Blashﬁeld,
1984; Beauchaine, 2003). For a technique with this bias to not uncover similar groups in
a split sample provides enhanced reason to accept their absence.

Regardless of the analytic technique employed in research, the nature of the
collected data will impact ﬁndings. While the measure of bullying utilized in this study
was nearly identical to that utilized in research elsewhere (Bosworth et al., 1999), it
differed considerably ﬂom the techniques most commonly employed in the ﬁeld.
Children were asked about involvement with speciﬁc behaviors during the past week
rather than experiences with a broadly deﬁned concept of bullying over a longer period,
usually linked to the school calendar. The relationship between the speciﬁc and summary
approaches for measuring bullying involvement is not clear, though each have been

strongly defended (see Solberg & Olweus, 2003; Wolke et al., 2001). However, the

64

impact of different reference periods has been speciﬁcally explored in bullying. When
identical stimulus questions were used on a large sample of Irish school children,
questions regarding bullying during the past week suggested higher rates of involvement
than when children were asked about experiences over the past term (O’Moore, Kirkham,
& Smith, 1997). Thus, it is likely the data about bullying utilized in this study had
qualitative and quantitative differences ﬂom typical research in the ﬁeld.

One thing the measures utilized in this study shared with typical methods was
difﬁculty operationalizing all aspects of the conceptual deﬁnition of bullying behavior
utilized. The Olweus method can neither authenticate power differentials nor conﬁrm
intent in the behaviors perceived as victimization. However, it does address the need for
them in the explanation of bullying behaviors provided to participants. The use of
archival data in this study left an even greater gap between the conceptual and operational
deﬁnitions of bullying and victimization. Of the three facets of the bullying deﬁnition,
intent, repetition, and power differential, only one was speciﬁcally operationalized in the
data. Repetition was measurable through reported rates of involvement. However, there
was no way to ensure that repetition of bullying or victimization experiences was
occurring within the same relationships since the individuals or groups involved at the
other end of self-reported bullying or victimization were not described at all. This
indifference to the relationships within which aggression occurred left no means of
addressing the power differential required in bullying. Finally, while aggressive intent
was generally clear in the questions regarding the commission of bullying deeds,

victimization experiences required the inference of others’ reasons for behavior.

65

Conceptual omissions were not the only wealmess of the bullying and
victimization scales in this study. As another limitation, though containing several
traditional types of bullying experience, the measures utilized for this study were far ﬂom
exhaustive. Six questions could not possibly cover the entire range of bullying
experiences with which children are involved. A glaring example of this was the absence
of questions regarding indirect or relational aggression. This deﬁciency possibly
impacted the gender differences in the comrrrission of bullying behaviors found in this
study. Another validity concern with this study’s approach arose for reasons less speciﬁc
to these scales. Like most measures of aggression, social desirability for some responses
over others must be considered for a survey that was completed in the classroom setting
(Bradbum, Sudman, & Wansink, 2004). This may partially explain how composite
victimization ﬂequencies could be considerably higher than frequencies for bullying
behaviors. The self-reported ﬂequencies of involvement posed an additional area of
potential weakness. To the extent that experiences happen regularly, accuracy in recall of
speciﬁc events becomes more difﬁcult (Bradbum, Rips, & Shevel, 1987). It is not hard to
imagine that for some children, behaviors like teasing or being teased occur often. At the
same time, being threatened or hitting someone are hopefully less ﬂequent experiences
for most children. When events are highly salient, some aspects may be recalled clearly
but they may also be prone to a telescoping effect (Bradbum , Sudman, & Wansink,
2004). In other words, they may be remembered as having occurred more ﬂequently than
was actually the case.

Directions for future research. Based on the results of this study, further

intentional examination of the ontological status of bullies as victims should be done. A

66

necessary ﬁrst step in that pursuit will be the development of new tools for measuring
children’s involvement with bullying as perpetrators and victims. If attempting to
incorporate the Olweus deﬁnition of bullying, this task presents signiﬁcant challenges.
These include incorporating an expansive range of behaviors potentially involved, the
demand of establishing repetition, and the difﬁculties establishing both intent and power
differential. However, techniques employed in new research offer some guidance
(Nishina & Juvonen, 2005). The authors of that study compiled daily reports of
victimization experiences using both closed and open ended response options. While this
helped track incident rates, it also provided insight into the actual experiences children
perceived as bullying. Further, narrative accounts of the experiences provided enough
detail for researchers to probe circumstances where misperceptions created a false belief
that bullying had occurred. Of course, the broadening of understanding potentially found
with new measurement tools must be accompanied by solid psychometric properties, if
the goal of accurately portraying the nature of bullying and victimization is to be realized.

New measurement tools will potentially be more valid and effective if they are
created and utilized with diverse populations. Evidence continues to mount suggesting
considerable cultural inﬂuence on bullying conceptualizations and involvement. It will be
imperative for American researchers to increasingly reduce their reliance on European
studies of bullying and victimization and continue to learn more about them as
experienced by children in this country ﬂom a broad range of communities and
backgrounds (Espelage & Swearer, 2003).

Researchers wishing to inform an understanding of the ontological status of

bullies and victims will beneﬁt if new measurement tools and large diverse samples are

67

incorporated. The need to utilize multiple taxometric techniques to help resolve this
question should be addressed as well. Though tested and familiar, cluster analysis is only
one of many options for scholars exploring the existence of unique groups in a
population. Since no single technique in this arena has attained universal acceptance as
best practice, the comparison of results ﬂom multiple approaches may be the only way to
resolve debates about the existence of bullies and victims as distinct populations.
Increased clarity on the nature of bullying and victimization for children should allow
reexamination of factors potentially linked to these problems. Gains in this area should
then inform intervention efforts.

Finally, future investigators should increasingly build bridges with parallel lines
of study. Experts in the areas of aggression, abuse, social psychology and cross-cultural
study may be among many who can contribute valuable understanding to the ﬁeld of
bullying research. These types of connections will be facilitated by the continuing
development of theoretical models for bullying.

Summary. This study explored the ontological status of bullies and victims and
found reason to question their existence as children with unique forms of pathology. In
other words, evidence supporting discrete classiﬁcations of students based on their
involvement with bullying experiences was not found. Instead of the impression that
relatively few children are involved as bullies or victims at school, this study added to the
growing body of literature indicating bullying and being bullied are a common
experience for many children. The lines between involved and uninvolved parties may
not be clear and existing techniques to distinguish them may generate artiﬁcial

boundaries. Far more extensive research will need to be done exploring the patterns of

68

bullying involvement among diverse populations before conclusive comments can be
made about the longstanding images of the isolated classroom bully and their small group
of victims. By taking pause to reconsider the existing ﬂamework for bullying
involvement, researchers may gain insight into the inconsistency of ﬁndings over the past
three decades and the role of ecological systems on bullying behaviors may become
clearer. If these things happened, the pragmatic goal of informing interventions, which

led to the research ﬁeld’s inception, may be better served.

69

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