Sociological Methods & Research http://smr.sagepub.com Studying Rare Events Through Qualitative Case Studies: Lessons from a Study of Rampage School Shootings DAVID J. HARDING, CYBELLE FOX and JAL D. MEHTA Sociological Methods Research 2002; 31; 174 DOI: 10.1177/0049124102031002003 The online version of this article can be found at: http://smr.sagepub.com/cgi/content/abstract/31/2/174 Published by: http://www.sagepublications.com Additional services and information for Sociological Methods & Research can be found at: Email Alerts: http://smr.sagepub.com/cgi/alerts Subscriptions: http://smr.sagepub.com/subscriptions Reprints: http://www.sagepub.com/journalsReprints.nav Permissions: http://www.sagepub.com/journalsPermissions.nav Citations (this article cites 36 articles hosted on the SAGE Journals Online and HighWire Press platforms): http://smr.sagepub.com/cgi/content/refs/31/2/174 Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. This article considers five methodological challenges in studying rare events such as school shootings. Drawing on the literature on causal analysis in macro-historical and other small-N research, it outlines strategies for studying school shootings using qualitative case studies and illustrates these strategies using data from case studies of two rampage school shootings: Heath High School in West Paducah, Kentucky, and Westside Middle School outside Jonesboro, Arkansas. Strengths and limitations are discussed as well as lessons for studying rare events. Studying Rare Events Through Qualitative Case Studies Lessons From a Study of Rampage School Shootings DAVID J. HARDING CYBELLE FOX JAL D. MEHTA Harvard University INTRODUCTION Lethal violence in America’s schools is a rare event. According to estimates by the Centers for Disease Control, the probability of a child dying in school in any given year from homicide or suicide was less than one in 1 million between 1992 and 1994 and slightly greater than one in 2 million between 1994 and 1999 (Kachur et al. 1996; Anderson et al. 2001). When one examines so-called rampage killings AUTHORS’ NOTE: This research was funded by grants from the National Academy of Sciences and the William T. Grant Foundation (Katherine Newman, principal investigator), by National Science Foundation Graduate Research Fellowships awarded to each of the authors, and by a National Science Foundation Integrative Graduate Education and Research Traineeship Grant (98070661). We thank Katherine Newman, Wendy Roth, Christopher Winship, and an anonymous reviewer for helpful discussions and comments. The authors can be contacted at the Department of Sociology, Harvard University, 33 Kirkland St., Cambridge, MA 02138; e-mail [email protected], [email protected], or [email protected]. SOCIOLOGICAL METHODS & RESEARCH, Vol. 31 No. 2, November 2002 174-217 DOI: 10.1177/004912402237293 © 2002 Sage Publications 174 Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. Harding et al. / STUDYING RARE EVENTS 175 such as the massacre at Columbine High School on April 20, 1999 (or attempts at such killings), the number of events drops to between 30 and 50 in the past three decades, depending on how one classifies such events. Despite their rarity, public concern over rampage school shootings has been high. Parents report fearing for their children’s safety at school, and many students suspect an attack could occur at their school.1 As exhibited by the myriad studies of school shootings by government and nonprofit agencies in the past half decade (e.g., O’Toole 2000; Anderson et al. 2001; Vossekuil, Reddy, and Fein 2000; National School Safety Center 2001; Dunn and Frost 2000; State of Colorado 2001; National Research Council and Institute of Medicine 2002), much of the concern derives from an inability to understand and predict such tragedies. Rampage school shootings occur in seemingly otherwise safe schools and communities, rural and suburban areas where students are predominantly White and working or middle class, communities that have previously escaped the youth violence associated with inner-city minority neighborhoods. The public has understandably demanded insight on the causes of such events and how to prevent them. The string of school shootings and the public concern over them provide sociologists and other social scientists an opportunity to inform public discourse and policy if only we can figure out how to study such extremely rare events. Social science methodologies traditionally used to study crime, delinquency, education, and the like do not fare well in explaining events as rare as rampage school shootings. Previous studies of rampage school shootings such as those conducted by the Federal Bureau of Investigation (O’Toole 2000), the U.S. Secret Service (Vossekuil et al. 2000), the Centers for Disease Control (Anderson et al. 2001), and academics (McGee and DeBernardo 1999; Verlinden, Hersen, and Thomas 2000; Meloy et al. 2001) have been quantitative in nature. They rely on identifying a population of events, gathering information on a sample of such events, and comparing and contrasting events to determine commonalities and differences. Unfortunately, these methods make it difficult to gather data on causal factors at various levels (micro, meso, macro) or to understand how various causal factors interact to produce school shootings. Of course, school shootings are not the only rare events of interest to sociologists and other social scientists. Rare events may be of interest Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. 176 SOCIOLOGICAL METHODS & RESEARCH to social scientists because they are of great concern to the public, involving great loss of life or great cost. Examples include hijackings (Holden 1986), nuclear accidents and other man-made disasters (Perrow 1984), and accidents such as the Challenger space shuttle explosion (Vaughan 1986, 1999). Rare events such as workplace shootings or other forms of mass murder (see Levin and Fox 1985; Fox and Levin 1994, 1998) may also be of interest to the public because, like school shootings, they create widespread fear. Other rare events are of interest to social scientists because, as a rupture of the routine, they shed light on social processes and social problems. Examples include race riots (Bergesen and Herman 1998; Olzak, Shanahan, and McEneaney 1996), mass suicide (Moore and McGehee 1989), and victim-precipitated homicide or “suicide by cop” (Hutson et al. 1998; Poussaint and Alexander 2000). Still other rare events may be of interest because of their inherent importance to the legitimacy of basic social institutions. For example, political scientists and political sociologists have long been interested in coups (O’Kane 1981), assassinations (Crotty 1998), and impeachments (Benedict 1998, Popp 2000). This article will explore the ways in which in-depth qualitative case studies can contribute to the study of rare events by drawing on lessons learned in our own research on two cases of rampage school shootings. It will discuss and illustrate strategies for understanding school shootings, focusing not on the specifics of a formal method of data gathering or data analysis but on the underlying logic or logics of using detailed data from a single case or small number of cases to understand necessary but not sufficient conditions for school shootings. We will focus on both the benefits and limitations of the types of analyses we describe and will comment on the potential for generalization beyond individual cases from such analyses. We begin by discussing five challenges in the study of school shootings and other rare events and draws on previous methodological work on rare events and small-N analysis to develop strategies for studying school shootings. The next section briefly summarizes our research on two school shooting cases, the shootings at Westside Middle School outside Jonesboro, Arkansas, and Heath High School in West Paducah, Kentucky. Then we explore strategies for explaining school shootings through qualitative case studies, illustrating the utility Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. Harding et al. / STUDYING RARE EVENTS 177 of such strategies by drawing on the two cases studied. The following section discusses the strengths and limitations of our strategies as well as avenues for future research. Finally, we conclude with lessons for studying rare events. CHALLENGES IN THE STUDY OF SCHOOL SHOOTINGS THE CASE DEFINITION PROBLEM One of the first problems we confront in studying school shootings is defining the relevant universe of cases that can realistically be called rampage school shootings. Consider the 1998 shooting in Fayetteville, Tennessee. In a school parking lot, Jacob David, an 18-year-old honor student, fatally shot a classmate who was dating his ex-girlfriend. Given that this shooting involved only one victim with whom the assailant had a personal grudge, does it qualify as a rampage school shooting? Consider also the incident in Conyers, Georgia, on May 20, 1999, in which T. J. Solomon, 15, opened fire in the lobby of his high school, injuring 6 students (Sullivan and Guerette 2002). Given that no one died as a result of this attack, should it be considered in the same group as the massacre at Columbine High School one month earlier? Finally, consider the shooting at Thomas Jefferson High School in East New York on November 21, 1991, in which Jason Bentley drew his gun and fired two shots when he thought another student in a hallway confrontation was reaching for a gun. One student was killed and one teacher wounded (Fullilove et al. 2002). Given that the attacker felt he was acting in self-defense, should it be compared to planned attacks? What factors distinguish a rampage school shooting from other types of shootings? The definition used to identify a positive case can have a significant impact not only on our assessment of how rare the event actually is but also on the substance of the theory that is subsequently developed to explain the phenomenon. We call this the case definition problem. Determining what a case is has generally been undertheorized in the social sciences (Ragin and Becker 1992). Classifying events as school shootings often depends on the question that is being asked. While some authors believe that one’s case and population of cases should be determined at the outset of the research, others believe Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. 178 SOCIOLOGICAL METHODS & RESEARCH that determining what a particular event is a case of should be an inductive or iterative process. This split, perhaps not surprisingly, often follows the quantitative-qualitative or variable oriented–case oriented methodological divides (Ragin 1997, 1998, 1999).According to Ragin, Howard Becker, who falls squarely on the inductive side of this debate, argued that researchers probably will not know what their cases are until the research, including the task of writing up the results, is virtually completed. What it is a case of will coalesce gradually, sometimes catalytically, and the final realization of the case’s nature may be the most important part of the interaction between ideas and evidence. (Ragin and Becker 1992:6) It should come as no surprise, then, that there is no consistent definition of school shootings or population of events called school shootings in what little empirical work exists. Some researchers have taken a very broad approach while others have taken a narrow approach.2 One of the advantages of taking a broad approach is a larger potential sample size. One might treat rampage school shootings as a particular instance of lethal school violence or perhaps even as an extreme manifestation of nonlethal school violence. Another way of increasing the number of cases that is sometimes used in comparative historical research is shifting the unit of analysis so as to compare and contrast subunits within a case (King, Keohane, and Verba 1994). The prototypical example is increasing the number of cases by comparing and contrasting states rather than simply taking the United States as a single case. However, one must be sure to have compelling theoretical reasons that legitimate shifting the unit of analysis or treating one event as a more extreme manifestation of another more common occurrence. Often in case-oriented research, the cases are purposefully selected because of their political or historical significance (Ragin 1997). We return to this issue in the discussion section. THE COMPARISON CASE PROBLEM A second problem for studying school shootings related to our first is identifying the relevant “nonevent” with which cases of the outcome could be contrasted. If we limit ourselves to studying cases in which Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. Harding et al. / STUDYING RARE EVENTS 179 school shootings occur, we cannot determine which causes are sufficient to produce a school shooting. However, given that the cause(s) may exist at different theoretical levels of analysis—individual, school, community, and even nation—a wide variety of comparative nonevents might seem appropriate. We might imagine comparing the shooter with nonshooters at the same school or comparing a school where a shooting occurred to another school in the same community, or different communities in the same nation, or compare the United States with a similar nation that has not had school shootings. That school shootings are extremely rare events suggests that cases in which they do occur may be somehow extreme on many causal variables, making selection of comparison cases even more difficult. We call this the comparison case problem. Some reviewers of the literature on comparison cases have claimed that an exclusive focus on positive cases, as we do here out of necessity, results in the problems of “selection on the dependent variable” that can plague both small and large N research (Geddes 1990).3 By this logic, if cases are chosen on the basis of the dependent variable, one sees only a truncated part of the distribution of the dependent variable, and this can induce bias. However, as Dion (1998) pointed out most recently, variation in the dependent variable is important only if one seeks to assess sufficient conditions. Dion noted that factors that are extremely unimportant from the perspective of sufficiency (perhaps less than 1/100 of 1 percent of youth with access to guns commit school shootings) can nonetheless be very important from the perspective of necessary factors (100 percent of the school shootings involved youth with access to firearms). From the perspective of identifying necessary but not sufficient factors, negative cases do not provide relevant information. THE DEGREES OF FREEDOM PROBLEM A third problem arises when there are a relatively small number of cases as well as a large number of potential causes. For example, there are only a handful of cases of rampage school shootings and almost a dozen variables that have been proposed as likely causes, including firearm availability, violent media, family breakdown, southern culture of violence, bullying, and so forth. With so many possible causes and Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. 180 SOCIOLOGICAL METHODS & RESEARCH so few cases, it is difficult to isolate the effect of any one variable. This problem is traditionally known as the degrees of freedom problem. A promising line of work to handle the degrees of freedom problem can be found in Skocpol’s States and Social Revolutions (1979). Skocpol made a strong case that this task can be taken on with the help of Mill’s (1974) methods of agreement and difference.4 Using Mill’s method of agreement, Skocpol argued that the combination of a weak state and agrarian sociopolitical structures conducive to peasant revolt are the common factors in three states that experienced social revolutions (France, Russia, and China). Using Mill’s method of difference, Skocpol claimed that this same combination of factors was not present in five comparison cases that did not experience revolutions (England, prerevolutionary Russia, Germany, Prussia, and Japan) and that the comparison cases were similar to the states experiencing social revolutions on other factors that scholars had argued precipitated revolutions. This allowed her to posit that this combination of conditions was both necessary and sufficient for explaining social revolutions. She ruled out causes proposed by other scholars, such as relative deprivation and urban worker revolts, because they are present but do not lead to the outcome in comparison cases. Thus, Skocpol highlighted the attractive nature of Mill’s logic in small-N research; it allows the researcher to evaluate different causal theories, even when there are more theories than data points (Lipjhart 1971). It is exactly this attractive feature of Mill’s (1974) methods that has come under attack by researchers who posit that Mill’s method of difference assumes a deterministic conception of causal social theories (Nichols 1986; Lieberson 1991, 1994; Goldstone 1997). The real world is probabilistic, these scholars argue. Sometimes, events are caused by unanticipated reasons or even random chance, and thus the enterprise of trying to place every data point into a causal theory is not realistic. Worse, the attempt to fit every instance (in large-N language to “account for all the variation”) after looking at the data amounts to data dredging and can produce distorted theories (Lieberson 1991). In reply, Skocpol (1986; Skocpol and Somers 1980) has defended a conception of research that works iteratively between induction and deduction in an effort to avoid armchair theorizing and find a theory that accurately reflects the data. Ragin (1997, 1998) argued that case-oriented research is not inherently deterministic but rather Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. Harding et al. / STUDYING RARE EVENTS 181 that determinism must be specifically theorized and that determinism and goodness of fit are separate issues. The debate over whether a single case study that disconfirms a prominent thesis is important for theory building splits along similar lines, with some suggesting that attempting to account for anomalies is central to the practice of theory building (Eckstein 1975; George 1979; Kuhn 1962) and others arguing that in a probabilistic world, a single disconfirming case study may not be evidence of anything more than chance or measurement error (King et al. 1994). Bypassing this debate over the merits of Mill’s (1974) methods, Mahoney (1999, 2000) provided three alternative strategies that can be used by small-N researchers (and are implicitly used by Skocpol) as they attempt to weigh their preferred explanation against competing hypotheses. When the three strategies are used at once, the researcher has triangulated the problem, giving added confidence to the conclusions of the research. In addition to Mill’s methods of agreement and difference, which he calls “nominal comparison,” qualitative researchers often use “ordinal comparison” and “within-case analysis.” Ordinal comparison is based on Mill’s (1974:398-406, 883-84) method of concomitant variation and seeks to establish a rank ordering of cases based on the degree to which given factors are present. For example, in Skocpol’s (1979) case, more of the conditions for state breakdown should be present in the cases of social revolutions than in nonrevolutions. This means that a single indicator of state breakdown may be present in the case of a nonrevolution and not present in a case of revolution, but, in aggregate, in cases in which there are more conditions for state breakdown, revolutions are more likely. This is more similar to the logic of variation in most large-N research, although in practice ordinal logic can be difficult when only a handful of events are being studied. The other important strategy that Mahoney (1999, 2000) identified that is widely practiced in small-N research is within-case analysis. He identified three major variants: pattern matching (Campbell 1975), process tracing (George and McKeown 1985), and causal narrative (Sewell 1996). We focus in this article on the first two.5 Pattern matching is an attempt to see whether all of the various implications of a theory are actually borne out by the evidence within a case. The more broadly divergent these implications are, the less likely they are to Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. 182 SOCIOLOGICAL METHODS & RESEARCH be explained by another theory and the more likely they are to be explained by the favored theory. This strategy is also looked favorably on by quantitative researchers who are also interested in qualitative research like King et al. (1994) because it essentially increases the number of observations by evaluating multiple implications of the same hypothesis within a single case. In process tracing, by contrast, the researcher uses a thick description of the sequence of events of a single case to identify the causal mechanisms at work in the sequence. This type of method is most useful when “temporal sequencing, particular events, and path dependence must be taken into account” (Mahoney 1999:1164). Within-case analysis has been formalized through event structure analysis and used in both ethnographic (Corsaro and Heise 1990) and comparative historical research (Griffin 1993; Isaac, Street, and Knapp 1994). Withincase analysis methods move away from a variable centered paradigm and toward a process or narrative paradigm (Abbott 1992). The combination of Mill’s (1974) methods and within-case analysis provides a good set of tools for tackling the degrees of freedom problem. By seeing whether various factors are present in all (or almost all) of the cases of school shootings, one could assess by Mill’s method of agreement whether they are necessary factors. We can gain additional confidence in our posited necessary factors by using process tracing to see whether the hypothesized causes actually played an important role in the shooting and pattern matching to see whether the hypothesized causes have all of the effects that our theories suggest that they should. However, our analytic task differs from that of comparative historicists both in that the number of negative cases is much greater and that it is not clear at what analytic level they should be chosen. If we could solve the comparison case problem and confidently select a representative sample of near misses, we might be able to establish sufficient conditions. Without these negative cases, we cannot apply Mill’s methods of difference, and thus we cannot establish sufficient conditions. THE COMBINED CAUSES PROBLEM A fourth problem in studying school shootings is that many rare events result from the combination of causes, or what Ragin (1998) calls “complexly combinatorial” causation. Because the events are rare but Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. Harding et al. / STUDYING RARE EVENTS 183 the universe of potential cases in which the events might occur is extremely large, many settings in which the event does not occur are exposed to many of the same causal factors. For instance, in the case of school shootings, some of the hypothesized causes are present at the national level. Examples include the availability of guns and exposure to media violence. Millions of children in thousands of communities have access to weapons and are exposed to violence on television, the Internet, movies, and video games, but only a few commit, attempt, or plan mass murder in their schools. In this situation, we would like to allow for the possibility that the explanation involves the combination of multiple causal factors, perhaps even arrayed in a specific sequence. How to identify such a theoretical combination of factors is a major challenge for any research of this kind. We refer to this as the combined causes problem. Process tracing is an important strategy for tackling the combined causes problem. If one argues that an interaction of multiple factors plays the causal role (rather than a model in which the presence of certain individual causes makes the outcome more likely), then it will be much easier to identify such interactions by looking holistically at individual cases than by looking at variables across cases. Also, by examining how the different factors come together in making the event happen, the researcher gains additional confidence in the conclusions. Of course, this entails the risk of conflating theory building with theory evaluation, but this problem could be solved by generating theory with one or two cases and then evaluating it on other cases. Ragin (1987, 2000) has provided the best explication of the advantages of case-oriented research over variable-oriented research in understanding the role of “causal configurations” as important explanatory combinations. He argued that in the variable-oriented research common in large-N analysis, the researcher seeks to establish the contribution that a single factor makes to the outcome, controlling for a wide variety of other variables. Here, the analyst is attempting to understand the effect of a single cause. Case-oriented research is valuable because it allows the researcher to understand complex configurations of factors that may lead to outcomes, even if their subsidiary components are not individually related to the outcomes. Here, the analyst is trying to understand the causes of a single effect. In theory, these combinations can be identified in large-N analyses through interaction effects, but Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. 184 SOCIOLOGICAL METHODS & RESEARCH in practice, when the interaction involves three or more causes, as real-world phenomena often do, they often cannot be assessed within large-N research because of problems of collinearity.6 We should note that various other models exist for how to combine causes. One such model is an additive or multiplicative risk factors model, in which different factors increase the risk of an event, and when enough factors are present to move the total risk above a certain threshold, the event occurs. In this model, the factors are in some sense exchangeable; it does not matter which factors are present or in which combination as long as the total risk reaches the threshold. Note that this is the model presumed in many quantitative analyses of binary outcomes (such as logit or probit models) in which independent variables or their interactions additively or multiplicatively increase or decrease the probability or odds of experiencing the outcome. THE DIFFERENT CAUSES PROBLEM A fifth problem occurs when seemingly similar rare events may have different sets of causes. Perhaps the easiest way to see this is to think about the role of copycat crimes. Two school shootings may share similar causes except one; in the second case, the perpetrator got the idea for the shooting from the prior shooting or copied the form of the shooting. In the second case, the copycat factor is an important causal factor, but in the first it is not. It is also possible that two school shootings may share no causes. In this case, it is reasonable to question whether the two shootings actually belong to different populations. Of course, trying to establish whether data are dissimilar enough to be partitioned into two or more populations of cases is one of the basic tasks of theory building, whether the events are rare or not, but such a partitioning may be more difficult when there are only a few cases with which to work. We refer to this problem as the different causes problem. Ragin (1987; see also Ragin 1999) is particularly interested in how different causal configurations can lead to the same outcome and thus provide perhaps the most thorough attempt to address the different causes problem. Ragin drew attention to the fact that most large N variable-oriented research assumes that causes are always (probabilistically) necessary and sufficient, such that variation in the Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. Harding et al. / STUDYING RARE EVENTS 185 independent variable X is linearly related to variation in the dependent variable Y (see Figure 1a). But in cases in which X is either necessary or sufficient, the plot will take a triangular form. If X is a necessary but not sufficient condition, when X is present, Y can be either absent or present, but when X is not present, there will be no instances of Y because the presence of X is necessary for the outcome (see Figure 1b). If X is a sufficient but not a necessary condition, then if X is absent, Y may or may not occur, but if X is present, Y will definitely occur because X is sufficient for the production of Y (see Figure 1c). Ragin’s examples generally focused on sufficient but not necessary factors for an outcome (e.g., revolutions can come about through rising expectations or through state breakdown). It is the role of the analyst to list the combination of present and absent factors in each case and then to narrow the field to establish the most parsimonious model of combinations of sets of causes that can explain an outcome. As previously mentioned, in the case of school shootings, the sheer number of negative cases in relation to positive cases suggests that sufficient factors are not likely to be found. Figure 1b likely describes quite well the data for any causal theory of school shootings. Any set of factors, like gun access and media violence, will be found in many youth who do not commit school shootings, and thus they are not sufficient factors. However, it is quite possible to use Ragin’s (1987, 1999) logic to identify different causal configurations of necessary factors that explain different types of school shootings. TWO SCHOOL SHOOTING CASES As part of a National Academy of Sciences study of lethal school violence (National Research Council and Institute of Medicine 2002), we conducted in-depth qualitative case studies of the rampage shootings at Heath High School in West Paducah, Kentucky, on December 1, 1997, and at Westside Middle School just outside Jonesboro, Arkansas, on March 24, 1998. These cases were assigned to our research team by the Case Studies of School Violence Committee. Both meet most scholarly and popular definitions of school shootings. The assailants were White boys, students at the schools they attacked, with no significant record of “problem behavior.” The shootings took place in racially Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. (A) Linear: X Necessary and Sufficient for Y Y :::::::: :::::::: 1 0 :::::::: :::::::: 0 1 (B) X Necessary but not Sufficient for Y X Y :::::::: :::::::: 1 0 :::::::: :::::::: :::::::: :::::::: X 0 1 (C) X Sufficient but not Necessary for Y Y 1 :::::::: :::::::: 0 :::::::: :::::::: 0 :::::::: :::::::: 1 X Figure 1: Ragin Diagrams for Necessary Causes and Sufficient Causes (points represent cases) SOURCE: Adapted from Ragin (1987). 186 Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. Harding et al. / STUDYING RARE EVENTS 187 homogeneous, middle- and working-class rural communities. Both shootings occurred on school grounds, and each had multiple victims who were also members of the school community. The shootings were planned in advance and were not motivated by interpersonal disputes with specific individuals who had wronged the shooters. Fieldwork was conducted in these communities in May and June of 2001. The research is based on participant observation and qualitative interviews with almost 200 community members including family members of some of the shooters; school faculty and administrators; students and parents; civic, community, and religious leaders; legal and police officials; and other community members. These data are supplemented by police and investigative materials, court records and depositions, psychological evaluations of one of the shooters, the shooters’ own writings, school district materials, and media reports. The purpose of our original investigation was to understand the causes of each shooting, to suggest measures to prevent future school shootings, and to understand how the communities were affected by the events. We focus here on causes. We briefly describe these two shootings below.7 Just before the morning bell rang at Heath High School on the day after Thanksgiving vacation, Michael Carneal, a 14-year-old freshman, pulled a handgun from his backpack and shot eight bullets into a group of students gathered for a morning prayer in the school lobby, killing three and wounding five. He put the gun he had stolen from a neighbor’s garage on the floor and surrendered to the school principal. Carneal, later diagnosed with a mild form of depression and the beginning stages of schizophrenia, complained that he had been teased and picked on by other students relentlessly and said after the shooting, “People will respect me now.” While he was not a social outcast and had friends and even a girlfriend, he was not central to any social group at the school. Carneal had joked about bringing guns to school and taking over the school with a small group of peers and had brought a gun to school and showed it to classmates on two occasions prior to the shooting. The week before the shooting, the boy whom classmates described as a jokester and prankster warned some classmates to stay out of the lobby on Monday morning and that “Something big is going to happen on Monday.” Carneal is the son of a respected lawyer and homemaker who were heavily involved in school and church events, and his sister was one of the school’s valedictorians. He plead guilty to three counts Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. 188 SOCIOLOGICAL METHODS & RESEARCH of murder, five counts of attempted murder, and one count of burglary and was sentenced to life in prison without parole for 25 years. The second incident took place just outside Jonesboro, Arkansas. Students and teachers were discussing their recent spring break when Andrew Golden, clad in camouflage clothing, came into Westside Middle School during fifth period and pulled the fire alarm. Golden then joined Mitchell Johnson, already in position on a wooded hill overlooking the school, as the students and teachers filed out of the school in response to the fire alarm. The 87 students and nine teachers who exited the west entrance of the building were met with a hail of gunfire that killed four students and a teacher and wounded 10 others. Earlier that morning, Johnson stole his mother’s van and picked up Golden, and the pair stole guns from Golden’s father and grandfather. They had an elaborate escape plan but were apprehended by police 200 yards from the school about 10 minutes after the shooting. The day before the shooting, Johnson told peers he “had a lot of killing to do” and that “tomorrow you will find out if you live or die.” Johnson’s family had recently moved to Arkansas from Kentucky, although he was born in Minnesota. His mother, a former corrections officer, was divorced and remarried, and the family was quite poor. Johnson had been sexually abused by a neighbor as a child and had an explosive temper that landed him in some trouble at school. Despite his occasional outbursts, Johnson was generally known by the adults at his school as an unusually polite boy, who did whatever he could to please adults. Golden is the son of postal employees. He was not considered a discipline problem at school but was known to neighbors as a menace, a boy who rode around on his bicycle with a sheathed hunting knife strapped to his leg. He was taught to hunt at a young age and was an expert marksman. Some residents claimed he tortured and killed cats. Too young for adult court, both boys were sentenced to juvenile detention until they turn 21, at which point they will be released. STRATEGIES FOR EXPLAINING SCHOOL SHOOTINGS The media and scholarly press have advanced almost a dozen hypotheses to account for school shootings such as those at Heath and Westside. Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. Harding et al. / STUDYING RARE EVENTS 189 These include media violence, bullying, gun culture, family problems, mental illness, biological predispositions, peer relations, demographic change, culture of violence, and copycatting, almost all of which offer some element of truth. Here, we explore strategies for making sense of the causes of school shootings based on in-depth data of the type gathered in qualitative case studies. Based on our qualitative case studies of two cases, we propose a theory of school shootings involving five necessary but not sufficient factors for school shootings. The development of this theory simultaneously employs two distinct logics of analysis: Mill’s (1974) method of agreement and within-case analysis. Mill’s (1974) method of agreement provides the overall logic for the theory. Each of the five factors is present in the two cases we studied. Two methods of within-case analysis—process tracing and pattern matching—convince us that these five factors played important roles in the shootings. We briefly summarize these five factors here as they will be important to the rest of our discussion. Further discussion and systematic empirical justification can be found in Newman et al. (forthcoming). While some of the five factors may seem tautological at first glance, their complexity will be revealed through the remainder of the article. The first and most obvious factor is gun availability. Clearly, a school shooting cannot occur unless a youth can attain unsupervised access to a weapon with which to commit his crime. The critical question is not whether the school shooter was able to access a gun but the ease with which youth in the community can get access to guns. The second necessary factor is the availability and adherence to a particular cultural script that supports a school shooting. The shooter must somehow believe that bringing a weapon to school and firing on his classmates will resolve an important problem, and cultural scripts provide a model for problem solving. In particular, the cultural script provides the rationale for a public attack on the institution as a whole rather than a targeted attack at individual teachers or students whom the attacker sees as the source of his problems. Such scripts might be provided by copying a previous school shooting, media violence, a culture of violence, or notions of masculinity. In the Heath case, for example, we believe that notions of masculinity and violent media provided such a script for Michael Carneal. Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. 190 SOCIOLOGICAL METHODS & RESEARCH The third necessary factor is the perception by the shooter of an extremely marginal social position within social worlds that are important to him. For the Heath and Westside cases, the relevant social worlds are the adolescent society centered around the school and the tightly knit rural community. In small communities such as these, the school itself is the only stage and the center of social activity. Within adolescent society, where identity is closely tied to peer relations and position in the social hierarchy, bullying and other forms of social exclusion can lead to marginalization and extreme forms of desperation and frustration. In a tightly knit rural community, where ties are multiplex, anonymity scarce, and homogeneity the rule, those who are different are easily marginalized. The fourth necessary factor is an individual problem that magnifies the impact of the shooter’s social marginalization. When a personal trauma, such as family breakdown, mental illness, abuse, or other forms of loss, is present, the individual’s emotional and psychological resources for dealing with social marginalization are reduced. In Heath, Michael Carneal’s mental illness and depression made him especially susceptible to and sensitive to social marginalization. In Westside, Mitchell Johnson’s experience of sexual abuse as a young child and problematic relationship with his father made him especially susceptible to social marginalization.8 The fifth necessary factor is a failure of the social support systems that are intended to catch troubled teens before their problems become so extreme as to lead to a school shooting. In both Heath and Westside, the organizational structure and culture of the school (structures and cultures certainly not unique to these two schools) made it difficult for faculty and staff to identify Michael Carneal, Mitchell Johnson, and Andrew Golden as potentially violent criminals and intervene to stop their descent into violence. Note that the five factors differ in their specificity. For example, while availability of guns is immediate and concrete, social marginalization is contextual and subjective. Moreover, the actual processes through which each factor contributes to the school shooting vary with each case. In this sense, the model is similar to Ragin’s (1987) Boolean algebra model in which there are multiple paths to the same outcome. However, in our model, it is not that there are different factors that could lead to the outcome but rather that within each necessary factor Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. Harding et al. / STUDYING RARE EVENTS Figure 2: 191 Venn Diagram of Five Necessary Causal Factors there are a variety of substitutable elements.9 Taken together, the five factors identify theoretical commonalities across cases. It bears repeating that Mill’s (1974) method of agreement produces only necessary but not sufficient conditions. Mill’s method of difference (or indirect method of difference) has the potential to produce sufficient conditions, but because our case studies do not include schools or communities that did not experience a school shooting, we cannot use these methods. There are likely many cases that possess all five factors but that have not experienced a school shooting. However, we do not expect a school shooting to occur in a case in which the five factors are not all present. This is the conventional meaning of necessary but not sufficient conditions. This idea is illustrated in Figure 2, which presents a Venn diagram of the universe of potential school shooting cases. Each of the five factors is represented by a circle enclosing all cases in which the factor is present. Only among cases in the shaded region on which all five circles overlap would we expect to see a school shooting incident, but not all cases within the shaded region must have an incident for the theory to be correct. Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. 192 SOCIOLOGICAL METHODS & RESEARCH QUALITATIVE CASE STUDY DATA Previous researchers with data on many cases have also attempted to identify common factors across school shooting cases (e.g., O’Toole 2000; Verlinden et al. 2000; Vossekuil et al. 2000). These researchers have not come up with the same set of factors as we have, however. For example, Verlinden et al. (2000) discussed 37 risk factors in six broad categories (individual, family, school/peer, social environmental, situational, and attack-related behaviors) that are common to at least some of the 10 school shooters they studied.10 We believe this difference is due to our qualitative case study method, which allows us to look at meso-level factors such as school organization and community culture. Quantitative researchers with a larger number of cases are often limited to factors easily measurable from media accounts, mostly micro-level factors. Meso-level data are hard to gather using traditional quantitative methodologies such as surveys because it is a property of the social system itself rather than the individual and may not be immediately clear to the individuals embedded within the social system.11 A few examples will serve to illustrate the value of qualitative case study data. An important meso-level phenomenon is the adolescent culture that left Michael Carneal, Andrew Golden, and Mitchell Johnson feeling marginalized and angry. Hidden from adult view but closely related to the local community culture and the actions of adults, the adolescent culture engenders rage in the socially unsuccessful and conceals threats from adult authority figures in a position to act to prevent them from being carried out. Two important aspects of adolescent society were revealed by our discussions with students and faculty.12 First, because young adolescents generally lack internally defined sets of goals and because externally defined markers of success such as academic achievement are seemingly disconnected from immediate real-life consequences, the opinions of others become a primary good for which adolescents compete. This helps us to understand the strong relation between status and peer approval in the social world of adolescence. Second and related, because adolescence is a period of identity establishment and because peers play such an important role in status hierarchies, finding a place in a peer group is an important aspect of identity development in adolescence. We observed a stark contrast Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. Harding et al. / STUDYING RARE EVENTS 193 between older and younger youth at Heath and Westside, for example. Older youth who have grown more comfortable with their identities had a much lower need for peer acceptance than younger youth. Within the peer-oriented adolescent culture, bullying, teasing, and exclusion serve to police the narrow boundaries of appropriate behavior, language, and clothing. Images of masculinity, femininity, and competence are imported from the wider local and national culture. Those who deviate from these images are labeled “gay,” perhaps the most damaging stigma in a conservative small town or rural area. With an understanding of this context, we set out to map the social world of each of the two schools we studied. Which social groups do youth divide themselves into, and to what degree is there a hierarchy among groups? Where are the shooters located in this social world? We received a wide array of often-contradictory responses from individuals differently located on the social map but were able to construct portraits of these worlds by triangulating from the comments of various respondents.13 For instance, in the Heath case, a group known as the “preps,” consisting of the cheerleaders, some athletes, and the most physically attractive students, sits atop the hierarchy. Directly below are a wide array of groups of relatively equal status such as the Goths, athletes more generally, “straight arrows” (band members and highly religious youth), high achievers (socially competent academic achievers), and “Future Farmers of America” (rural working class). At the bottom of the pyramid are the druggies, nerds, and vocational education students. The prayer group into which Michael Carneal fired consisted of students from primarily the high-achiever and straight-arrow groups. Michael Carneal had attempted to be part of three of these groups— the high achievers, the straight arrows, and the Goths—but in all three he failed. He followed his sister’s footsteps into the band, where by her senior year she was a section leader, but Michael was one of two students forced to sit out of competitions early in the season because there were not enough uniforms. Despite the wishes of his parents, he did not do well enough in class to be a high achiever, although again this was an arena in which his sister excelled, becoming one of the school’s valedictorians. He then turned to the Goths, a group of mostly older students who rejected the wider social norms around clothing, musical taste, and Christianity that pervade the school. They Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. 194 SOCIOLOGICAL METHODS & RESEARCH sometimes openly clashed with the prayer group, talking loudly during prayer meetings in the school lobby. In an attempt to fit in, Michael gave money and gifts, which he claimed were stolen, to members of the Goth group and to others. But Michael never seemed to fit in anywhere. He described himself as a tagalong among those whom others might have considered his friends and suffered under the shadow of his older sister who was successful in the social, academic, and extracurricular realms. Whether correct or not, he believed no one cared about him. His attack on the prayer circle can be understood within the context of his social marginalization. While certainly not the whole story behind the shooting and Michael’s marginalization, it is important that Michael was attacking members of groups that he had failed to enter, the high achievers and the straight arrows, in another attempt to gain favor with the Goths. However, he was also attacking an entire social structure that had left him without a group in which to construct a positive identity. The Westside adolescent hierarchy is similar to Heath’s structure but consists of two tiers instead of three. At the top of the pecking order are the athletes, the cheerleaders, and a few others who are graced either with money or, especially for girls, beauty. Below them come the rest: the band kids, the high achievers, and those that will in high school become the Future Farmers of America. One or two students sit outside the social structure entirely and are considered loners. Like Michael, Mitchell was not a loner, but he was also not popular.14 While Michael tried to fit into a group he could call his own, Mitchell aspired not to be a part of a particular clique but simply to be well liked and popular. Because Mitchell came from a poor family, he could not gain entry to the top social tier through wealth. While he did play football and basketball, being an athlete was by no means a guarantee of popularity. It certainly did not help Mitchell’s popularity when he was kicked off the basketball team for self-mutilation in the weeks before the shooting. Moreover when Mitchell bragged about his supposed exploits on the football field, his fellow team members publicly and ruthlessly cut him down to size. Mitchell had friends and even girlfriends, but he had no social group, and most important to Mitchell, he was marginal to the groups he most hoped to impress. Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. Harding et al. / STUDYING RARE EVENTS 195 In part a response to his social failures, Mitchell tried to carve his own path and gain respect through other means: He threw gang signs and used to boast that he had been a member of a gang in Minnesota and was now a member of the “Westside Bloods.” These attempts, however, got him nowhere. His peers found it hard to believe that a 13year-old White boy from Minnesota was the seasoned gang member he claimed to be, so they labeled him a “gang wannabe.” Teachers also remember Mitchell being overly concerned with his looks, asking some on several occasions whether he looked good and whether his hair was well coiffed. But no matter how hard he tried, Mitchell was not as popular and as liked as he wished he could become. Although Mitchell was rumored to have had a hit list, Mitchell and Andrew were more than 90 yards from their victims when they fired indiscriminately into the crowd of students and faculty. Like Michael, Mitchell was attacking the entire social structure that had denied him the attention and the respect he so craved. In sum, understanding the local adolescent culture in which school shooters perceive themselves to be slighted and marginalized requires in-depth, qualitative data. We based our analyses of the adolescent culture and the place of the shooters within it on participant observation at school and school events, interviews with students and faculty, and the statements of the shooters regarding their peer relations. Only by comparing and contrasting multiple views of the same people, structures, and events and by probing teenagers about things they see as seemingly obvious interpretations can we hope to understand the adolescent cultures of schools and how school shooters fit into them. WITHIN-CASE ANALYSIS The identification of the five factors using Mill’s (1974) method of agreement described above is only made possible by a within-case analysis of the types described by Mahoney (2000) as process tracing and pattern matching. Process Tracing Process tracing helps the researcher to understand how each of the five factors operates in a specific case and how the factors interact. Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. 196 SOCIOLOGICAL METHODS & RESEARCH Examining a school shooting case as a process leads us to seek to understand the links between stages in the process as well as the links between the individual actors and the actions taken. Critically important in understanding these processes is understanding the meanings that individual actors attach to various stages and actions. We illustrate the value of process tracing by examining how the masculinity script played a role in both the Heath High School and Westside Middle School shootings. At the heart of Michael Carneal’s shame and frustration was his inability to establish a masculine identity within the adolescent society of Heath High School. Interviews conducted by the police and by psychiatrists following the shooting suggest that he interpreted the torment he perceived from bullying, teasing, and exclusion as a direct assault on his masculinity, an important form of identity, especially in a conservative community. Michael was distraught that he was unable to stop either the physical bullying from older or stronger boys or the constant teasing from other peers. An important part of the assault on his masculinity was an incident in the eighth grade in which the school newspaper labeled him as gay. Following this incident, Michael’s grades plummeted, and by his account, the bullying increased and became focused on his sexual orientation. He was routinely called “gay,” “faggot,” and “pussy.” The magnitude of these slights was quickly revealed in our interviews with other adolescents in the Heath community, who almost uniformly described being called gay as the worst possible insult, far worse than being non-White, poor, overweight, or unattractive. Furthermore, our own observations in the school and community revealed that the term gay has taken on a general connotation of incompetence or negativity. Dropping one’s tray in the cafeteria is “gay,” as is having to stay after school for detention. In this culture, sexual orientation, masculinity, and competence are closely linked. Furthermore, physical prowess is an important aspect of masculinity. Michael’s inability to respond to bullying and teasing effectively only magnified the problem, reinforcing the threat to his masculinity. Seeking help from adults would not address Michael’s problem because a “man” handles his own problems. Police and psychological interviews also revealed that Michael viewed the shooting as a way to earn respect from his peers. It was an opportunity for him to assert his masculinity on a public stage, for all to see. Cultural notions of masculinity identify aggression and physical Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. Harding et al. / STUDYING RARE EVENTS 197 prowess as means of earning and maintaining respect. To be authentic, respect must be achieved by the individual, not conferred by authority figures or protectors. Such notions emphasize action over talk, closing off other potential methods of resolving problems, such as soliciting help from parents or teachers. Thus, notions of masculinity affected not just Michael’s perceived marginality but also the form that he used to address it, a violent attack that, in his mind, could demonstrate to others that he was worthy of respect. After the attack, Michael told a psychiatrist that his life was better because “people respect me now.” In sum, simply knowing that Michael Carneal was bullied and called “gay” and “faggot” by his peers does not convince us that these events played a role in the shooting at Heath. Rather, we traced the importance of these actions by showing how notions of masculinity provided a script for his school shooting. We examined the meaning of sexual orientation and masculinity in the local culture and the events that surrounded the bullying and labeling that Michael experienced and then examined his own statements to understand how he interpreted the bullying and how the shooting related to his perceptions of others’ views of his masculinity. Process tracing also helps to reveal how factors in our model interact in an individual case. We continue the example of the Heath High School shooting and Michael Carneal’s perceptions of social marginality to show how his perceptions of marginality were influenced by his own mental illness, a personal trauma in our five-factor model. In stark contrast to the account we provide above is information from interviews with Michael’s peers that he was not teased or bullied any more than any other students at Heath and that he himself was somewhat of a bully. Furthermore, Michael appeared to have friends and even a girlfriend, perhaps the ultimate proof of a young man’s masculinity. Michael’s steadily intensifying mental illness explains this discrepancy. Psychologists and psychiatrists who examined or treated Michael after the shooting diagnosed him with a form of schizophrenia (“schizotypal personality disorder”) and mild depression (“dysthymia”). He had engaged in a pattern of odd behavior, paranoia, and misinterpretation of social interactions consistent with these disorders prior to the shooting. He believed assailants were lurking underneath the floor in his bedroom and peering at him through air ducts in the Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. 198 SOCIOLOGICAL METHODS & RESEARCH bathroom. He covered himself with several towels whenever he went to the bathroom; often announced, “I know you are in here,” when entering his bedroom; and hid knives underneath his mattress. He had unreasonable fears, such as a fear that his family would be robbed if they went to a restaurant or that he, his father, and a family friend would be mugged walking across a quiet college campus en route to a basketball game. He told those who interviewed him that he had no friends and that he heard people calling him stupid behind his back. None of these fears and behaviors connected to his mental illness directly explain why Michael Carneal shot his classmates, but they do explain why his perceptions of his social position differ from those of his peers. Michael’s mental illness led him to misunderstand social relations at Heath High School, magnifying the importance of teasing and bullying to the point where he believed he was not respected by his peers and that bringing guns to school was the only way to earn that respect. In sum, while simply noting that Michael was mentally ill does not convince us that his mental illness played a role in the shooting, a closer look at the events leading up to the shooting and the perceptions of those involved suggests an important role for mental illness. This example also shows how factors at different levels of analysis can interact to produce a rare event such as a school shooting. Michael’s mental illness, an individual-level factor, informed the perceived and real marginalization within the adolescent culture, a meso-level factor. Turning to the Westside case, process tracing also helps us to understand how Mitchell’s early violent and repeated sexual abuse by a neighborhood boy caused him to be especially concerned with his sexuality, with projecting a masculine image and thwarting any wouldbe attackers. The early abuse clearly left its mark. When he was 11 years of age, Mitchell was caught molesting a 2-year-old, and when he was 13, he racked up hundreds of dollars of credit card debt on his father’s card while making sex-talk phone calls. His teachers and peers also said that Mitchell was unusually preoccupied and invested in his relationships with girls, once growing despondent enough over a breakup that he threatened suicide. One staff member recalled that Mitchell had a bad-boy image and was overprotective of his little brother, who was also sexually abused by the same neighborhood boy. One day, Mitchell told her that he felt sorry for his brother because his brother was “not very tough.” Mitchell’s obsession with projecting an Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. Harding et al. / STUDYING RARE EVENTS 199 image of toughness through his supposed membership in gangs can be seen as both a way to prove his manhood and as a means through which he hoped to stave off any further abuse. To ensure his safety, Mitchell even found himself a protector, making quick friends with the biggest student in his class. In the same way that Michael’s mental illness led him to misperceive the social relations at Heath, Mitchell’s early sexual abuse also caused him to underestimate his own popularity as well as causing him to be especially sensitive to the attacks on his manhood. In the weeks leading up to the shooting, Mitchell started to spiral downhill; he was kicked off the basketball team (an important avenue in the adolescent society for popularity), his girlfriend broke up with him, and his father threatened that he would have to move back to Minnesota (where he was assaulted) because of his misuse of his father’s credit card. Like Michael, Mitchell started to threaten his peers, saying that “something big was going to happen” and that “tomorrow you will find out if you live or die.” But again, his peers were unmoved, thinking he was all talk. He might have chosen to direct his anger and pain in any number of directions: at the boy who had sexually assaulted him, for example, or at his father with whom he had an especially troubled— some have even said verbally abusive—relationship. But he directed his anger instead at the school, at the staff and students who were obviously unimpressed by his claims to manhood and toughness. The well-thought-out plan and overwhelming firepower signaled that he was not all talk and that he and his threats in the weeks before the shooting should be taken seriously. In sum, process tracing helps us to understand how Mitchell’s early sexual abuse and own feelings of insecurity magnified the ordinary slights and affronts to his ego that are so common within the adolescent society. It also helps us to understand why earning respect by such a public display of masculine bravado was very important to him, providing a script for the shooting. Pattern Matching Pattern matching involves examining data to see whether theories developed from prior research, armchair theorizing, or cross-case comparisons are relevant to a particular case. A theory contains predictions Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. 200 SOCIOLOGICAL METHODS & RESEARCH about patterns in the data, and with detailed data, these predictions can be compared with the actual events. Pattern matching differs from process tracing in that it specifically involves theory testing rather than theory generation or explication. In practice, however, the two may be quite similar. Pattern matching may be particularly useful for examining the role of macro-level causal factors in a particular case. For a macro-level cause (such as a regional or national gun culture) to convincingly be part of a causal account, it must be manifested locally in the particular event of interest. We take as an example the availability of guns. The number of guns in the United States has doubled since 1970 to about 200 million (Cook, Moore, and Braga 2001). How is this national trend manifested in the Heath and Westside communities? While obviously guns played a role in both the Heath and Westside shootings, is it fair to say that the easy availability of guns in these two communities played a role? The gun availability theory predicts that (1) the shooters will have little trouble identifying a source of weapons and securing them, and (2) their possession of guns will not serve as a warning that violence will occur sometime in the future. Conversely, if the gun availability theory was not relevant, we might expect the shooters to go to great lengths to find weapons and the possession of weapons by adolescents to set off warnings among members of the community. Both these conditions appear to be met in the Heath case. Michael Carneal was able to identify two nearby sources of weapons. The first was his father’s pistol and shotguns that were stored in his parents’ bedroom closet; the pistol was in a locked box. Michael stole his father’s pistol weeks before the shooting and brought it to school to show to friends, then later gave the gun to a neighborhood youth who threatened to tell the police he had the gun. Michael’s father did not discover that the pistol was missing until the police told him they had recovered it after the shooting. Michael stole the shotguns from his father the weekend before the shooting and brought them to school with him the day of the shooting. The second source was a neighbor’s garage, where a pistol, five rifles, and ammunition were stored in a locked cabinet. Because Michael had shot guns with the neighbor and his son, he knew where the key was hidden for the gun cabinet. Michael stole the pistol from the neighbor’s garage and brought it to school with him the last day before Thanksgiving vacation. Again he showed Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. Harding et al. / STUDYING RARE EVENTS 201 the pistol to peers, who were reportedly unimpressed because the .22 caliber pistol was “small.” He stole the five rifles on Thanksgiving Day. The near ubiquity of guns in Heath was also supported by our interviews with other adolescents, almost all of whom said they could get a gun if they wanted to. Although Michael went to great pains to hide the stolen guns from his family and school officials, his possession of the guns did not provoke a reaction from other members of the community. As mentioned, he got little reaction from classmates who saw him with guns in school on two occasions prior to the shooting, despite the fact that he told people that “something big is going to happen on Monday” and warned others not to be in the lobby Monday morning. The weekend before the shooting, he brought the pistol and three of the rifles to a friend’s house, and the two practiced shooting a pink rubber ball in the backyard. Their shots woke a neighbor, but he did nothing besides yell at them to keep quiet. The friend’s older brother, a senior at Heath High School at the time, also saw the guns and did nothing other than warn the boys not to get in any trouble. We see similar but not identical patterns in the Westside case. Andrew Golden and Mitchell Johnson had only slightly more trouble securing their weapons than Michael Carneal. The morning of the shooting, they went first to Andrew’s parents’ house. Most of the guns owned by his parents were locked in a gun safe, which the boys were unable to open even with the aid of a blowtorch. They did, however, take three unsecured pistols from the Golden home. Next, they drove to Andrew’s grandfather’s house. Andrew’s grandfather was an avid hunter and had an entire wall of guns secured only by a cable lock. The boys found a set of cable clippers and cut the cable, taking four handguns and three rifles. Without Andrew, Mitchell would not have had such easy access to guns. Because his stepfather had a criminal record, he was not allowed to have guns in the household. However, Mitchell did have a gun of his own that was stored at the home of a family friend. The availability of guns was also supported by our interviews with Westside adolescents. In the Westside case, we cannot know whether the boys would have needed to conceal their possession of weapons had they not used them almost immediately, but some evidence suggests this might not have been the case. First, Andrew Golden’s family was well known as an Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. 202 SOCIOLOGICAL METHODS & RESEARCH avid hunting family, even by area standards. His grandfather worked for the Arkansas Fish and Game Commission, and his parents ran a local gun club. Andrew was given his first gun at age six, practiced shooting at a local shooting range, and won awards for his marksmanship. He brought toy guns to school to play with during recess and even drew two guns on a school project to design a family coat of arms—a drawing his teacher later remarked she had thought was cute because it indicated the family bonded over hunting. It would not have been unusual for Andrew to have a gun in some situations, for example, when supervised by an adult on a hunting trip or at the firing range. Second, Andrew was often seen riding around his neighborhood on his bicycle with a hunting knife strapped to his leg. He was known as a menace in the neighborhood, threatening to shoot other children, and neighborhood children said they saw him killing cats. While neighborhood parents were concerned enough about this to forbid their children from playing with Andrew, apparently none of this was reported to authorities, perhaps because the neighbors were afraid of the Golden family. Third, the boys made threats at school in the days before the shooting. The boys told students that they “had a lot of killing to do” and that “something big is going to happen tomorrow.” We do not want to overstate the normalization of guns in the Heath and Westside communities. In neither community would a middle school or high school student with a gun go unnoticed outside of a set of narrowly prescribed situations, such as a hunting trip. Certainly, in this day and age, it would not be acceptable to adults for a youth to bring a gun onto school property. However, these are communities in which a significant portion of adolescents regularly uses firearms for legitimate and legal purposes, mostly hunting. For this reason, it is not considered unusual, deviant, or threatening for youth to have weapons. A youth taking target practice in the backyard or carrying a knife does not provoke an official response because these actions are not considered predictors of violence, as they likely would be in other communities. In sum, the data in both the Heath and Westside cases are consistent with the theory that the easy availability of guns was an important factor in these school shootings. This example illustrates how pattern matching can be used to assess the relevance of a macro-level theory to a specific rare event. Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. Harding et al. / STUDYING RARE EVENTS 203 DISCUSSION We now return to the five challenges that frame this article. We consider the strengths and limitations of our research in light of these challenges and note possible avenues for future research. THE CASE DEFINITION PROBLEM One particular strength of our method is that pattern matching allows for the possibility of testing the model on other rampage school shootings. This process will help evaluate the generalizability of the findings from our two case studies. The best source of data is of course other qualitative case studies of the same type of event. To successfully employ pattern matching, we must first consider the case definition problem. The shootings at Heath High School and Westside Middle School are both widely accepted cases of school shootings in the national media. Because school shootings are public events with an established public discourse, and because we wish to inform this discourse and the policy that may come out of it, we began with the categories as they were defined in the public discourse, paying close attention to the phenomenological nature of such categories and the differences between seemingly similar cases. But during the course of our research, as we established the causes of these two particular shootings, we were better able to define the universe of cases to which these two incidents belong. Based on the essential aspects of the two cases we studied and our more limited knowledge of other cases, we identified the following four characteristics as important in defining what we call rampage school shootings.15 1. The location of the incident is a “public stage” either on the school property or at a school-related function. 2. The shooters must be current or former students of the school. 3. There must be multiple victims (although the injuries do not have to be fatal) or, at the very least, multiple targets. 4. While some victims may be targeted specifically because they have wronged the shooter, there are typically others who are chosen only for their symbolic significance (the principal, the preps, the prayer circle, the jocks) or are shot at random. Clearly, there are other shootings at schools that would fail to meet our definition of a rampage school shooting. The Fayetteville case Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. 204 SOCIOLOGICAL METHODS & RESEARCH described above, for instance, would fail to meet our definition because there was only one victim (and one target), and the assailant chose his victim because of an interpersonal dispute over a girl. At this phase in our research, we are most confident that our theory applies to other rampage school shootings. However, because we have studied only two cases in depth, we cannot claim to have tested our theory on anything approaching a representative sample of cases of rampage school shootings. The best we can do is attempt to do pattern matching on other cases. Qualitative case studies have been done of two other rampage school shootings: in Conyers, Georgia (Sullivan and Guerette 2002), and in Edinboro, Pennsylvania (DeJong, Epstein, and Hart 2002).16 While the data available on these cases are not entirely comparable, we have examined the studies of these cases, and they are consistent with our five-factor model. Second to qualitative case study data, the next best source of data on rampage school shootings is media accounts and quantitative studies. These sources of data do not have the depth of information one would like, especially information to do effective within case analyses.17 One could also compare the causes of rampage school shootings to the causes of other sociologically similar events that are perhaps less rare, such as workplace rampage shootings. In effect, this involves reframing a rare event as a more extreme version of a more common event. Here, the assumption is that factors causing the rare event and the more common event are similar enough that something can be gained by studying the more common event. For school shootings, one might study other forms of youth violence, delinquency, or suicide to generate school shooting theories, although we have not yet done so. If school shootings are similar to other lethal events or extreme manifestations of nonlethal violence, one might combine these events to increase sample size and thereby avoid some of the difficulties inherent in small-N research. COMPARISON CASE PROBLEM The public understandably desires a theory of school shooting with predictive power or at least a profile of school shooters that can help target preventative resources more effectively. Unfortunately, among Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. Harding et al. / STUDYING RARE EVENTS 205 law enforcement experts, there is consensus that creating a school shooter profile is impossible (see O’Toole 2000; Vossekuil et al. 2000; Reddy et al. 2001). One might argue that a serious limitation of our method is its failure to deliver a model with predictive power. Ideally, we would find comparison cases of nonevents, which would allow us to determine whether sufficient causes exist. A theory based on necessary and sufficient causes would give our model predictive power. We believe, however, that no such theory will likely ever be developed because of the difficulty of selecting comparison cases. Choosing a relevant nonevent can be quite problematic, and depending on the cases one picks, the results can be drastically different. It is tempting to compare school shootings to the “near misses” that have made headlines recently, such as the foiled attempt in New Bedford, Massachusetts, last year in which a group of disaffected students planned to smuggle guns and explosives into New Bedford High School to shoot their classmates and faculty. By comparing a school shooting to a near miss, the analyst can examine the role of the factor or factors that distinguish the two cases. Foiled attempts tend to be cases in which the school or other individuals in the community learned of the plot and were able to successfully intervene so as to avert the tragic outcome. In New Bedford, one of the students involved in the plot warned school officials. One might assume that these cases would have four out of the five necessary conditions present—that is, all factors except for the failure of social support component. This sort of a comparison would be illustrative, although there is often no way of knowing that the shooting would have ever actually taken place short of a confession. Yet potentially, there are many other near misses, cases that never make it to the headlines because they do not involve the intervention of a third party. For example, potential assailants may not be able to access the necessary weapons to carry out an intended attack. These near misses do not make the headlines because the potential shooter does not make his intentions public. Selecting only certain types of near misses for comparison will lead the analyst to emphasize only certain sufficient conditions, potentially leading to incorrect conclusions. The causes that are sufficient could change with the near miss cases studied. Near misses are not the only relevant comparisons. One might, for example, study individuals in the same environment who do not Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. 206 SOCIOLOGICAL METHODS & RESEARCH commit school shootings, or study schools or communities where school shootings have not occurred. If we take the former instance (and thereby attempt to control for meso- and macro-level factors), we cannot ignore the effect of the shooting on the social dynamics of the school or community. If we take the latter instance and compare communities where school shootings have not occurred to communities where they have, we face two serious problems. First, a community that has yet to have a school shooting is not necessarily a community that will never have a school shooting. In essence, one would be comparing communities that have experienced school shootings with communities that have yet to experience a school shooting.18 Second, there is a substantial risk that a sample of nonevents is somehow unrepresentative of all nonevents. While this hazard is also present when one conducts large-N quantitative studies, the risk of choosing an unrepresentative sample increases if the sample of nonevents is small enough to allow for in-depth qualitative analysis. DEGREES OF FREEDOM PROBLEM While our method does not solve the degrees of freedom problem, we think it is misguided to try to isolate the effect of a single cause in school shootings. Our five-factor model predicts that a change in a particular factor will not lead to a school shooting unless the other four factors are present. Thus, trying to estimate the effect of a single factor controlling for other factors is not only unfeasible, we claim that it is the wrong way to study this phenomenon. The great strength of our approach is that a nominal comparison framework allows us to identify a common set of causes across our two cases, and our narrative approach ensures that the necessary conditions we identified were actually important causes in the shootings. Furthermore, our method does allow us to test competing theories about the causes of school shootings. For example, it has been hypothesized that bullying is a leading cause of school violence. Our research suggests that while bullying may contribute to the social marginalization of youth, by itself bullying is not a necessary cause of school shootings. More important than any objective metric of abuse is the way the shooter perceives himself in the adolescent social order— a perception that may be influenced by bullying or teasing but could Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. Harding et al. / STUDYING RARE EVENTS 207 be influenced by other factors as well. This helps explain why some of their peers claim the shooters were either not bullied or treated no worse than were their fellow students. While our methods do not rule out other factors that may help explain school shootings that we have not studied in depth, we can rule them out as necessary conditions since they are not important in our two cases. COMBINED CAUSES PROBLEM One possible weakness in developing a complex theory that points to a combination of causes based on only two cases is that we might have highlighted a different combination of factors had we started with two entirely different cases. Indeed, in an ideal world we would have started with the entire universe of school shooting cases and sent field teams to each of those sites to do the type of fieldwork we were able to do in Paducah and Jonesboro. We could then look across all of these cases and identify the common set of factors using nominal comparison, process tracing, and pattern matching. Obviously, we do not live in such an ideal world. Rather, we live in a world that has school shootings and a world in which social scientists are constrained by often quite limited resources. Like most qualitative researchers, we began by building a theory based on a small number of cases and hope future research will refine it by studying more cases. An advantage of using the method of agreement is that the necessary factors we identified suggest hypotheses about variation in the frequency of school shootings over time, space, and social group. Our model suggests that a change in the prevalence of one or more of our five factors should be at the source of variation in school shootings because such a change would increase the number of cases in which all five factors are present.19 The magnitude of such an increase depends on the prevalence and distribution of the other factors in the universe of potential cases, however. If the increase in one factor occurred solely in cases in which at least one of the other four were always absent, we would observe no variation.20 DIFFERENT CAUSES PROBLEM We have identified what we believe is a common set of causes for rampage school shootings. However, the model says nothing about Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. 208 SOCIOLOGICAL METHODS & RESEARCH additional causes that may be relevant for individual cases other than Heath or Westside. Consider a hypothetical school shooting that has our five necessary conditions but in which the influences of a satanic cult are also at work—as they are rumored to have been in the Pearl, Mississippi, shooting.21 Our theory does not preclude the possibility that additional causes, such as cult influences, are also at work in other rampage school shootings such as that in Pearl. However, knowing that cult influences are a factor in Pearl and not in Heath and Westside is not essential in determining likely points of intervention. One advantage of a model of necessary factors such as our five-factor model is that it suggests avenues for prevention. If the model is correct, then intervening in any one of the five areas should be sufficient to prevent a school shooting, even if additional causes, such as cult influences, are also at work in other school shootings. As long as we attack any of the five necessary causes, we are likely to influence the probability of school shootings. However, it is possible that our model only applies to a subset of school shootings and that an entirely different causal model is at work in some other school shootings. One example is urban versus rural school shootings. Urban school shootings may not share the five necessary conditions that we have developed for rural school shootings. In that case, we might return to our case definition problem and reevaluate what Heath or Westside is a case of and then divide the population of school shootings into two: “urban school shootings” and “rural school shootings.” Finally, it is also possible that our model applies only to the two cases we have studied in depth, in which case our theory is not much of a theory. Only by testing our theory against other cases can we actually determine whether there are really multiple models or one set of necessary conditions that fits most school shootings. CONCLUSION—LESSONS FOR STUDYING RARE EVENTS When we first began this project, we were quite skeptical about drawing conclusions from case studies of extremely rare events such as school shootings and worried that we would be able to provide little more than a detailed description of the two cases that we studied. In particular, Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. Harding et al. / STUDYING RARE EVENTS 209 we were concerned with five methodological challenges to drawing inferences from qualitative case studies. These include the difficulty of defining a relevant universe of cases and identifying comparison cases, the degrees of freedom problem, and grappling with how causal factors combine and whether seemingly similar events would have different sets of causes. Since then, our views have changed. We hope we have convinced the reader that it is possible to abstract away from the specifics of the two cases to develop a theory of rampage school shootings that suggests avenues for prevention. Borrowing the logics of necessary but not sufficient conditions and within-case analysis from comparative historical research, we have attempted to provide a useful theoretical account of the causes of school shootings based on our qualitative case studies. This account involves five necessary factors common to both cases, factors that can be shown to be relevant to each shooting through process tracing. Pattern matching has allowed us to test the applicability of factors hypothesized to be important to school shootings in previous research or the popular media. We have rejected some and accepted others. A number of other types of rare events share with rampage school shootings characteristics that pose special challenges for researchers. These characteristics include extreme rarity, the difficulty of defining appropriate comparison cases, the potential for causal factors operating at multiple theoretical levels, and the potential for important interaction between causal factors. Other types of rare events that likely share these characteristics include hijackings, suicide bombings, workplace shootings or other mass murders, riots, mass suicides, coups, political assassinations, and impeachments, for instance. We believe that the lessons learned in studying school shootings can be applied to other types of rare events. To summarize, these lessons include the following: (1) Valuable conclusions, such as those about prevention, can be drawn even without comparison cases by focusing on identifying necessary but not sufficient conditions; (2) qualitative case study data can be quite valuable because they allow for the connection of causal factors to outcomes through process tracing; (3) even research involving a small number of cases can be valuable when it suggests hypotheses for future research; (4) pattern matching can be used to test the applicability of theories to individual cases provided the researcher has sufficiently Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. 210 SOCIOLOGICAL METHODS & RESEARCH detailed data about the cases; and (5) nominal comparison of only a few cases allows for the researcher to reject some potential necessary conditions. Finally, we hope this has provided the skeptic with further evidence of the utility of small N research. When a complex configuration of causes operates, the methods described here may have an advantage over traditional large N methods such as regression analysis because they can more easily deal with multiple interactions. Take as an example the Venn diagram in Figure 2, imagining that both positive and negative cases of school shootings appear on the diagram (assuming for the moment that the issue of defining a universe of cases and determining appropriate comparison cases has been resolved). If the five-factor model of necessary but not sufficient conditions is correct, the positive cases will be concentrated in the shaded region where the five factors overlap, but negative cases will appear throughout the diagram, including within the shaded region (since these are necessary but not sufficient conditions, some negative cases may also have all five factors). How would a regression analysis handle these data? If the analyst suspected that the model involved a five-way interaction, the regression equation would include the interaction term for the five factors plus the five factors entered as separate variables. Assuming that our model is the “true model,” the analyst would find that the interaction term was nonzero and highly significant, but the other terms were not statistically different from zero. However, it is hard to see how, in practice, the analyst would ever arrive at the right model, given that standard practice is to begin with single variables and then test combinations of interaction terms. In all likelihood, the analyst would end up concluding that each factor individually increased the probability of a shooting and that lower order interaction terms did as well, a quite different model than the “true model” that we posited.22 NOTES 1. A Gallup poll conducted in August 2000 found that 26 percent of American parents feared for their children’s safety at school. The day after the Columbine shooting, 16 months earlier, 50 percent of parents said they feared for their children’s safety at school. Twenty-nine percent of 500 high school students polled by ABC News in March 2001 said that they saw some risk of Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. Harding et al. / STUDYING RARE EVENTS 211 an attack at their school, while 40 percent saw some risk immediately following the Columbine attack. See Gembrowski (2001). 2. The U.S. Secret Service’s National Threat Assessment Center identified 37 school shootings involving 41 attackers that occurred between 1974 and 2000. They chose cases in which the assailants were current or recent students at the school and in which the attacker or attackers chose the school “for a particular purpose (and not simply as a site of opportunity)” (Vossekuil, Reddy, and Fein 2000). The Secret Service report therefore excluded shootings that were related to drugs, gangs, or interpersonal disputes unrelated to school. The FBI, in contrast, based their report about school shootings on only 18 cases, which included both successful school shootings (which they do not define) as well as foiled attempts (O’Toole 2000). Last, the Centers for Disease Control and Prevention (CDC) recently published a study that was also meant to shed light on the problem of lethal violence in schools. Their study, however, included all school-associated violent deaths between 1994 and 1999 and therefore omitted school shootings in which no death occurred and included acts of lethal violence in which no gun was used. The CDC defined a case as a homicide, suicide, legal intervention, or unintentional firearm-related death of a student or non-student in which the fatal injury occurred 1) on the campus of a public or private elementary or secondary school, 2) while the victim was on the way to or from such a school, or 3) while the victim was attending or traveling to or from an official school-sponsored event. (Anderson et al. 2001:2695) 3. Quantitative methodologists have long been concerned with modeling rare events, but their procedures are not very helpful in explaining school shootings because these methods require large databases containing both instances and noninstances of the event of interest. Their concerns include modeling relationships between events over time, as in Nelson’s (1980) models of multiple criminal victimization over time or clustering events such as cases of rare diseases (e.g., Symons, Grimson, and Yuan 1983), selecting appropriate control cases from among a large group of potential controls in the case-control method (e.g., Lacy 1997; Sanchez and Higle 1992), and adjusting for biases caused by using standard statistical procedures on large data sets in which events of interest are extremely rare (e.g., King and Zeng 2001). 4. A reviewer noted that social scientific writing using Mill’s (1974) “method of difference” might be more aptly characterized as using Mill’s “indirect method of difference.” In the method of difference, each comparison case is matched on all factors and differs only in the causal factor and the outcome. This closely approximates the laboratory experiment. The indirect method of difference is similar to the direct method of difference in that all positive cases have the causal factor or factors. But the method differs in that no single negative case is matched exactly on all relevant factors with the positive cases. Rather, the negative cases collectively possess all the other relevant factors in the positive cases that might account for the positive outcome. (The negative cases still differ from the positive cases in only the hypothesized cause or causes.) This method is generally more appropriate for observational data, although Mill argued that neither method is appropriate for social science. See Mill (1974:388-97, 881-83). 5. Causal narrative involves comparing sequences of events across cases. For example, Abell’s (1987, 2001) work on comparative narratives showed how processes in different cases can be compared to derive a common narrative structure of a class of events. While the causal narrative method could be very useful in studying school shootings, we do not employ the method in our research because we studied only two cases. 6. When three-way interaction terms are placed in regression models, each of the individual variables in isolation and then in each possible combination are generally also included in the Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. 212 SOCIOLOGICAL METHODS & RESEARCH model. For example, if we think that the interaction term X × Y × Z should be in our model, it is also standard practice to include variables X, Y , Z, X × Y , X × Z, and Y × Z. When all of those variables and possible interactions are present, however, it is likely that our original variable of interest, X × Y × Z, will be highly collinear with the other variables (see also Ragin 1999). 7. More details can be found in Harding, Mehta, and Newman (2002); Fox, Roth, and Newman (2002); and Newman et al. (forthcoming). 8. Unfortunately, we know little about Andrew Golden’s life and cannot confidently evaluate the problems he was facing at the time of the shooting. 9. Our general model of five necessary conditions written in Ragin’s Boolean algebra is A × B × C × D × E. However, within each factor, there are multiple elements that might satisfy the condition. These can be indicated with lowercase letters so that that the model is (a1 + a2 + a3 + . . .) × (b1 + b2 + b3 + . . .) × (c1 + c2 + c3 + . . .) × (d1 + d2 + d3 + . . .) ×(e1 + e2 + e3 + . . .), where the multiplication sign indicates “logical and” and the plus sign indicates “logical or.” We thank an anonymous reviewer for this point. 10. Despite the labels Verlinden, Hersen, and Thomas (2000) put on their categories, most of the 37 risk factors are individual-level factors. For example, the category “school/peer” includes poor coping and social skills, feels rejected by peers, feels picked on, low school commitment/achievement, intolerance/prejudicial attitudes, socially isolated, and antisocial peer group, only the last two of which are actually properties of the school or peer group. Similarly, the category “social environmental” includes access to firearms, fascination with weapons and explosives, and preoccupation with violent media/music. 11. Of course, it is possible to measure properties of a social system quantitatively. Usually, this involves aggregating individual responses or characteristics (as in poverty rates for neighborhoods) or using an individual respondent’s assessment (as in the number of employees at a firm). Recent efforts have measured “social characteristics” of groups through direct observation. See, for example, Sampson and Raudenbush (1999) on measuring disorder in urban neighborhoods. 12. These aspects of adolescence were prominently identified by Coleman (1961) and Erikson (1968). 13. For a discussion of triangulation in contested events, see Roth and Mehta (2002 [this issue]). 14. For the sake of brevity, we only present information on Mitchell Johnson in this section. 15. For a theoretical justification of our definition of rampage school shooting, see Newman et al. (forthcoming). 16. The National Academy of Sciences volume that contains these two studies (National Research Council and Institute of Medicine 2002) also contains case studies of two school shootings in urban schools (Fullilove et al. 2002; Hagan, Hirschfield, and Shedd 2002). They do not meet our criteria for rampage school shootings because they were not planned in advance, and the victims were chosen because they had wronged the offender, not for their symbolic significance. 17. In Newman et al. (forthcoming), we plan to examine other cases of school shootings to see whether they conform to our model. 18. In a sense, the same problem can be said to occur when one is comparing countries that have had revolutions to ones that have not. But the researcher who is studying events or phenomena as they are unfolding faces different challenges than one whose subject is more clearly bounded. 19. It is not necessarily the case that variations over time, space, and social group can be accounted for by changes in the causes of individual events, however. See Lieberson (1997) Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution. Harding et al. / STUDYING RARE EVENTS 213 for a discussion of the difference between explaining a distribution and explaining individual events. 20. For example, an important question about school shootings is why they increased during the 1990s. One hypothesis is that cultural scripts involving the use of violence are more available now, perhaps because previous shootings provide a model to copy or because of an increase in violent video games. A second hypothesis suggests that schools’ ability to identify and aid troubled youth has declined over time, perhaps because of a gradual shift to larger schools or more emphasis on high-stakes testing and other “objective” measures of school performance. Another important question that we do not explore here is why school shootings are occurring in suburban and rural communities and among White boys. Again, the model suggests that one or more of the necessary factors is more common in these settings or among these populations. 21. We are not suggesting that cult influences were actually at work in the Pearl case. 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Vossekuil, Bryan, Marisa Reddy, and Robert Fein. 2000. “Safe School Initiative: An Interim Report on the Prevention of Targeted Violence in Schools.” Washington, DC: U.S. Secret Service National Threat Assessment Center, U.S. Department of Education, and National Institute of Justice. David J. Harding is a Ph.D. candidate in sociology and social policy at Harvard University and a fellow in the Harvard Multi-Disciplinary Program on Inequality and Social Policy. In addition to school violence, his interests include racial differences in incarceration, the geographic concentration of poverty, and urban policy as well as qualitative and quantitative methodology. Cybelle Fox is a Ph.D. candidate in sociology and social policy at Harvard University, a doctoral fellow in the Harvard Multi-Disciplinary Program on Inequality and Social Policy, and a recipient of a National Science Foundation Graduate Research Fellowship. Her other research interests focus on race, immigration, and the politics of redistribution. Jal D. Mehta is a Ph.D. candidate in sociology and social policy at Harvard University and a doctoral fellow in the Harvard Multi-Disciplinary Program on Inequality and Social Policy. A National Science Foundation graduate fellow, his previous work focused on the role of social-psychological mechanisms in perpetuating social stratification and sponsoring social mobility and on racial differences in achievement. His research interests include combining normative political theory on justice with empirical research on poverty and inequality. Downloaded from http://smr.sagepub.com at KENTUCKY UNIV on November 9, 2007 © 2002 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution.
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