tPP Preliminary Statistical Report #4 of 5

The following report was completed by statistics students utilizing a version of tPP dataset as of March 13, 2019. These analyses are focused on developing models for future use, and the interpretations and conclusions they contain reflect a dataset still in development, and only a superficial engagement with the wider literature on political violence. We continue to expand, improve and refine the data, and as such, these analyses should be seen as preliminary and subject to change. This views expressed in these reports belong solely to the authors, and do not necessarily reflect the findings of tPP team and are subject to further inquiry and revision.



Below you will find the non-technical analytical summary and selected visualizations for Team #3 (Change over time) of 5.

This report was authored by Daniel Cirkovic, Yi Jing, Samantha Thompson, & Xuemeng Wang. To download the complete report, including the statistical source code, click here.



0.1 Non-Technical Report

0.1.1 Introduction

The Prosecution Project (tPP) is a collection of data that specifically investigates patterns in political violence and terrorism occurring in the United States from 1990 to the present. Data is continuously being added, so updates to the following analysis may need to occur when more recent data becomes available. Our analysis focuses on characteristics of the terrorists, and their acts, including demographics, religion, prosecution types, ideology, tactic, targeting, and group affiliation. Our goal is to show visually and statistically analyze how these variables change over time.[/su_expand]

0.1.2 Methodology

In order to more clearly detect variable changes, we split the data into time periods separated by major terrorist events. We decided to take this approach to not just evenly split the entire time period (events are not evenly spaced, but amount of data included in each period is fairly similar), but to also see if these major events induced any specific patterns within the variables. We try to depict the reasoning behind these changes, but all of this is subjective – correlation is not necessary causation. The only conclusions we can draw for certain, come from the statistical tests performed, relating to the overall change of each variables’ categories over time.

Some of the variables included many categories; and in order to fit them all into one graph, with enough data available within each category per period, we only took the categories with the highest frequencies – while combining some categories together. This was done on a case by case basis, and more information on how this was completed is in the Appendix. NA’s for that variable were deleted only for that variable, making sure to leave the data in the complete data set in case there were values (not NA) for the other variables.

In order to find differences in each variable over time, we summed each category within the variable and time period, and divided it over the total amount per time period. This gives us the frequency of each category per period, so that we can test if it has differences over time.

The tests we used for this are the Pearson Chi-Square Test, Fisher Exact Test, and Cramer’s V Statistics. Because of the minimal amount of data in some categories per time period, the Fisher Exact Test is included because it has more relaxed rules on data size, contrary to the Pearson Chi-Square Test which is testing similar things. Cramer’s V is a little bit different in that it measures how important the period is in determining each categories count.

These tests do not tell us if the variables’ categories are increasing or decreasing over time, so we created bar charts where all bars are equal to 100%, and within each period the categories are split into percentages.

We additionally wanted to see if any of the variables impacted the counts of another variable over time. To do this, we selected racial/ethnic group to compare with time against (1) prison sentence length, (2) plea and (3) tactic. The Cochran-Mantel Haenszel test was used in order to test the differences over time with now two variables and time, whereas we only had one with time in all previous tests.

0.1.3 Conclusion

We saw that characteristics of terrorists and their acts of terrorism have significant changes over the time period the data was collected in as of now. By using both visualizations and statistical tests, these changes can be closer investigated by importance and size, as each variable has its differences. Overall, the key variables to assign the most importance to based on the statistical tests are Othered Status, Citizenship, Tactic, and Group Affiliation. This is why the visualizations included in this report are chosen, and explored/researched reasons for these changes along with the directions of their differences.

0.2 Technical Report

0.2.1 Introduction

Terrorism in the United States peaked in the late 1960’s and early 1970’s, followed by a precipitous decline (Ross et al, 1989). Despite this decline, terrorism seems ever more present. Large scale media coverage and the development of social media have often been cited as contributors to discerned prevalence of terrorism (Weimann et al, 2014). Further, media coverage of events such as 9/11 has framed many attacks as “Muslims/Arabs/Islam working together in organized terrorist cells against a Christian America”. On the other hand, domestic terrorists often receive the label of “troubled individuals” (Powell, 2011). Thus, there is strong evidence of media coverage affecting the perception of terrorist attacks in the United States. Given the Prosecution Project (tPP) dataset, trends in terrorist activity are analyzed by grouping events into periods delineated by large scale media events and detecting any changes between said periods. This organization of events may allow for the detection of changes in terrorism, perhaps due to perpetrators attempting to imitate previous attacks covered in the media.

0.2.2 Methodology

In order to recognize the patterns in demographics, prosecution types, ideology, tactic, targeting, sentence length, informant, and group affiliation over time, each event was organized into different time periods separated by major terrorist attacks in the United States. The events of interest are listed below:

The purpose of this delineation is to determine whether these events, largely covered in the media, trigger “copycat” terrorist attacks (known as contagion) or somehow impact a variable’s distribution in time periods near said events (Nacos, 2010).

Once each event was grouped, the frequencies of each variable category were computed within each time period and compared using 2-way contingency tables. That is, each variable had its own contingency table with the rows representing the categories given in the variable of interest, and the columns representing the time periods described earlier. Often, multiple categories were either condensed or removed due to sparseness of information (see Appendix for the exact breakdown of tables). The difference in distribution of the categories across time will be tested using both a Pearson Chi-Square Test and Fisher Exact Test.

The Pearson Chi-Square Contingency Table Test tests homogeneity of the time periods. More specifically, it decides whether or not there is a difference between the proportions of the categories of a certain variable across the time periods. For example, if the gender variable were to be considered, it would test whether the proportion of events committed by males and females has changed over time. However, it does not indicate the direction of these changes (Lachin, 2011).

Most of the variables, however, violate the expected count assumption of the Pearson Test. The test assumes that the expected counts in each of the cells are greater than five, but much of the tables contains zero values in multiple categories. Despite this violation, the Pearson Chi-Square Test is quite robust with these small expected cell frequencies (Camili, 163). To ensure this infraction does not impact results, an additional Fisher Exact Test is performed.

Fisher’s Exact Test again tests a difference between time periods in each of the variable category proportions. Specifically, it counts the number of possible tables that could be constructed with the given marginal totals. Then, it computes the proportion of those tables that are more extreme than the observed table, giving a p-value (Raymond et al, 1995). Since this could amount to a large number of tables, a bootstrap simulation with 2000 replicates is considered. This test relaxes the assumptions given by the Pearson Chi-Square Test.

Trends will be visually analyzed using proportional, stacked bar charts. Along with the Pearson Chi-Square tests, Cramer’s V statistics were computed. Cramer’s V is a measure of association between two categorical values ranging from 0 to 1. The higher Cramer’s V, the stronger the relationship between period and the given variable is (Acock et al, 1979).

Finally, the interaction between racial/ethnic group, prison sentence length, and time is considered. Perhaps, over time, certain races will have differing sentence lengths, whether that be a result of discrimination, ethnic tendencies, or other factors. A three dimensional table will be considered with a Cochran-Mantel Haenszel Test applied. This test is an extension of the Chi-Square Test, and, in general, tests for differences in the joint and marginal distributions of three variables (Lachin, 2011).

In each table, any unknown observations were not considered, since they add no information to the story, other that adding sample size and changing inference in a direction that may not necessarily be honest.

0.2.3 Results

From the collection of two-way tables, the distribution of most variables have changed over time. Only the distribution of death sentencing and gender seemed homogenous over time, as both the Fisher and Chi-Square tests failed to detect a difference in their distributions. The uniformity of gender and death sentencing throughout the periods is not surprising, as the vast majority of events in the dataset were perpetrated by men and did not result in a death sentencing of the perpetrator. More interesting insights can be gathered visually.

The three-way tables invites some interesting insights. When comparing ethnicity, sentence length (categorized by every 100 months), and time period, there was no significant difference found between the distributions of the categories within each of the groups. The same results was reached when comparing ethnicity, plea, and time period. However, the Cochran-Mantel-Haenszel Test found a significant difference between the distribution of ethnicity and tactic over the time periods.

The following proportional, stacked bar charts show us how, and the direction of change, on the variables we felt were key to this analysis.

We see in Figure 1 that the amount of terrorism acts by Non-U.S. citizens has consistently decreased over time, with it reaching very minimal counts by 2015 to present day. In 2011, the Department of Homeland Security defined a new term of “specially designated countries” to be countries “that have shown a tendency to promote, produce, or protect terrorist organizations or their members.” In 2003, the Department of Homeland Security provided US border crossings with a list of 52 countries that fell under this term – in order to increase border security against possible terrorists. The list was continually updated and changed until present day. From 2007 to 2017, the US Border Patrol apprehended 45,006 immigrants from any of these countries to have ever been on the list. There have been zero attacks committed by illegal border crossings from any of the listed special designated countries. However, foreigners who have entered legally from these countries are responsible for 99.5% of all murders and 94.7% of all injuries committed by terrorists in the US from 1975 through the end of 2017 (Bier). We see that 9/11 may have spiked this trend that a successful strategy for foreign terrorism is to first enter legally, or to have a US citizen commit the act. After 9/11, the amount of non-US citizens to commit acts of terrorism is at its peak and then its decline. All terrorists involved in 9/11 were non-US citizens. This decrease in non-US citizens being able to commit acts of terrorism is likely the cause of increased security. However, terrorism is evolving so that the US may no longer be looking for non-US citizens to be committing these acts, as our graph shows.

Figure 2 is very interesting in how group affiliation overall changes over time. Not looking into specific terrorist events, but at each group over time, we see that Al Qaeda has decreased consistently over time, but the Islamic State has increased – by large amounts especially in more recent years. There are many factors that play into this variable’s directional changes, and we will try to summarize what we think is the cause the best that we can. Bin Laden, the previous leader of Al Qaeda, was killed in 2011. Period 6 is after the year 2009, and the period that we first start to see the decrease of Al Qaeda. This may be due to their leader dying, but some additional cause of conflict between groups could also play a role. Let’s start at the beginning. Period 4 is after 9/11, an event Al Qaeda wished to take credit for, and therefore Al Qaeda is strong and on the rise here. In period 5, which is after 2006 when Al Shabab was formed, we see a heavier Al Shabab presence seen. Al Shabab was known to be tied to Al Qaeda, and they declared official allegiance to them in 2012. We see both Al Qaeda and Al Shabab decrease after period 8 (2012), which is what we would expect as Al Qaeda was weakened, so was Al Shabab because of their affiliation. We now start to see the rise of ISIS, who have taken advantage of the weakened Al Qaeda and Al Shabab, in order to make their presence more known. Although these groups have similar views, they are not supportive of one another, and have different tactics on how they wish to be heard. We can see how the changes in tactic over time graph below reflects these different groups, by which tactic they decided to use.

Going back on what we discuss in the previous paragraph, we can see in Figure 3 that when Al Qaeda was in greater power, the categories of tactic that are most prevalent are crimes like Arson, Chemical or biological weapon deployment, and Explosives. These are all tactics that support Al Qaeda’s goal to plot terrorism spectaculars to electrify the Muslim world. Whereas, ISIS viewpoint is to aim to control territory and expand their ideology. This can be seen as why once ISIS are in more power, the popular tactics are Providing material/financial support to terrorist organizations, Firearms, and Armed intimidation/standoff – all ways to overtake, build their organization, and control.

Additionally, from Figure 3, we see rises in tactic that could be the result of the major acts of terrorism we split the periods by. Explosives seem to increase from period 1 to period 2, which is after the Oklahoma City Bombing. Also, after the Aurora Theater Shooting, there seems to be a drastic decrease in civilian firearms, while there is an increase in armed intimidation/standoff. On another note, we see perjury/obstruction of justice slowly appear and begin to increase from past to present. This could be the cause of laws changing over time, so as stricter laws are implemented, more people may be convicted.

Other notable changes where graphics are not included are listed here. The terrorists’ religion shows changes over time like after the Charleston Church Shooting, no Christians committed acts of terrorism. This could be due to the shooting happening in a Christian church, making other Christians less likely to commit any crimes or act out. The Veteran Status changing over time plot shows that after 9/11, the amount of veterans that committed acts of terrorism decreased drastically – then fluctuating but never again reaching the amount of terrorism acts before 9/11. Another change we see around 9/11 occurs in the ideological affiliation. We see that after 9/11 there is a massive increase in No Affiliation ideologies. This could be because groups were trying to draw attention away from themselves after all the security measures put into place after 9/11. We also see a huge increase in Rightist ideologies after the Charleston Church Shooting. This is interesting to note because the man that committed this act of terrorism was a 21-year-old white supremacist, who most likely believed in a rightist ideology. After the death of Trayvon Martin, State jurisdiction for acts of terrorism increased largely, possibly due to the pressure on local police following this event. The increase in verdict of charged but not tried over time can be due to possible ongoing cases as we get closer to present day. After the first major act of terrorism, we see more informants coming forward to prevent terrorist events.

The three-way tables invites some interesting insights. When comparing ethnicity, sentence length (categorized by every 100 months), and time period, there was no significant difference found between the distributions of the categories within each of the groups. The same results were reached when comparing ethnicity, plea, and time period. However, the Cochran-Mantel-Haenszel Test found a significant difference between the distribution of ethnicity and tactic over the time periods.

To further inspect these differences, a stacked bar plot was developed. Ethnicity was limited to only the white and middle eastern groups, as they provided interesting insight. Over time, it seems that of crimes in the data set committed by people of middle eastern ethnicity, the proportion of those crimes that included providing financial support to terrorist organizations has increased drastically over each time period. This occurrence spawned right before the 9/11 attacks. Crimes perpetrated by white individuals in Period 2, post Oklahoma City Bombing, started to consist mainly of explosives, perhaps furthering the idea of similar “copycat” crimes being committed after large media coverage of terrorist attacks. Similarly, after the Aurora shooting, white criminals seemed to heavily gravitate towards armed intimidation to commit their crimes as well. Other ethnicity plots can be seen in the Appendix.

0.2.4 Conclusion

The analysis provides some evidence that “copycat” terrorism or contagion impact the distribution of multiple characteristics of terrorist attacks over time. These changes are especially prevalent in the distribution of tactics across ethnicity and othered status after key events such as the Oklahoma City Bombing, 9/11, and the Aurora Shooting. Further, Ideological Affiliation trended towards Rightist Leanings after the Charleston Church Shooting, while Group Affiliation has seen a recent increase in attacks perpetrated by the Islamic State, despite the decrease in attacks perpetrated by Al-Qaeda. The claim that characteristics of these terrorist attacks are associated with the selected time periods are both bolstered by the results given by Chi-Square Tests and Cramer’s V quantitates. Of course, the Chi-Square Tests only say that period and terrorist attacks are associated and do not imply mechanism. However, the bar charts provide the context to our hypothesis. The analysis is limited by sparseness of events in some categories in which measures were taken to combat.

0.3 References

Acock, Alan C., and Gordon R. Stavig. “A measure of association for nonparametric statistics.” Social Forces 57, no. 4 (1979): 1381-1386.

Bier, David, and Alex Nowrasteh. “45,000 ‘Special Interest Aliens’ Caught Since 2007, But No U.S. Terrorist Attacks from Illegal Border Crossers.” Cato Institute, 17 Dec. 2018, www.cato.org/blog/45000-special-interest-aliens-caught-2007-no-us-terrorist-attacks-illegal- border-crossers.

Camilli, Gregory, and Kenneth D. Hopkins. “Applicability of chi-square to 2× 2 contingency tables with small expected cell frequencies.” Psychological Bulletin 85, no. 1 (1978): 163.

Garrett Grolemund, Hadley Wickham (2011). Dates and Times Made Easy with lubridate. Journal of Statistical Software, 40(3), 1-25. URL http://www.jstatsoft.org/v40/i03/.

H. Wickham. ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York, 2016.

Hadley Wickham (2017). tidyverse: Easily Install and Load the ‘Tidyverse’. R package version 1.2.1. https://CRAN.R-project.org/package=tidyverse

Jeffrey B. Arnold (2019). ggthemes: Extra Themes, Scales and Geoms for ‘ggplot2’. R package version 4.1.1. https://CRAN.R-project.org/package=ggthemes

Lachin, John M. Biostatistical Methods: The Assessment of Relative Risks. 3rd ed. Hoboken: Wiley, 2011.

Nacos, Brigitte L. “Revisiting the contagion hypothesis: Terrorism, news coverage, and copycat attacks.” Perspectives on Terrorism 3, no. 3 (2010).

Powell, Kimberly A. “Framing Islam: An analysis of US media coverage of terrorism since 9/11.” Communication Studies 62, no. 1 (2011): 90-112.

Raymond, Michel, and François Rousset. “An exact test for population differentiation.” Evolution 49, no. 6 (1995): 1280-1283.

Ross, Jeffrey Ian, and Ted Robert Gurr. “Why terrorism subsides: A comparative study of Canada and the United States.” Comparative Politics 21, no. 4 (1989): 405-426.

Weimann, Gabriel. New terrorism and new media. Vol. 2. Washington, DC: Commons Lab of the Woodrow Wilson International Center for Scholars, 2014.

See full report for complete contingency tables, stacked bar plots, and r code for age, gender, othered status, ethnicity, religion, veteran status, citizenship, jurisdiction, plea, verdict, length of sentence, death sentence, ideology, tactic, physical target, ideological target, informant, group affiliation, FTO affiliation.

Leave a Reply

Your email address will not be published. Required fields are marked *