4.2: How do magnet and charter schools represent new visions of public education?
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By: jyaeg001
Learning Objectives
- Define the terms "magnet school" and "charter school."
- Explain how the school populations of magnet and charter schools are chosen.
- List the pros and cons of magnet and charter schools.
- Summarize what the research about these two forms of education reveals.
- Explain the concerns that teachers and parents should have about magnet and charter schools.
Introduction
In the early 1980s, the National Commission on Excellence in Education issued a report card for the public schools of the United States that showed a sharp decline in students’ achievement scores (Noll, 2005). As a response to the news that the United States was no longer a leading country in preparing its youth for the future, educational reforms were initiated in many public school districts. Magnet schools and charter schools were two approaches that stirred excitement among parents and many educators. Exactly what are these alternative forms of education termed magnet and charter schools? Who is allowed to attend magnet and charter schools? What do proponents and critics say about magnet and charter schools? According to the research, how to magnet and charter schools compare with traditional public schools and what are the implications of the research findings for parents and teachers?
What is a magnet school?
A magnet school is designed to do just what its name suggests: attract students. Within any student population, there are children with a variety of interests and career aspirations. Magnet schools offer specialized curriculums that appeal to particular student groups, such as young people who want to study in depth such areas as foreign languages, drama, computer technology, or advanced sciences. These schools are under the umbrella of a larger school district and may even be housed in an existing school that also offers a traditional curriculum (Villaverde, 2003). Magnet schools receive at least part of their funding from the sponsoring public school district. In addition, because magnet schools can assist in attracting racially mixed student populations from different socio-economic backgrounds, federal government grants related to desegregation are available to help support the costs of some schools (Villaverde, 2003).
Who is allowed to attend a magnet school?
The student population of magnet schools can be chosen in more than one way. The enrollment process often begins with the parents of an interested student filling out an application. Some districts choose students solely on the basis of a lottery that includes applicants from different income levels, neighborhoods, ethnic backgrounds, gender, and races. Other districts also have application requirements related to minimum academic achievement levels. Parents list their first, second, and third choice for magnet school attendance on their applications. Waiting lists are compiled for those students who do not receive immediate placement. With these restrictions, free choice is more accurately termed controlled choice (Archbald, 2004).
What is a charter school?
A charter school is a “publicly funded school that is typically governed by a group or organization under a contract or charter with the state…In return for funding and autonomy, the charter school must meet accountability standards” (National Center for Education Statistics, 2007, par.2). The charters list the school’s goals, details about the programs offered, specifics about student body selection, and the criteria that will be used for assessment (Buckley and Schneider, 2007). The charters have time constraints that typically range from three to five years. At the end of that time period, the charter-granting overseers, such as state officials, make a continuance decision based on how the terms of the charter have been met. A charter school may be founded by teachers or administrators within a school district, by a group of parents, or even by a private or community organization. Federal grants are available to assist with the initial costs, and funds also come from the school districts whose students are being served by the charter school (Peterson, 2003). Like magnet schools, most charter schools are focused on providing more effective, innovative programs than parents are offered in traditional public schools (Buckley and Schneider, 2007).
Who is allowed to attend a charter school?
Since charter schools receive state and federal funding, they need to meet the same diversity requirements as public schools and “reflect the social/ethnic makeup of their district” (Noll, 2005, p. 226). There is an application process that may require meeting certain other criteria, such as passing an audition if the charter school has a curriculum that emphasizes theatrical arts. Many schools have no restrictions and often choose the student population on the basis of lottery outcomes. Using the lottery is a way to fairly decide who gains admittance to these schools with much smaller enrollments than most public schools (Noll, 2005).
What do proponents say about magnet and charter schools?
1. Proponents of magnet and charter schools believe that these schools provide much-desired options for parents who are dissatisfied with the job that public schools are doing. Magnet and charter schools are especially appealing to those parents whose children are from lower socio-economic backgrounds and have been placed in schools with below average achievement statistics (Peterson 2003).
2. Magnet and charter schools encourage competition and make public schools more aware of and more involved in improving their curriculums, teachers’ performance, and administration procedures (Villaverde, 2003).
3. When compared with most traditional public schools, both magnet and charter schools offer better student-teacher ratios and smaller, more personal school environments that help prevent student dropouts and capitalize on students’ interests (Noll 2005).
Note
The director of the organization called Friends of Choice in Urban Schools stated about alternative schools that they “provide choices for parents, opportunities for teachers, and better schooling right now to some kids, rather than making them wait for yet another system-wide overhaul” (Buckley and Schneider, 2007, p. 285).
What do critics say about magnet and charter schools?
1. These special schools can drain school districts’ budgets and result in districts having less money to meet the needs of a much larger percentage of students (Peterson, 2003).
2. Magnet and charter schools have failed to attract diverse student populations that match the composition of the communities’ school districts, and the existing diversity requirements are not being enforced (Archbald, 2004).
3. The average achievement scores of students in magnet and charter schools are not higher than those of traditional public schools (Buckley and Schneider, 2007).
What does the research reveal about magnet and charter schools?
1. Use of public funds and effects on school districts : A Western Michigan University study (1998) concluded that "charter schools may not be living up to their promise of educational innovation and more effective use of public money” (Noll, 2005, p. 227). An extensive UCLA study of California charter schools (1998) in ten school districts found “no evidence that charter schools can do more with less” (Noll, 2005. p. 226). Marc Bernstein, a New York school district superintendent, explains that when money is taken from public school districts for the operation of charter and magnet schools, “there are but two choices: raise taxes or reduce programming. Either choice has serious consequences for public education” (Noll, 2005, p. 228).
2. Diversity of student populations in magnet and charter schools : A 2003 study of magnet schools across the nation was reported in Sociology of Education . The researchers examined the effect of magnet school choice on the socio-economic stratification in school districts with magnet school as compared with the socio-economic stratification in school districts without magnet schools. The study did not find a positive growth in the socio-economic redistribution of students as a result of offering magnet school choices (Archbald, 2004). Similar research findings of charter schools were reported earlier in a Minneapolis study (1997) and a Texas study (2002). The reason for this failure of specialty schools to redistribute students more equitably along socio-economic lines was believed to be due to parents’ reluctance to have their children bussed long distances and due to parents’ reluctance to “face the prospect of their child being in a small minority…parents were likely to sort themselves along racial/ethnic lines” (Buckley and Schneider, 2007, p. 122). A 2004 study of magnet schools reported in the Journal of Education for Students Placed at Risk found that magnet schools did not significantly affect racial and class segregation because many magnet schools have entrance requirements that can only be met by students from higher income areas (Neild, 2004).
3. Achievement : Magnet and charter schools typically attract higher achieving students, so it could be predicted that achievement scores of students attending these schools would be higher than students in traditional public schools. However, a November 2004 report by the National Assessment Governing Board concluded from its testing of elementary students in public school and elementary students in charter schools that the average achievement scores of those students enrolled in charter schools were lower than those students in public schools (National Education Association, 2008). The UCLA study of seventeen California charter schools (1998), mentioned above, also did not find an increase in academic scores (Noll, 2005). Finally, in 2006, the Public Policy Institute of California studied the magnet and charter schools in the city of San Diego and concluded that “on the whole, there was no systematic improvement or deterioration in test scores from participating in a choice program” (Betts and Rice, 2006, p. 184).
Conclusion: What are the considerations for parents and teachers in relation to magnet and charter schools?
There are success stories among the many magnet and charter schools started across the nation, but the overall research findings concerning average achievement levels are not favorable to these school reforms. Parents may want to consider using their influence to encourage school districts to offer innovative educational programs for all students, rather than creating or encouraging separate schools. Teachers may need to voice their concerns about the financial resources that are siphoned from the school districts for these unproven schools that serve a small proportion of the community’s children. This outflow of tax dollars affects the curriculums that public schools can afford. Both parents and teachers should be concerned about the fact that specialty schools can further segregate children along racial, socio-economic, and ethnic lines since school choice can often mean choosing to attend a school with students of the same backgrounds. Rather than creating the diversity that was intended by these school reforms, school choice could actually foster the growth of the very prejudices that a free public education for all was meant to eliminate.
References
Archbald, D. (2004). School choice: magnet schools and the liberation model. Sociology of Education , 77 (4), 283-310.
Betts, J. and Rice, L. (2006). Does School Choice work: Effects on Student Integration and Achievement . San Diego, CA: Public Policy Institute of California.
Buckley, J. and Schneider, M. (2007). Charter Schools: Hope or Hype? Princeton, NJ: Princeton University.
National Center for Education Statistics. (2007). Contexts of elementary and secondary education: school choice. Retrieved September 14, 2008 from nces.ed.gov/programs/coe/2007/section4/indicator32.
National Education Association. (2008). Charter schools. Retrieved September 15, 2008 from www.nea.org/charter/index.html
Neild, R. (2004). The effects of magnet schools on neighborhood high schools: an examination of achievement among entering freshmen. Journal of Education for Students Placed at Risk, 9 (1), 1-21.
Noll, J. (2005). Taking Sides: Educational Issues. Dubuque, IA: McGraw-Hill/Dushkin.
Peterson, P. (2003). The Future of School Choice . Stanford, CA: Hoover Institution.
Villaverde, L. (2003). Contemporary Education Issues: Secondary Schools. Santa Barbara, CA: ABC-CLIO.


5: College Level Critical Thinking and Reading Last updated Save as PDF Page ID 128597 Dave Dillon Grossmont College 5.1: Words of Wisdom- Thinking Critically and Creatively 5.2: Comprehending College Level Reading by Using the Reading Apprenticeship Approach 5.3: Getting the Most Out of Your Textbooks 5.4: Reading Textbooks 5.5: Context Clues and Close Reading for Literature 5.6: Reading and Notetaking 5.6.1: Prelude to Reading and Notetaking 5.6.2: The Nature and Types of Reading 5.6.3: Effective Reading Strategies 5.6.4: Taking Notes 5.6.5: Summary 5.6.6: Career Connection 5.6.7: Rethinking 5.6.8: Where do you go from here? 5.7: Listening and Note-Taking 5.7.1: Preparation for Note-Taking 5.7.2: Taking Notes in Class


5.11: Why It Matters- Ethics and Social Responsibility
Why learn about ethics and social responsibility?
Generally speaking, students believe that there are two primary reasons to act ethically:
- Acting ethically is the right thing to do from a moral perspective;
- If you act unethically, then you might get caught and be punished.
Neither of these is a bad reason to apply principles of ethics and social responsibility, but it is worth considering another reason, as well. In most cases strong ethical behavior leads to strong business results. Behaving ethically is actually good business. Let’s look at two different auto companies whose track records on ethical behavior have had very different outcomes.
Tesla and Social Responsibility
Tesla, Inc. was founded in 2003 by a group of engineers who wanted to prove that electric cars could be better than gasoline-powered cars. They hoped to build cars that wouldn’t require the tradeoffs in power and comfort of electric cars in the past. The founders pledged that each new generation of cars would be increasingly affordable, helping the company work toward its mission: “to accelerate the world’s transition to sustainable energy.” [1]
In order to design and build luxury electric cars, Tesla invented a number of new technologies that it patented in order to protect its competitive advantage. In June 2014 the company announced that it was releasing access to all of its patents, making its technological advances open to competitors and inventors. In the announcement, company CEO Elon Musk said, “Tesla Motors was created to accelerate the advent of sustainable transport. If we clear a path to the creation of compelling electric vehicles, but then lay intellectual-property land mines behind us to inhibit others, we are acting in a manner contrary to that goal. Tesla will not initiate patent lawsuits against anyone who, in good faith, wants to use our technology.” [2]
Tesla has a mission with an emphasis on social responsibility; it strives to develop products that have both a societal and economic benefit. Industry analysts and consumers alike see this as a distinct advantage in the marketplace. Investment analyst Seeking Alpha explains:
Companies like Toyota Motor and Honda are already pushing for gas-less cars and more and more efficiency from their cars. Tesla is not single-handedly pushing this, but it is part of the overall push to improve one of the most important aspects of our country—how we envision the car. Yet, the company extends beyond this—challenging how we vision luxury, how we understand how to build a car, and what the future electric grid could look like. [3]
Volkswagen and Ethical Behavior
The car company Volkswagen (which is part of the larger Volkswagen Group) does not have a formal mission statement, but its goal is “to offer attractive, safe, and environmentally sound vehicles that can compete in an increasingly tough market and set world standards in their respective class.” [4]
In September 2015, the Environmental Protection Agency announced that Volkswagen had installed special software in its cars to manipulate emissions levels (making it appear that the cars are less polluting than they are). A week later Volkswagen disclosed that 11 million diesel vehicles contained the devices, and CEO Martin Winterkorn resigned. The price of Volkswagen stock plunged—losing 30 percent of its value overnight—and the company scrambled to understand what had happened and control the damage to its reputation.
In the months following the discovery of the deceptive devices, investigators identified a team of Volkswagen employees who had hatched the plan and implemented it over a number of years. An internal evaluation identified a “culture of tolerance” for rule breaking at the company. It also came to light that Volkswagen’s emphasis on “results at any cost” had contributed to the breach in ethical standards. Industry experts believe that the company’s violation of consumers’ trust will be will be exceedingly difficult to repair and that it may take years to rebuild the Volkswagen brand.
- “About Tesla,” Tesla, accessed September 23, 2019, www.tesla.com/about↵
- Musk, Elon. “All Our Patent Are Belong To You,” Tesla, June 12, 2014, www.tesla.com/blog/all-our-patent-are-belong-you. ↵
- “Tesla: Social Responsibility Scorecard Shows Strengths And Weaknesses,” Seeking Alpha, Jan 6, 2015, seekingalpha.com/article/2801365-tesla-social-responsibility-scorecard-shows-strengths-and-weaknesses. ↵
- Jurevicius, Ovidijus. “Mission statement of Volkswagen,” Strategic Management Insight. September 14, 2013, https://www.strategicmanagementinsight.com/mission-statements/volkswagen-mission-statement.html . ↵
Contributors and Attributions
- Why It Matters: Ethics and Social Responsibility. Provided by : Lumen Learning. License : CC BY: Attribution
- Tesla Model S. Authored by : Al Abut. Located at : https://www.flickr.com/photos/alabut/4276454889/ . License : CC BY-SA: Attribution-ShareAlike
- VW Jetta TDI. Authored by : RightBrainPhotography. Located at : https://www.flickr.com/photos/rightbrainphotography/3526674386/ . License : CC BY-NC-ND: Attribution-NonCommercial-NoDerivatives


17.1: THE STRUCTURE OF THE JUVENILE JUSTICE SYSTEM
CHAPTER 17 - JUVENILLE JUSTICE
THE STRUCTURE OF THE JUVENILE JUSTICE SYSTEM [163]
The juvenile justice system is used to handle cases in which minors are convicted of criminal offences, using early intervention in delinquency cases to discourage future adult criminal behavior. The juvenile justice process involves nine major decision points: (1) arrest, (2) referral to court, (3) diversion, (4) secure detention, (5) judicial waiver to adult criminal court, (6) case petitioning, (7) delinquency finding/adjudication, (8) probation, and (9) residential placement, including confinement in a secure correctional facility (see Juvenile Justice Process flow chart).
The majority of cases are first referred to the juvenile justice system through contact with police. Probation officers, school officials, or parents usually refer to the remaining cases. The most common offenses referred to court are property offenses (roughly 92%), followed by person offenses (89.5%), drugs (88.2%), and general delinquency charges (81.6%). Other referrals come from schools, family, or social workers or probation officers.
At the intake stage, probation officers or attorneys determine whether or not the case needs the attention of the juvenile court or if it can be handled informally, such as diversion to probation or a drug treatment program. If the case progresses to court, the authorities need to determine if the youth can be released to a parent/guardian or if the youth needs to be held in a secure detention center. When determining this, the court needs to assess the risk the youth poses to society and if the youth poses a flight risk. In some cases, the parent cannot be located or, if located, refuses to take custody of the youth. In these cases, the juvenile is remanded to custody. The decision to detain or release the juvenile will be made by the judge at a detention hearing.
If the case is handled in court, the county attorney needs to file a petition. When the youth has a formal hearing, it is called an adjudication rather than a trial in adult court. The adjudication of youth as delinquent can result in either dismissal of the charges or confinement at a secure institution. In most juvenile cases, the least restrictive option is usually sought, so the youth is usually put on probation or some sort of community treatment. Formal processing is less common than informal processing involving diversion or community-based programming.
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Think About It… Working with Youth When I graduated from college with a BA in psychology, I applied for a job working with the Division of Youth Corrections in Denver, CO. I worked in a Residential Treatment Facility (RTC), which used behavior modification techniques, assigned caseworkers to each youth and their families, and attempted to help the kids learn problem-solving skills and accountability. Youth were confined for a variety of reasons, from committing gang affiliated drive-by shootings, to youth who were designated dependent youth through social services and had nowhere else to go. We had high-risk kids, low-risk kids, conduct disorder and mental health kids all together on the same unit. Having the mix of all these different kids is not a great formula; the low-risk kids learn negative behavior from the high-risk kids, and the conduct disorder kids victimize the mental health kids. In an ideal institution, these different populations would all be on separate units. Working with youth is hard. They push boundaries, are angry, try to manipulate those around them, and reject authority. However, working with youth is exceptionally rewarding. They are kids. They come from abusive and neglectful homes and are yearning for approval and love. For example, one boy in our facility was named Josh. He was a super angry and violent sixteen-year-old who was sentenced for committing aggravated assault. Through working with counselors and caseworkers, we discovered his anger was hiding immense sadness. He lashed out at those around him when he was sad because he had no way to show his feeling other than through aggression. Many months of working with him, encouraging him to journal, express his feelings, talk with others, use other tools to help him with his sadness led to amazing results. He left our facility after more than a year, graduated from high school and even went to college! Getting the individualized attention helped Josh change. He became a success story of the juvenile justice system. Working with youth takes patience, consistency, and compassion. It is one of the most difficult jobs there is, but it is possible to be a very positive influence in the lives of kids who need it the most. If you are interested in working with youth, plan on committing to at least a year. Incarcerated kids are used to having people give up on them and disappoint them, so you do not want to add to their negative experiences. Show up, follow through, and be optimistic about a better future for justice-involved youth. |
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Pin It! In re Gault (1967) [165] Gerald “Jerry” Gault, a 15-year-old Arizona boy, was taken into custody for making obscene calls to a neighbor’s house. After the neighbor, Mrs. Cook filed charges, Gault and his friend were taken to the Juvenile Detention Home. At the time he was taken into custody, his parents were at work and the arresting officers made no effort to contact them nor did they leave a note about the arrest or where they were taking their son. They finally learned of his whereabouts from the family of the friend who was arrested with him. When the habeas corpus hearing was held two months later, Mrs. Cook was not present, no one was sworn in prior to testifying, and no notes were taken. He was released and scheduled to reappear a few months later for an adjudication hearing. In the following hearing, again, Mrs. Cook was not present and again, no official transcripts of the proceeding were taken. The official charge was “making lewd phone calls.” The maximum penalty for an adult charge with this was a $50 fine or not more than two months in jail. Gault was found guilty and sentenced to 6 years in juvenile detention. Gault’s parents filed a writ of habeas corpus which was eventually heard by the Supreme Court. The Supreme Court ruled that juveniles are entitled to due process rights when the court proceedings may result in confinement to a secure facility. The specific due process rights highlighted in this case include (1) fair notice of charges; (2) right to counsel; (3) right to confront and cross-examine witnesses; and (4) privilege against self-incrimination. The Court held that the Due Process Clause of the Fourteenth Amendment applies to juvenile defendants as well as adult defendants. “Juvenile court history has again demonstrated that unbridled discretion, however benevolently motivated, is frequently a poor substitute for principle and procedure.” |
PREVENTING DELINQUENCY [166]
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Learning Objective |
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Learning Objective: Key Points |
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Learning Objective: Key Terms |
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JUVENILE DELINQUENCY
Juvenile delinquency is participation in illegal behavior by minors. Most legal systems prescribe specific procedures for dealing with juveniles, such as juvenile detention centers and courts. A juvenile delinquent is a person who is typically under the age of 18 and commits an act that would have otherwise been charged as a crime if the minor was an adult. Depending on the type and severity of the offense committed, it is possible for persons under 18 to be charged and tried as adults.
Juvenile delinquency can be separated into three categories:
- Delinquency: crimes committed by minors that are dealt with by the juvenile courts and justice system;
- Criminal behavior: crimes dealt with by the criminal justice system;
- Status offenses: offenses which are only classified as such because one is a minor, such as truancy, also dealt with by the juvenile courts.
Young men disproportionately commit juvenile delinquency. Feminist theorists and others have examined why this is the case. One suggestion is that ideas of masculinity may make young men more likely to offend. Being tough, powerful, aggressive, daring, and competitive becomes a way for young men to assert and express their masculinity. Alternatively, young men may actually be naturally more aggressive, daring, and prone to risk-taking. According to a study led by Florida State University criminologist Kevin M. Beaver, adolescent males who possess a certain type of variation in a specific gene are more likely to flock to delinquent peers. The study, which appeared in the September 2008 issue of the Journal of Genetic Psychology, is the first to establish a statistically significant association between an affinity for antisocial peer groups and a particular variation (called the 10-repeat allele) of the dopamine transporter gene (DAT1).
There is also a significant skew in the racial statistics for juvenile offenders. When considering these statistics, which state that Black and Latino teens are more likely to commit juvenile offenses, it is important to keep the following in mind: poverty is a large predictor of low parental monitoring, harsh parenting, and association with deviant peer groups, all of which are in turn associated with juvenile offending. The majority of adolescents who live in poverty are racial minorities.
Family factors that may have an influence on offending include:
- the level of parental supervision,
- the way parents discipline a child,
- particularly harsh punishment,
- parental conflict or separation,
- criminal parents or siblings,
- parental abuse or neglect,
- the quality of the parent-child relationship.
Delinquency prevention is the broad term for all efforts aimed at preventing youth from becoming involved in criminal or other antisocial activity. Because the development of delinquency in youth is influenced by numerous factors, prevention efforts need to be comprehensive in scope. Prevention services may include activities like substance abuse education and treatment, family counseling, youth mentoring, parenting education, educational support, and youth sheltering. Increasing availability and use of family planning services, including education and contraceptives, helps to reduce unintended pregnancy and unwanted births—which are risk factors for delinquency.
Juvenile Delinquency : Juvenile delinquency refers to antisocial or illegal behavior by children or adolescents, for dealing with juveniles, such as juvenile detention centers. There are a multitude of different theories on the causes of crime, most if not all of which can be applied to the causes of youth crime.
TERRORISM [168]
Terrorism is an act of violence intended to create fear, which is then leveraged in order to achieve goals.
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Criticize an instance in history in which the term “terrorist” or “terrorism” has been misused to describe a religious group, government, or revolutionary action, using the definition of terrorism in this text |
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Learning Objective: Key Points |
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Learning Objective: Key Terms |
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Terrorism is the systematic use of terror, especially as a means of coercion. Although the term lacks a universal definition, common definitions of terrorism refer to violent acts intended to create fear (terror). These acts are perpetrated for a religious, political, or ideological goal, and deliberately target or disregard the safety of non-combatants (civilians).
Terrorism has been practiced by a broad array of political organizations for furthering their objectives. It has been practiced by right-wing and left-wing political parties, nationalistic groups, religious groups, revolutionaries, and ruling governments. An abiding characteristic is the indiscriminate use of violence against noncombatants to gain publicity for a group, cause or individual. Therefore, the power of terrorism comes from its ability to leverage human fear to help achieve these goals.
DEFINING TERRORISM [169]
There is an old saying that “one person’s freedom fighter is another person’s terrorist.” This saying indicates some of the problems in defining terrorism precisely. Some years ago, the Irish Republican Army (IRA) waged a campaign of terrorism against the British government and its people as part of its effort to drive the British out of Northern Ireland. Many people in Northern Ireland and elsewhere hailed IRA members as freedom fighters, while many other people condemned them as cowardly terrorists. Although most of the world labeled the 9/11 attacks as terrorism, some individuals applauded them as acts of heroism. These examples indicate that there is only a thin line, if any, between terrorism on the one hand and freedom fighting and heroism on the other hand. Just as beauty is in the eyes of the beholder, so is terrorism. The same type of action is either terrorism or freedom fighting, depending on who is characterizing the action.
Although dozens of definitions of terrorism exist, most take into account what are widely regarded as the three defining features of terrorism: (a) the use of violence; (b) the goal of making people afraid; and (c) the desire for political, social, economic, and/or cultural change. A popular definition by political scientist Ted Robert Gurr (1989, p. 201) captures these features: “The use of unexpected violence to intimidate or coerce people in the pursuit of political or social objectives.”
As the attacks on 9/11 remind us, terrorism involves the use of indiscriminate violence to instill fear in a population and thereby win certain political, economic, or social objectives.
TERRORISTS
The terms “terrorism” and “terrorist” carry strong negative connotations. These terms are often used as political labels to condemn such violence as immoral, indiscriminate, or unjustified or to condemn an entire segment of a population. However, some groups, when involved in a liberation struggle, have been called terrorists by the Western governments or media. In some liberation struggles, these same persons can become the leaders or statesman of these liberated nations. Thus, the perpetrators of terrorism can widely vary; terrorists can be individuals, groups or states. According to some definitions, clandestine or semi-clandestine state actors may also carry out terrorist acts outside the framework of a state of war.
The 9/11 attacks spawned an immense national security network and prompted the expenditure of more than $3 trillion on the war against terrorism.
Terrorism is hardly a new phenomenon, but Americans became horrifyingly familiar with it on September 11, 2001. The 9/11 attacks remain in the nation’s consciousness, and many readers may know someone who died on that terrible day. The attacks also spawned a vast national security network that now reaches into almost every aspect of American life. This network is so secretive, so huge, and so expensive that no one really knows precisely how large it is or how much it costs (Priest & Arkin, 2010). However, it is thought to include 1,200 government organizations, 1,900 private companies, and almost 900,000 people with security clearances (Applebaum, 2011). The United States has spent an estimated $3 trillion since 9/11 on the war on terrorism, including more than $1 trillion on the wars in Iraq and Afghanistan whose relevance for terrorism has been sharply questioned. Questions of how best to deal with terrorism continue to be debated, and there are few, if any, easy answers to these questions.
Not surprisingly, sociologists and other scholars have written many articles and books about terrorism. This section draws on their work to discuss the definition of terrorism, the major types of terrorism, explanations for terrorism, and strategies for dealing with terrorism. An understanding of all these issues is essential to make sense of the concern and controversy about terrorism that exists throughout the world today.
TYPES OF TERRORISM
When we think about this definition, 9/11 certainly comes to mind, but there are, in fact, several kinds of terrorism—based on the identity of the actors and targets of terrorism—to which this definition applies. A typology of terrorism, again by Gurr (1989), is popular: (a) vigilante terrorism, (b) insurgent terrorism, (c) transnational (or international) terrorism, and (d) state terrorism. Table 17.1 “Types of Terrorism” summarizes these four types.
Table 17.1 Types of Terrorism
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Vigilante terrorism |
Violence committed by private citizens against other private citizens. |
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Insurgent terrorism |
Violence committed by private citizens against their own government or against businesses and institutions seen as representing the “establishment.” |
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Transnational terrorism |
Violence committed by citizens of one nation against targets in another nation. |
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State terrorism |
Violence committed by a government against its own citizens. |
Vigilante terrorism is committed by private citizens against other private citizens. Sometimes the motivation is racial, ethnic, religious, or other hatred, and sometimes the motivation is to resist social change. The violence of racist groups like the Ku Klux Klan was vigilante terrorism, as was the violence used by white Europeans against Native Americans from the 1600s through the 1800s. What we now call “hate crime” is a contemporary example of vigilante terrorism.
Insurgent terrorism is committed by private citizens against their own government or against businesses and institutions seen as representing the “establishment.” Insurgent terrorism is committed by both left-wing groups and right-wing groups and thus has no political connotation. US history is filled with insurgent terrorism, starting with some of the actions the colonists waged against British forces before and during the American Revolution, when “the meanest and most squalid sort of violence was put to the service of revolutionary ideals and objectives” (Brown, 1989, p. 25). An example here is tarring and feathering: hot tar and then feathers were smeared over the unclothed bodies of Tories. Some of the labor violence committed after the Civil War also falls under the category of insurgent terrorism, as does some of the violence committed by left-wing groups during the 1960s and 1970s. A relatively recent example of right-wing insurgent terrorism is the infamous 1995 bombing of the federal building in Oklahoma City by Timothy McVeigh and Terry Nichols that killed 168 people.
Transnational terrorism is committed by the citizens of one nation against targets in another nation. This is the type that has most concerned Americans at least since 9/11, yet 9/11 was not the first time Americans had been killed by international terrorism. A decade earlier, a truck bombing at the World Trade Center killed six people and injured more than 1,000 others. In 1988, 189 Americans were among the 259 passengers and crew who died when a plane bound for New York exploded over Lockerbie, Scotland; agents from Libya were widely thought to have planted the bomb. Despite all these American deaths, transnational terrorism has actually been much more common in several other nations: London, Madrid, and various cities in the Middle East have often been the targets of international terrorists.
State terrorism involves violence by a government that is meant to frighten its own citizens and thereby stifle their dissent. State terrorism may involve mass murder, assassinations, and torture. Whatever its form, state terrorism has killed and injured more people than all the other kinds of terrorism combined (Gareau, 2010). Genocide, of course is the deadliest type of state terrorism, but state terrorism also occurs on a smaller scale. As just one example, the violent response of Southern white law enforcement officers to the civil rights protests of the 1960s amounted to state terrorism, as officers murdered or beat hundreds of activists during this period. Although state terrorism is usually linked to authoritarian regimes, many observers say the US government also engaged in state terror during the nineteenth century, when US troops killed thousands of Native Americans (D. A. Brown, 2009).
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Pin It! Religious Terrorism Religious terrorism is performed by groups or individuals, the motivation of which is typically rooted in faith-based tenets. Terrorist acts throughout the centuries have been performed on religious grounds with the hope to either spread or enforce a system of belief, viewpoint or opinion. Religious terrorism does not in itself necessarily define a specific religious standpoint or view, but instead usually defines an individual or group interpretation of that belief system ‘s teachings. |
EXPLAINING TERRORISM
Genocide is the deadliest type of state terrorism. The Nazi holocaust killed some 6 million Jews and 6 million other people.
Why does terrorism occur? It is easy to assume that terrorists must have psychological problems that lead them to have sadistic personalities, and that they are simply acting irrationally and impulsively. However, most researchers agree that terrorists are psychologically normal despite their murderous violence and, in fact, are little different from other types of individuals who use violence for political ends. As one scholar observed, “Most terrorists are no more or less fanatical than the young men who charged into Union cannon fire at Gettysburg or those who parachuted behind German lines into France. They are no more or less cruel and coldblooded than the Resistance fighters who executed Nazi officials and collaborators in Europe, or the American GI’s ordered to ‘pacify’ Vietnamese villages” (Rubenstein, 1987, p. 5).
Contemporary terrorists tend to come from well-to-do families and to be well-educated themselves; ironically, their social backgrounds are much more advantaged in these respects than are those of common street criminals, despite the violence they commit.
If terrorism cannot be said to stem from individuals’ psychological problems, then what are its roots? In answering this question, many scholars say that terrorism has structural roots. In this view, terrorism is a rational response, no matter how horrible it may be, to perceived grievances regarding economic, social, and/or political conditions (White, 2012). The heads of the US 9/11 Commission, which examined the terrorist attacks of that day, reflected this view in the following assessment: “We face a rising tide of radicalization and rage in the Muslim world—a trend to which our own actions have contributed. The enduring threat is not Osama bin Laden but young Muslims with no jobs and no hope, who are angry with their own governments and increasingly see the United States as an enemy of Islam” (Kean & Hamilton, 2007, p. B1). As this assessment indicates, structural conditions do not justify terrorism, of course, but they do help explain why some individuals decide to commit it.
THE IMPACT OF TERRORISM
The major impact of terrorism is apparent from its definition, which emphasizes public fear and intimidation. Terrorism can work, or so terrorists believe, precisely because it instills fear and intimidation. Anyone who might have happened to be in or near New York City on 9/11 will always remember how terrified the local populace was to hear of the attacks and the fears that remained with them for the days and weeks that followed.
Hardly anyone likes standing in the long airport security lines that are a result of the 9/11 attacks. Some experts say that certain airport security measures are an unneeded response to these attacks.
Another significant impact of terrorism is the response to it. As mentioned earlier, the 9/11 attacks led the United States to develop an immense national security network that defies description and expense, as well as the Patriot Act and other measures that some say threaten civil liberties; to start the wars in Iraq and Afghanistan; and to spend more than $3 trillion in just one decade on homeland security and the war against terrorism. Airport security increased, and Americans have grown accustomed to having to take off their shoes, display their liquids and gels in containers limited to three ounces, and stand in long security lines as they try to catch their planes.
People critical of these effects say that the “terrorists won,” and, for better or worse, they may be correct. As one columnist wrote on the tenth anniversary of 9/11, “And yet, 10 years after 9/11, it’s clear that the ‘war on terror’ was far too narrow a prism through which to see the planet. And the price we paid to fight it was far too high” (Applebaum, 2011, p. A17). In this columnist’s opinion, the war on terror imposed huge domestic costs on the United States; it diverted US attention away from important issues regarding China, Latin America, and Africa; it aligned the United States with authoritarian regimes in the Middle East even though their authoritarianism helps inspire Islamic terrorism; and it diverted attention away from the need to invest in the American infrastructure: schools, roads, bridges, and medical and other research. In short, the columnist concluded, “in making Islamic terrorism our central priority—at times our only priority—we ignored the economic, environmental and political concerns of the rest of the globe. Worse, we pushed aside our economic, environmental and political problems until they became too great to be ignored” (Applebaum, 2011, p. A17).
To critics like this columnist, the threat to Americans of terrorism is “over-hyped” (Holland, 2011b). They acknowledge the 9/11 tragedy and the real fears of Americans, but they also point out that in the years since 9/11, the number of Americans killed in car accidents, by air pollution, by homicide, or even by dog bites or lightning strikes has greatly exceeded the number of Americans killed by terrorism. They add that the threat is overhyped because defense industry lobbyists profit from overhyping it and because politicians do not wish to be seen as “weak on terror.” And they also worry that the war on terror has been motivated by and also contributed to prejudice against Muslims (Kurzman, 2011).
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Learning Objective: Key Takeaways |
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Learning Objective: For Your Review |
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THE USA PATRIOT ACT [175]
After the 9/11 terrorist attack in 2001, Congress passed the USA Patriot Act. The U.S. Department of Justice’s website has a page entitled Preserving Life & Liberty. ( https://www.justice.gov/archive/ll/highlights.htm ) The top of that page states the following regarding the Patriot Act.
The Department of Justice’s first priority is to prevent future terrorist attacks. Since its passage following the September 11, 2001 attacks, the Patriot Act has played a key part – and often the leading role – in a number of successful operations to protect innocent Americans from the deadly plans of terrorists dedicated to destroying America and our way of life. While the results have been important, in passing the Patriot Act, Congress provided for only modest, incremental changes in the law. Congress simply took existing legal principles and retrofitted them to preserve the lives and liberty of the American people from the challenges posed by a global terrorist network.
Congress enacted the Patriot Act by overwhelming, bipartisan margins, arming law enforcement with new tools to detect and prevent terrorism: The USA Patriot Act was passed nearly unanimously by the Senate 98-1, and 357-66 in the House, with the support of members from across the political spectrum.
The Act Improves Our Counter-Terrorism Efforts in Several Significant Ways:
- The Patriot Act:
- allows investigators to use the tools that were already available to investigate organized crime and drug trafficking. Many of the tools the Act provides to law enforcement to fight terrorism have been used for decades to fight organized crime and drug dealers and have been reviewed and approved by the courts. As Sen. Joe Biden (D-DE) explained during the floor debate about the Act, “the FBI could get a wiretap to investigate the mafia, but they could not get one to investigate terrorists. To put it bluntly, that was crazy! What’s good for the mob should be good for terrorists.” (Cong. Rec., 10/25/01)
- allows law enforcement to use surveillance against more crimes of terror. Before the Patriot Act, courts could permit law enforcement to conduct electronic surveillance to investigate many ordinary, non-terrorism crimes, such as drug crimes, mail fraud, and passport fraud. Agents also could obtain wiretaps to investigate some, but not all, of the crimes that terrorists often commit. The Act enabled investigators to gather information when looking into the full range of terrorism-related crimes, including chemical-weapons offenses, the use of weapons of mass destruction, killing Americans abroad, and terrorism financing.
- allows federal agents to follow sophisticated terrorists trained to evade detection. For years, law enforcement has been able to use “roving wiretaps” to investigate ordinary crimes, including drug offenses and racketeering. A roving wiretap can be authorized by a federal judge to apply to a particular suspect, rather than a particular phone or communications device. Because international terrorists are sophisticated and trained to thwart surveillance by rapidly changing locations and communication devices such as cell phones, the Act authorized agents to seek court permission to use the same techniques in national security investigations to track terrorists.
- allows law enforcement to conduct investigations without tipping off terrorists.  Therefore, federal courts in narrow circumstances long have allowed law enforcement to delay for a limited time when the subject is told that a judicially approved search warrant has been executed. Notice is always provided, but the reasonable delay gives law enforcement time to identify the criminal’s associates, eliminate immediate threats to our communities, and coordinate the arrests of multiple individuals without tipping them off beforehand. These delayed notification search warrants have been used for decades, have proven crucial in drug and organized crime cases, and have been upheld by courts as fully constitutional.
- allows federal agents to ask a court for an order to obtain business records in national security terrorism cases. Examining business records often provides the key that investigators are looking for to solve a wide range of crimes. Investigators might seek select records from hardware stores or chemical plants, for example, to find out who bought materials to make a bomb, or bank records to see who’s sending money to terrorists. Law enforcement authorities have always been able to obtain business records in criminal cases through grand jury subpoenas and continue to do so in national security cases where appropriate. These records were sought in criminal cases such as the investigation of the Zodiac gunman, where police suspected the gunman was inspired by a Scottish occult poet and wanted to learn who had checked the poet’s books out of the library. In national security cases where use of the grand jury process was not appropriate, investigators previously had limited tools at their disposal to obtain certain business records. Under the Patriot Act, the government can now ask a federal court (the Foreign Intelligence Surveillance Court), if needed to aid an investigation, to order production of the same type of records available through grand jury subpoenas. This federal court, however, can issue these orders only after the government demonstrates the records concerned are sought for an authorized investigation to obtain foreign intelligence information not concerning a U.S. person or to protect against international terrorism or clandestine intelligence activities, provided that such investigation of a U.S. person is not conducted solely on the basis of activities protected by the First Amendment.
- The Patriot Act facilitated information sharing and cooperation among government agencies so that they can better “connect the dots.” The Act removed the major legal barriers that prevented the law enforcement, intelligence, and national defense communities from talking and coordinating their work to protect the American people and our national security. The government’s prevention efforts should not be restricted by boxes on an organizational chart. Now police officers, FBI agents, federal prosecutors and intelligence officials can protect our communities by “connecting the dots” to uncover terrorist plots before they are completed. As Sen. John Edwards (D-N.C.) said about the Patriot Act, “we simply cannot prevail in the battle against terrorism if the right hand of our government has no idea what the left hand is doing” (Press release, 10/26/01) Prosecutors and investigators used information shared pursuant to section 218 in investigating the defendants in the so-called “Virginia Jihad” case. This prosecution involved members of the Dar al-Arqam Islamic Center, who trained for jihad in Northern Virginia by participating in paintball and paramilitary training, including eight individuals who traveled to terrorist training camps in Pakistan or Afghanistan between 1999 and 2001. These individuals are associates of a violent Islamic extremist group known as Lashkar-e-Taiba (LET), which operates in Pakistan and Kashmir, and that has ties to the al Qaeda terrorist network. As the result of an investigation that included the use of information obtained through FISA, prosecutors were able to bring charges against these individuals. Six of the defendants have pleaded guilty, and three were convicted in March 2004 of charges including conspiracy to levy war against the United States and conspiracy to provide material support to the Taliban. These nine defendants received sentences ranging from a prison term of four years to life imprisonment.
- The Patriot Act:
- updated the law to reflect new technologies and new threats. The Act brought the law up to date with current technology, so we no longer have to fight a digital-age battle with antique weapons-legal authorities leftover from the era of rotary telephones. When investigating the murder of Wall Street Journal reporter Daniel Pearl, for example, law enforcement used one of the Act’s new authorities to use high-tech means to identify and locate some of the killers.
- allows law enforcement officials to obtain a search warrant anywhere a terrorist-related activity occurred. Before the Patriot Act, law enforcement personnel were required to obtain a search warrant in the district where they intended to conduct a search. However, modern terrorism investigations often span a number of districts, and officers therefore had to obtain multiple warrants in multiple jurisdictions, creating unnecessary delays. The Act provides that warrants can be obtained in any district in which terrorism-related activities occurred, regardless of where they will be executed. This provision does not change the standards governing the availability of a search warrant but streamlines the search-warrant process.
- allows victims of computer hacking to request law enforcement assistance in monitoring the “trespassers” on their computers. This change made the law technology-neutral; it placed electronic trespassers on the same footing as physical trespassers. Now, hacking victims can seek law enforcement assistance to combat hackers, just as burglary victims have been able to invite officers into their homes to catch burglars.
- The Patriot Act:
- increased the penalties for those who commit terrorist crimes. Americans are threatened as much by the terrorist who pays for a bomb as by the one who pushes the button. That’s why the Patriot Act imposed tough new penalties on those who commit and support terrorist operations, both at home and abroad.
- prohibits the harboring of terrorists. The Act created a new offense that prohibits knowingly harboring persons who have committed or are about to commit a variety of terrorist offenses, such as: destruction of aircraft; use of nuclear, chemical, or biological weapons; use of weapons of mass destruction; bombing of government property; sabotage of nuclear facilities; and aircraft piracy.
- enhanced the inadequate maximum penalties for various crimes likely to be committed by terrorists: including arson, destruction of energy facilities, material support to terrorists and terrorist organizations, and destruction of national-defense materials.
- enhanced a number of conspiracy penalties, including for arson, killings in federal facilities, attacking communications systems, material support to terrorists, sabotage of nuclear facilities, and interference with flight crew members. Under previous law, many terrorism statutes did not specifically prohibit engaging in conspiracies to commit the underlying offenses. In such cases, the government could only bring prosecutions under the general federal conspiracy provision, which carries a maximum penalty of only five years in prison.
- punishes terrorist attacks on mass transit systems.
- punishes bioterrorists.
- eliminates the statutes of limitations for certain terrorism crimes and lengthens them for other terrorist crimes.
The government’s success in preventing another catastrophic attack on the American homeland since September 11, 2001, would have been much more difficult, if not impossible, without the USA Patriot Act. The authorities Congress provided have substantially enhanced our ability to prevent, investigate, and prosecute acts of terror.
CYBER CRIME [176]
TYPES OF CYBERCRIME
Crime has evolved with the advancements of the internet and social media. The parallel between technology and the types of crimes that are committed is astonishing. As technology became more readily available to the masses, the types of crimes committed shifted over time. A clear distinction has been formed based on the involvement of cybertechnology in crime. Crimes that would not exist or be possible without the existence of cybertechnology are true Cybercrimes. To be most accurate, these crimes can be classified as cyberspecific crimes. Crimes that can be committed that do not necessarily need cybertechnology to be possible, but are made easier by its existence, are known as cyber-related crimes. Of Cyber-related crimes, there are two distinct categories that can be identified. The first are Cyber-assisted crimes. These are crimes in which cybertechnology is simply used to aid a crime, such as committing tax fraud or being assaulted with a computer. The other category is known as Cyberexacerbated crimes, which are crimes that have increased significantly due to cybertechnology.
CYBER-ASSISTED CRIMES
Cyber-assisted crimes are the most basic crimes that can be committed with the use of cybertechnology. Put simply, these are essentially normal crimes that have occurred throughout time on a regular basis. The only difference is that cybertechnology has played some small part in the crime. Property damage, for example, is one kind of cyber-assisted crime. If someone destroys your computer or cellphone, it constitutes as property damage but can also be classified as a cyber-assisted crime. Similarly, if you are assaulted with a phone, printer, computer or other device, the attack constitutes as assault but can also be classified as a Cyber-assisted crime.
The most common type of cyber-assisted crime that you will see is fraud. Fraud typically is a crime that does not require much thought to actually commit. As a crime, it has always been relatively easy to commit. With the use of cybertechnology, it only becomes much easier to actually carry out from start to finish.
CYBEREXACERBATED CRIMES
Cyberexacerbated crimes are a type of cyber-related crime, but they are much worse than cyber-assisted crimes. These crimes have increased significantly due to cybertechnology. Most crimes have evolved to maintain their own categories due to the sheer volume of crimes and their slight uniqueness due to their ease with the use of cybertechnology.
Cyberbullying is defined as the “intentional and repeated harm inflicted on people through the use of computers, cellular telephones, and other electronic devices.” Previously something that happened offline only, cyberbullying is a huge crime that leads to victims suffering from low self-esteem, depression, and sometimes even driving them to commit suicide. With the use of the internet, it is possible for people to receive thousands of hateful comments from individuals at a single time.
Cyberstalking is exactly what one would think, except occurring in a digital space. Cybertechnology allows for criminals to keep tabs on people, watching all of their online activity and making it very uncomfortable for victims to even want to utilize things such as their own personal social media. Perhaps the most disconcerting thing is that the perpetrator can always be online.
Internet pedophilia and pornography are some of the more disturbing cyberexacerbated crimes. Due to the ability for communities of like-minded individuals to be easily formed online, pedophiles are able to form online communities and facilitate the creation and dissemination of child pornography.
CYBERSPECIFIC CRIMES
Cyberspecific crimes do not exist without the internet as we know it. Because of that, these are the most unique cybercrimes and could be considered as the only “true” cybercrimes. Cybertrespassing is one of these crimes. At its core, cybertrespassing takes its roots from actual trespassing. Essentially, perpetrators gain access to stores of information that they otherwise should not have access to because of the lack of permissions. The reason why this is so dangerous is because it opens the door for cybertrespassing to easily become a data breach if information is taken.
Cybervandalism is another form cyberspecific crime. Taking its roots from actual vandalism, cybervandalism began harmlessly with the defacing of websites on the internet. While annoying, it didn’t necessarily present any damage. It wasn’t until cyberattacks with the intent of harming computers were created that cybervandalism became a huge issue.
TYPES OF CYBER ATTACKS
Viruses are pieces of computer programming code that causes a computer to behave in an undesirable way. Viruses can be attached to files or stored in the computer’s memory. Viruses may be programmed to different things such when they are downloaded or activated by a specific action for example viruses attached to file will infect that computer and any file created or modified on that machine. Viruses may also have programmed to display a message when certain activities are performed to execute the virus. Worms like viruses bury themselves in the memory of a machine and then duplicates itself with help from any help. It can send itself through emails and other connections. Phishing is when hackers try to obtain financial or other confidential information from Internet users, typically by sending an e-mail that looks as if it is from a legitimate organization, usually a financial institution, but contains a link to a fake Web site that replicates the real one. These con - artists urge the recipient of such emails to take action for rewards or avoid consequences. Hackers may use a backdoor within a computer system that is vulnerable, this allows them to remain undetected while they access important information. Key-logger programs allow attackers to view information that has been logged into a particular machine undetected. Botnets are a collection of computers that could be spread around the world; they are connected to the internet and controlled by one single computer.
Summary
As the 21 st century progresses, technology and crime will continue to become more closely linked; technology is changing the face of crime and policing is adapting as a result. Yet many of the core motivations behind policing and the philosophies utilized in making policing policies will continue to shape the field of law and law enforcement. Technology and goals may shift but good policework is derived from self-awareness, emotional intelligence, community consciousness, and adaptability.


1.14.42: L'Hospital's Rule
In several important cases, analysis of thermodynamic properties of solutions (and liquid mixtures) requires consideration of a term having the general form \(x \, \ln (x)\) where \(x\) is an intensive composition variable; e.g. molality, concentration or mole fraction. The accompanying analysis requires an answer to the question --- what value does the product \(x \, \ln (x)\) take in the limit that \(x\) tends to zero. But \(\operatorname{limit}(x \rightarrow 0) \ln (x)=-\infty\). The thermodynamic analysis has to take account of the answer to this question. In fact most accounts assume that the answer to the above question is ‘zero’. Confirmation that the latter statement is correct emerges from application of L’Hospital’s Rule (G. F. A. de l’Hospital, 1661-1704, marquis de Saint-Mesme). This rule allows the evaluation of terms having indeterminate forms. Most applications of this method usually involve the ratio of two terms each being a function of \(x\).
If \(\mathrm{f}(\mathrm{x}) / \mathrm{F}(\mathrm{x})\) approaches either [0/0] or \([\infty / \infty]\) when \(x\) approaches a , and \(\mathrm{f}^{\prime}(\mathrm{x}) / \mathrm{F}^{\prime}(\mathrm{x})\) [where \(\mathrm{f}^{\prime}(\mathrm{x})\) and \(\mathrm{F}^{\prime}(\mathrm{x})\) are first derivatives of \(\mathrm{f}(\mathrm{x})\) and \(\mathrm{F}(\mathrm{x})\)] approaches a limit as \(x\) approaches a , then \(\mathrm{f}(\mathrm{x}) / \mathrm{F}(\mathrm{x})\) approaches the same limit.
If \(f(x)=x^{2}-1\) and \(F(x)=x-1\)
then \(\frac{f(x)}{F(x)}=\frac{x^{2}-1}{x-1}\) and \(\frac{f^{\prime}(x)}{F^{\prime}(x)}=\frac{2 \, x^{2}}{1}\)
then
\[\operatorname{limit}(x \rightarrow 1) \frac{f^{\prime}(x)}{F^{\prime}(x)}=2 \nonumber \]
Hence,
\[\operatorname{limit}(x \rightarrow 1) \frac{f(x)}{F(x)}=2 \nonumber \]
This rule can be proved using three assumptions.
- In the neighborhood of \(x = a\), \(F(x) \neq 0 \text { if } x \neq \mathrm{a}\).
- \(f(x)\) and \(F(x)\) are continuous in the neighbourhood of \(x = \mathrm{a}\) except perhaps at \(\mathrm{a}\).
- \(\mathrm{f}^{\prime}(x)\) and \(\mathrm{F}^{\prime}(x)\) exist is some neighborhood of \(x = \mathrm{a}\) (except perhaps at \(x = \mathrm{a}\)) and do not vanish simultaneously for \(x \neq \mathrm{a}\).
In the present context the terms under consideration have a different form. With reference to the term, \(x \, \ln (x)\),
\[f(x)=\ln (x) \text { and } F(x)=1 / x \nonumber \]
Then \(\mathrm{f}^{\prime}(\mathrm{x})=1 / \mathrm{x}\) and \(\mathrm{F}^{\prime}(\mathrm{x})=-1 / \mathrm{x}^{2}\).
Hence, \(\mathrm{f}^{\prime}(\mathrm{x}) / \mathrm{F}^{\prime}(\mathrm{x}) = -\mathrm{x}\).
Thus
\[\operatorname{limit}(x \rightarrow 0) \mathrm{f}^{\prime}(x) / \mathrm{F}^{\prime}(\mathrm{x})=0 \nonumber \]
Hence,
\[\operatorname{limit}(x \rightarrow 0) x \, \ln (x)=0 \nonumber \]


11.3: The Exponential Distribution
Here, we will discuss another brand name random variable, the Exponential random variable which is related to the Poisson random variable discussed a few sections ago.
Definition: Let \( \theta > 0 \). Suppose \( X \) is a random variable who has the following density function:
\[
f(x) =
\begin{cases}
\frac{1}{\theta}e^{-x/\theta} & \text{if} ~ x \geq 0 \ \\
0 , & \text{otherwise} \\
\end{cases}
\nonumber\ \]
Then we say \( X \) is an Exponential random variable with parameter \( \theta \) and we write \( X \sim Exp(\theta) \).
Notice that the Exponential random variable is something which is not totally new for us since we actually studied the \(Exp(\frac{1}{10}) \) random variable in the last section! Additionally, recall that the point of a random variable is to model some sort of quantity under certain assumptions and so we can ask, "what does the Exponential random variable model?"
Recall that the Poisson random variable models the number of occurrences in a given interval (for instance, the number of earthquakes per week). This number was a discrete-type of random variable that follows the Poisson distribution with parameter or rate or mean \( \lambda \). However, suppose we were interested in modeling the waiting time between successive occurrences (for instance, we wished to model the time elapsed between two successive earthquakes). Then it can be shown that the waiting time between the next occurrence is an Exponential random variable with parameter \( \theta = \frac{1}{\lambda} \).
Theorem: If \( X \sim Exp(\theta) \) then
\begin{align*}
\mathbb{E}[X] = \theta ~~\text{and} ~~ \mathbb{V}ar[X] = \theta^2
\end{align*}
Theorem: If \( X \sim Exp(\theta) \) then the cumulative distribution of \(X\) is given by:
\[
F(x) =
\begin{cases}
0 & \text{if} ~ x < 0 \\
1 - e^{-x/\theta}, & \text{if} ~ x \geq 0 \\
\end{cases}
\nonumber\ \]
Customer arrive in a certain shop according to a Poisson process with a mean rate of \( \lambda = 1/3 \) customers per minute. What is the probability that the shopkeeper will have to wait more than five minutes for the arrival of the first customer?
- Answer
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According to the interpretation of the Exponential random variable, if we have a Poisson process with rate \( \lambda \), then the waiting time for the next customer is going to be an exponential random variable with parameter \( \theta = \frac{1}{\lambda}\). Since customers arrive to the store with rate \(\lambda = 1/3 \), then the waiting time for the next customer is going to be distributed as an Exponential random variable with parameter \( \theta = \frac{1}{\lambda} = \frac{1}{1/3} = 3 \). So if \( X \) models the waiting time for the next customer, then it follows that \( X \sim Exp(3) \). That is, \(X\) has the following density:
\[
f(x) =
\begin{cases}
\frac{1}{3}e^{-x/3} & \text{if} ~ x \geq 0 \ \\
0 , & \text{otherwise} \\
\end{cases}
\nonumber\ \]Hence
\begin{align*}
P(\text{the waiting time is more than} ~ 5 ~ \text{minutes} ) &= P(X > 5) \\
&= \int_{5}^{\infty} \frac{1}{3}e^{-x/3} ~ dx \\
&= e^{-5/3} \\
& \approx 0.1889
\end{align*}Note that we can achieve the same answer by utilizing the cdf:
\begin{align*}
P(\text{the waiting time is more than} ~ 5 ~ \text{minutes} ) &= P(X > 5) \\
&= 1 - P(X \leq 5) \\
&= 1 - F(5) \\
&= 1 - (1 - e^{-5/3}) \\
&= e^{-5/3} \\
& \approx 0.1889
\end{align*}
Example: Suppose that a certain type of electronic component has an exponential distribution with a mean life of 500 hours. If $X$ denotes the lifetime of this component then find \( P(X > 900 | X > 300) \).
- Answer 1
-
Let \( X \) model the lifetime of the component. From the problem, we know that \( X \sim Exp(\theta)\). The problem tells us the mean is 500 hours and for an Exponential random variable, the mean and parameter are the same thing! So we know that \( X \sim Exp(500)\). That is, the density is given by
\[
f(x) =
\begin{cases}
\frac{1}{500}e^{-x/500} & \text{if} ~ x \geq 0 \ \\
0 , & \text{otherwise} \\
\end{cases}
\nonumber\ \]Thus we have
\begin{align*}
P(X > 900 | X > 300) &= \frac{P\bigg( \{X > 900 \} \cap \{X > 300 \} \bigg)}{P(X > 300)} \\
&= \frac{P(X > 900)}{P(X>300)} \\
&= \frac{\int_{900}^{\infty} \frac{1}{500}e^{-x/500} ~ dx }{\int_{300}^{\infty} \frac{1}{500}e^{-x/500} ~ dx } \\
&= \frac{e^{-900/500}}{e^{-300/500}} \\
& = e^{-6/5} \\
& \approx 0.3012
\end{align*}
- Answer 2
-
Or, as noted in the last problem, we can use the cdf to our advantage to avoid the integration.
Alternative Solution:
\begin{align*}
P(X > 900 | X > 300) &= \frac{P\bigg( \{X > 900 \} \cap \{X > 300 \} \bigg)}{P(X > 300)} \\
&= \frac{P(X > 900)}{P(X>300)} \\
&= \frac{1 - P(X \leq 900)}{1 - P(X \leq 300)} \\
&= \frac{1 - F(900)}{1 - F(300)} \\
&= \frac{1 - (1 - e^{-900/500})}{1 - (1 - e^{-300/500})} \\
&= \frac{e^{-900/500}}{e^{-300/500}} \\
& = e^{-6/5} \\
& \approx 0.3012
\end{align*}


6.5: Chinese Solo Repertoire - Attack on All Sides and Spring River in the Flower Moon Night
At the same time that European composers were producing vivid programmatic works, a parallel tradition of program music was flourishing in China. We will consider two examples from the literature for solo instruments, which is predominantly programmatic. One piece will portray a historical battle, while the other will reflect on the contents of a famous poem. Although Chinese music follows different rules than European music, is it not difficult for a Western listener to understand what this music is about. This is due both to the use of mimesis and to a cross-cultural agreement about the representation of calm and energetic moods in sound.
When we discuss this music, however, we will have to do so in slightly different terms than we have so far. Although Chinese musicians have developed a variety of notational systems that have allowed musical compositions to be preserved, they have not always prioritized notation or valued the authority of the composer. Individual pieces are usually passed down directly from performer to performer by means of oral tradition , while the names of composers are seldom recorded. As a result, we are not always able to identify the authors of this repertoire or determine when the pieces were written.
The history of music in China extends back for thousands of years, and some of the instruments date to antiquity. This is not to say, however, that the music has remained unchanged, or that all of the repertoire items are old. As we saw in Chapter 4, Beijing opera dates only to the late 18th century, and alternative opera traditions have continued to emerge and change. In the sphere of instrumental music, the use of individual instruments—as well as their physical structure— transformed with the passage of time. We will encounter two instruments, the pipa and the guqin. In doing so, we will consider their history, construction, and use in the performance of program music.
Pipa: Attack on All Sides
The pipa is a type of lute used in a variety of Chinese musical traditions. It dates back to at least the 3rd century, although it did not acquire its modern form until the 20th century. Like most of the instruments commonly used in Chinese music, the pipa was probably imported from
Central Asia or India along the Silk Road trade route. At first, it was used only to accompany singing and dancing, but during the Tang dynasty (618-907) a repertoire of solo pipa music emerged. As such, the pipa repertoire is among the oldest in the Chinese tradition. The instrument was historically favored by both aristocrats and working musicians, and was long associated with women—specifically, courtesans.
The pipa has a distinctive, pear-shaped body and is played in an upright position. Modern instruments have twenty-four frets spaced according to the Western chromatic scale. The frets on the neck have a unique wedge shape, such that a player’s finger does not in fact touch the neck when the string is depressed. The pipa’s four strings can be tuned to a variety of pitches. Although they used to be silk, the fact that pipa strings have been manufactured out of steel since the 1950s gives the modern instrument a powerful sound. This is further accentuated by the fact that the player wears picks on the fingers of her right hand.
A great deal of the traditional pipa repertoire has survived into the present day due to the publication of four collections in the 19th century. The notation used in these collections, known as gongche , is completely unrelated to Western staff notation . Instead of mapping pitches and rhythms onto a graph, as staff notation does, it represents pitches with numbers and rhythms with dots and lines. In the context of a tradition that is primarily aural, however, such notation was used only to document music for preservation or reference. It was not used to learn unfamiliar music or in performance.
Attack on All Sides 9 is the most popular piece in the pipa repertoire. It is also very difficult, however, and is usually only performed by the most accomplished players. The earliest notated version appears in an 1818 collection, but it is impossible to say when (or by whom) it was in fact composed. Attack on All Sides is an example of a “large” composition, containing many distinct sections. (The pipa repertoire also includes “small” compositions, which are shorter and have a single section.) While Attack on All Sides can always be recognized and identified, some published versions omit sections that are included elsewhere. Therefore, not every performance is identical. No single version can be identified as “correct.” This can be contrasted with most music in the European concert tradition, for which there is generally understood to exist a single authoritative version.
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9. Attack on All Sides Performance: Jiaju Shen |
As with Beijing opera, pipa solos are divided into “civil” and “martial,” the latter having to do with military themes. Attack on All Sides is most certainly a martial composition. It portrays a famous battle that took place in 202 BC between the armies of two Chinese provinces, Western Chu and Han, who were fighting for dominion over China. The conflict ended with the Battle of Gaixia, in which the Han troops kidnapped the Chu general’s wife and used her to lure the enemy troops into a canyon. There, they fell victim to the “ambush from ten sides”—another common title for this piece. The battle itself hinged on musical warfare, for the Han sought to defeat their enemy by psychological means. To this end, they sang Chu folk songs throughout the night, with the effect of making the demoralized enemy homesick and inspiring soldiers to desert. The Chu general, Xiang Yu, is said to have composed a song of his own that same night. His lament, The Song of Gaixia , is still performed today. Tradition holds that he first sang the verses in alternation with his wife, who, feeling that she was at fault for the defeat, subsequently killed herself with his sword. The battle ended with Xiang Yu’s suicide on the banks of the Wu river.
All of this is captured in Attack on All Sides . The fact that this composition is made up of many sections allows the performer to explore the various emotions and activities of the battle scene. In the first sections, we bear witness to the assembling Han troops. The energy of the music communicates their vitality and resolution, but we also hear the drums and bugles of battle. The battle itself is captured by a variety of virtuosic pipa techniques that produce rapid sequences of notes. After the battle, however, the music becomes mournful—a reflection of Xiang Yu’s sorrow at his loss. The final word goes to the victor, however, and the piece concludes with a representation of the Han general’s triumph.
Guzheng: Peng Xiuwen, Spring River in the Flower Moon Night
The oldest extant guzheng dates to about 500 BC. The guzheng is a type of zither , and its plucked strings run along the face of a resonant wood box. Each string passes over an individual wooden bridge, which can be moved to adjust the pitch. Players use picks on the fingers of the right hand to pluck the strings to one side of the bridges, while using the left hand either to pluck strings on the right-hand side or to press or pull the strings on the other side. This causes pitch fluxuations, which are carefully controlled and used to ornament the melody. As with the pipa, the strings of the guzheng, once silk, have been made of steel since the 1950s. They increased in number from thirteen to twenty-one around the same time. The strings are tuned to the pitches of the pentatonic scale , which is common in Chinese music. We might think of these as the first, second, third, fifth, and sixth notes of the major scale.
Because the modern guzheng is so different from the ancient instrument, performers tend to favor recently-composed pieces that make use of its full range. Such is the case with our example, Spring River in the Flower Moon Night , which is the work of Peng Xiuwen (1931-1996). Following the establishment of the People’s Republic of China in 1949, Peng became a leading figure in the development of post-revolution Chinese music. In particular, he contributed to the development of the Chinese orchestra—an ensemble type that dates only to the 1930s. In most traditional forms of Chinese ensemble music, only one of each instrument is included, and the performers are granted the freedom to embellish their individual parts. In a Chinese orchestra, on the other hand, instruments of the same type are gathered into sections, and they use notated music to play in unison under the leadership of a conductor . This approach is obviously modelled on the European orchestra, and its popularity at first reflected Chinese admiration for Western technological achievements.
Peng became director of the China Broadcasting Chinese Orchestra, one of the most important ensembles of its type, in 1956, when he was only twenty-four years old. In addition to improving the tuning and balance of the orchestra, he arranged a large number of pieces from the European repertoire for Chinese orchestra and composed original pieces. One of these was Spring River in the Flower Moon Nigh t,10 which soon became even more popular with solo guzheng players. As we will see, its pentatonic pitch content and meditative mood suit the instrument well.
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Spring River in a Flower Moon Night 10. Composer: Peng Xiuwen Performance: Bei Bei He (2016) |
The title Spring River in the Flower Moon Night refers to a famous poem written by Zhang Ruoxu around the turn of the 8th century. The poem has inspired countless artistic interpretations over the centuries, including paintings and musical compositions. As the title might suggest, Zhang’s poem describes the moonlit Yangtze river. After several evocative passages that conjure the beauty of the scene, however, he turns to themes of longing and loss, meditating on the ephemerality of life and the sorrows of travellers who leave their loved ones behind.
In his composition, Peng strives to evoke the full range of emotions contained in the poem. The guzheng version of Spring River in the Flower Moon Night requires a variety of techniques, including rapid tremolo picking on a single string, strums (both delicate and energetic), left-hand bends that add notes to the melody, and left-hand bends that are merely ornamental. Peng’s ultimate goal is to leave the listener in the same state of sorrowful tranquility that they would experience upon reading the poem.


7.8: Applications of Magnetic Forces and Fields
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Learning Objectives
By the end of this section, you will be able to:
- Explain how a mass spectrometer works to separate charges
- Explain how a cyclotron works
Being able to manipulate and sort charged particles allows deeper experimentation to understand what matter is made of. We first look at a mass spectrometer to see how we can separate ions by their charge-to-mass ratio. Then we discuss cyclotrons as a method to accelerate charges to very high energies.
Mass Spectrometer
The mass spectrometer is a device that separates ions according to their charge-to-mass ratios. One particular version, the Bainbridge mass spectrometer, is illustrated in Figure \(\PageIndex{1}\). Ions produced at a source are first sent through a velocity selector, where the magnetic force is equally balanced with the electric force. These ions all emerge with the same speed \(v = E/B\) since any ion with a different velocity is deflected preferentially by either the electric or magnetic force, and ultimately blocked from the next stage. They then enter a uniform magnetic field \(B_0\) where they travel in a circular path whose radius R is given by Equation 11.4.2 , \(r = \frac{mv}{qB}\). The radius is measured by a particle detector located as shown in the figure.
The relationship between the charge-to-mass ratio q / m and the radius R is determined by combining Equation 11.4.2 and Equation 11.7.2 :
\[\frac{q}{m} = \frac{E}{BB_0R}. \nonumber \]
Since most ions are singly charged \((q = 1.6 \times 10^{-10}C)\), measured values of R can be used with this equation to determine the mass of ions. With modern instruments, masses can be determined to one part in \(10^8\).
An interesting use of a spectrometer is as part of a system for detecting very small leaks in a research apparatus. In low-temperature physics laboratories, a device known as a dilution refrigerator uses a mixture of He-3, He-4, and other cryogens to reach temperatures well below 1 K. The performance of the refrigerator is severely hampered if even a minute leak between its various components occurs. Consequently, before it is cooled down to the desired temperature, the refrigerator is subjected to a leak test. A small quantity of gaseous helium is injected into one of its compartments, while an adjacent, but supposedly isolated, compartment is connected to a high-vacuum pump to which a mass spectrometer is attached. A heated filament ionizes any helium atoms evacuated by the pump. The detection of these ions by the spectrometer then indicates a leak between the two compartments of the dilution refrigerator.
In conjunction with gas chromatography, mass spectrometers are used widely to identify unknown substances. While the gas chromatography portion breaks down the substance, the mass spectrometer separates the resulting ionized molecules. This technique is used with fire debris to ascertain the cause, in law enforcement to identify illegal drugs, in security to identify explosives, and in many medicinal applications.
Cyclotron
The cyclotron was developed by E.O. Lawrence to accelerate charged particles (usually protons, deuterons, or alpha-particles) to large kinetic energies. These particles are then used for nuclear-collision experiments to produce radioactive isotopes. A cyclotron is illustrated in Figure \(\PageIndex{2}\). The particles move between two flat, semi-cylindrical metallic containers D1 and D2, called dees . The dees are enclosed in a larger metal container, and the apparatus is placed between the poles of an electromagnet that provides a uniform magnetic field. Air is removed from the large container so that the particles neither lose energy nor are deflected because of collisions with air molecules. The dees are connected to a high-frequency voltage source that provides an alternating electric field in the small region between them. Because the dees are made of metal, their interiors are shielded from the electric field.
Suppose a positively charged particle is injected into the gap between the dees when D2 is at a positive potential relative to D1. The particle is then accelerated across the gap and enters D1 after gaining kinetic energy qV , where V is the average potential difference the particle experiences between the dees. When the particle is inside D1, only the uniform magnetic field \(\vec{B}\) of the electromagnet acts on it, so the particle moves in a circle of radius
\[r = \frac{mv}{qB} \label{11.32} \]
with a period of
\[T = \frac{2\pi m}{qB}. \label{11.33} \]
The period of the alternating voltage course is set at T , so while the particle is inside D1, moving along its semicircular orbit in a time T /2, the polarity of the dees is reversed. When the particle reenters the gap, D1 is positive with respect to D2, and the particle is again accelerated across the gap, thereby gaining a kinetic energy qV . The particle then enters D2, circulates in a slightly larger circle, and emerges from D2 after spending a time T /2 in this dee. This process repeats until the orbit of the particle reaches the boundary of the dees. At that point, the particle (actually, a beam of particles) is extracted from the cyclotron and used for some experimental purpose.
The operation of the cyclotron depends on the fact that, in a uniform magnetic field, a particle’s orbital period is independent of its radius and its kinetic energy. Consequently, the period of the alternating voltage source need only be set at the one value given by Equation \ref{11.33}. With that setting, the electric field accelerates particles every time they are between the dees.
If the maximum orbital radius in the cyclotron is R , then from Equation \ref{11.32}, the maximum speed of a circulating particle of mass m and charge q is
\[v_{max} = \frac{qBR}{m}. \nonumber \]
Thus, its kinetic energy when ejected from the cyclotron is
\[\frac{1}{2}mv_{max}^2 = \frac{q^2B^2R^2}{2m}. \nonumber \]
The maximum kinetic energy attainable with this type of cyclotron is approximately 30 MeV. Above this energy, relativistic effects become important, which causes the orbital period to increase with the radius. Up to energies of several hundred MeV, the relativistic effects can be compensated for by making the magnetic field gradually increase with the radius of the orbit. However, for higher energies, much more elaborate methods must be used to accelerate particles.
Particles are accelerated to very high energies with either linear accelerators or synchrotrons. The linear accelerator accelerates particles continuously with the electric field of an electromagnetic wave that travels down a long evacuated tube. The Stanford Linear Accelerator (SLAC) is about 3.3 km long and accelerates electrons and positrons (positively charged electrons) to energies of 50 GeV. The synchrotron is constructed so that its bending magnetic field increases with particle speed in such a way that the particles stay in an orbit of fixed radius. The world’s highest-energy synchrotron is located at CERN, which is on the Swiss-French border near Geneva. CERN has been of recent interest with the verified discovery of the Higgs Boson (see Particle Physics and Cosmology ). This synchrotron can accelerate beams of approximately \(10^{13}\) protons to energies of about \(10^3\) GeV.
Example \(\PageIndex{1}\): Accelerating Alpha-Particles in a Cyclotron
A cyclotron used to accelerate alpha-particles \((m = 6.64 \times 10^{-27} kg, \, q = 3.2 \times 10^{-19}C)\) has a radius of 0.50 m and a magnetic field of 1.8 T. (a) What is the period of revolution of the alpha-particles? (b) What is their maximum kinetic energy?
Strategy
- The period of revolution is approximately the distance traveled in a circle divided by the speed. Identifying that the magnetic force applied is the centripetal force, we can derive the period formula.
- The kinetic energy can be found from the maximum speed of the beam, corresponding to the maximum radius within the cyclotron.
Solution
- By identifying the mass, charge, and magnetic field in the problem, we can calculate the period: \[T = \frac{2\pi m}{qB} = \frac{2\pi (6.64 \times 10^{-27} kg)}{(3.2 \times 10^{-19}C)(1.8 T)} = 7.3 \times 10^{-8} s. \nonumber \]
- By identifying the charge, magnetic field, radius of path, and the mass, we can calculate the maximum kinetic energy: \[\frac{1}{2} mv_{max}^2 = \frac{q^2B^2R^2}{2m} = \frac{(3.2 \times 10^{-19}C)^2(1.8 T)^2(0.50 m)^2}{2(6.65 \times 10^{-27}kg)} = 6.2 \times 10^{-12}J = 39 \, MeV. \nonumber \]
Exercise \(\PageIndex{1}\)
A cyclotron is to be designed to accelerate protons to kinetic energies of 20 MeV using a magnetic field of 2.0 T. What is the required radius of the cyclotron?
0.32 m


5.17: Introduction to Using a Decision Tree
What you’ll learn to do: describe the components and use of a decision tree
Despite the limitations of strict rational decision making, there is no doubt that it still has significant value—especially as we refine and improve our abilities to predict costs and market outcomes for our potential actions. When a business feels it has a reasonably accurate measurement of potential costs and a reasonable prediction of likely future outcomes, that data can be used to calculate the likely value of decision pathways. A useful tool for this is the decision tree, which we are going to learn about now.
Contributors and Attributions
CC licensed content, Original
- Introduction to Decision Trees. Authored by : Aaron Spencer and Lumen Learning. License : CC BY: Attribution


12.2: Randomization Tests - Two Conditions
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Learning Objectives
- Compute a randomization test of the difference between independent groups
The data in Table \(\PageIndex{1}\) are from a fictitious experiment comparing an experimental group with a control group. The scores in the Experimental Group are generally higher than those in the Control Group with the Experimental Group mean of \(14\) being considerably higher than the Control Group mean of \(4\). Would a difference this large or larger be likely if the two treatments had identical effects? The approach taken by randomization tests is to consider all possible ways the values obtained in the experiment could be assigned to the two groups. Then, the location of the actual data within the list is used to assess how likely a difference that large or larger would occur by chance.
| Experimental | Control |
|---|---|
| 7 | 0 |
| 8 | 2 |
| 11 | 5 |
| 30 | 9 |
First, consider all possible ways the \(8\) values could be divided into two sets of \(4\). We can apply the formula from the section on Permutations and Combinations for the number of combinations of \(n\) items taken \(r\) at a time and find that there are \(70\) ways.
\[_{n}\textrm{C}_r = \frac{n!}{(n-r)!r!} = \frac{8!}{(8-4)!4!} = 70\]
Of these \(70\) ways of dividing the data, how many result in a difference between means of \(10\) or larger? From Table \(\PageIndex{1}\)you can see that there are two rearrangements that would lead to a bigger difference than \(10\):
- the score of \(7\) could have been in the Control Group with the score of \(9\) in the Experimental Group and
- the score of \(8\) could have been in the Control Group with the score of \(9\) in the Experimental Group
Therefore, including the actual data, there are \(3\) ways to produce a difference as large or larger than the one obtained. This means that if assignments to groups were made randomly, the probability of this large or a larger advantage of the Experimental Group is \(3/70 = 0.0429\). Since only one direction of difference is considered (Experimental larger than Control), this is a one-tailed probability. The two-tailed probability is \(0.0857\) since there are \(6/70\) ways to arrange the data so that the absolute value of the difference between groups is as large or larger than the one obtained.
Clearly, this type of analysis would be very time consuming for even moderate sample sizes. Therefore, it is most useful for very small sample sizes.
An alternate approach made practical by computer software is to randomly divide the data into groups thousands of times and count the proportion of times the difference is as big or bigger than that found with the actual data. If the number of times the data are divided randomly is very large, then this proportion will be very close to the proportion you would get if you had listed all possible ways the data could be divided. The link below goes to a web page that can do these calculations.


 The video below introduces you to some principles for creating daily task lists. When you are finished, move to the next section to choose strategies for managing your tasks.
Managing Daily Tasks Video Transcript
By the time you’ve finished the day today, what will you have accomplished? In this video, you will learn to create a system to manage your daily to-do list, so that you can prioritize effectively and use your time efficiently. For every task you have to complete, you need to decide:
1. When do I need to finish this by?
2. How much time will it take? and
3. Is this task a priority, or can it wait until later?
 So, how do you make a daily task list? First, you will want to find the format that works best for you. Some people prefer to use a paper planner. Others prefer to use the reminders function on their phone, or another task list app. Choose the format that meets your needs the best. Second, you will need to divide your work into tasks that are specific, measurable, and achievable. In general, a task should be anything that you can complete in a single work period – for example, in an hour or less. If you have a large project, break it down into smaller tasks.
Third, you will need to assign your tasks to a specific day. Make sure that each day’s task list is reasonable and achievable.
Fourth, prioritize each day’s tasks. What tasks must be finished today. Be sure that you complete these before moving on to lower priority tasks. After the most important things have been done, move on to the less urgent tasks.
 Most often, you will move the task to another day. You might also decide that the task isn’t important, and delete it from your list.
Finally, be sure to reward yourself for a day’s work well done. If you are able to create an effective motivational system for yourself, you will be less likely to procrastinate, and more likely to finish your most important work each day.
To summarize, a daily to-do list can help you stay on track and achieve your most important goals. Choose a tool that works for you, organize your tasks, prioritize them, and work through your list each day.