The Runs Test for Random Sequences

Given a sequence of data, one question that we may wonder is if the sequence occurred by chance phenomena, or if the data is not random. Randomness is hard to identify, as it is very difficult to simply look at data and determine whether or not it was produced by chance alone. One method that can be used to help determine if a sequence truly occurred by chance is called the runs test. The runs test is a test of significance or hypothesis test. The procedure for this test is based upon a run, or a sequence, of data that have a particular trait. To understand how the runs test works, we must first examine the concept of a run. Sequences of Data We will begin by looking at an example of runs. Consider the following sequence of random digits: 6 2 7 0 0 1 7 3 0 5 0 8 4 6 8 7 0 6 5 5 One way to classify these digits is to split them into two categories, either even (including the digits 0, 2, 4, 6 and 8) or odd (including the digits 1, 3, 5, 7 and 9). We will look at the sequence of random digits and denote the even numbers as E and odd numbers as O: E E O E E O O E O E E E E E O E E O O The runs are easier to see if we rewrite this so that all of the Os are together and all of the Es are together: EE O EE OO E O EEEEE O EE OO We count the number of blocks of even or odd numbers and see that there are a total of ten runs for the data. Four runs have length one, five have length two and one has length five Conditions With any test of significance, it is important to know what conditions are necessary to conduct the test. For the runs test, we will be able to classify each data value from the sample into one of two categories. We will count the total number of runs relative to the number of the number of data values that fall into each category. The test will be a two-sided test. The reason for this is that too few runs mean that there is likely not enough variation and the number of runs that would occur from a random process. Too many runs will result when a process alternates between the categories too frequently to be described by chance. Hypotheses and P-Values Every test of significance has a null and an alternative hypothesis. For the runs test, the null hypothesis is that the sequence is a random sequence. The alternative hypothesis is that the sequence of sample data is not random. Statistical software can calculate the p-value that corresponds to a particular test statistic. There are also tables that give critical numbers at a certain level of significance for the total number of runs. Runs Test Example We will work through the following example to see how the runs test works. Suppose that for an assignment a student is asked to flip a coin 16 times and note the order of heads and tails that showed up. If we end up with this data set: H T H H H T T H T T H T H T H H We may ask if the student actually did his homework, or did he cheat and write down a series of H and T that look random? The runs test can help us. The assumptions are met for the runs test as the data can be classified into two groups, as either a head or a tail. We keep going by counting the number of runs. Regrouping, we see the following: H T HHH TT H TT H T H T HH There are ten runs for our data with seven tails are nine heads. The null hypothesis is that the data is random. The alternative is that it is not random. For a level of significance of alpha equal to 0.05, we see by consulting the proper table that we reject the null hypothesis when the number of runs is either less than 4 or greater than 16. Since there are ten runs in our data, we fail to reject the null hypothesis H0. Normal Approximation The runs test is a useful tool to determine if a sequence is likely to be random or not. For a large data set, it is sometimes possible to use a normal approximation. This normal approximation requires us to use the number of elements in each category and then calculating the mean and standard deviation of the appropriate normal distribution.

Irony in The Cask of Amontillado, a Story by Edgar Allan Poe

In his short story â€Å"The Cask of Amontillado,† Edgar Allan Poe tells a tale of murder through the protagonist of the story, Montresor. He is recalling the event years after it happened. Fortunato, the man who gave Montresor a â€Å"thousand injuries . . . [and] ventured upon insult† is walled up in Montresor’s wine cellar. The details of the injuries and insult are never disclosed to the reader, all that is known is that the narrator—Montresor—is angered to the point of homicide. Irony is the key factor in creating an atmosphere of mystery and suspense. Poe uses the setting along with the victim’s name to ultimately enhance the irony in this tale of revenge. The backdrop is one of fun and frivolity, yet the story is bound for a dark and deadly turn. While many people are having a wonderful time at the carnival, Montresor has been plotting murder. Fortunato’s name itself is an ironic aspect of this short story. The name of the victim is more than just a name. The creator of Behind the Name, Mike Campbell writes that Fortunato is a name in Italian, Portuguese and Spanish; Campbell notes that Fortunato stems from â€Å"the Late Latin name Fortunatus meaning ‘fortunate, blessed, happy’† (Campbell); this choice of name is ironic because Fortunato the character turns out to be extremely unfortunate. Both of these ironic aspects help to create suspense in the story. Montresor’s words throughout this story are steeped in irony. When they first meet Montresor says, â€Å"My dear Fortunato, you areShow MoreRelatedFor the Love of God, Poe! Essay1359 Words   |  6 PagesIt is not at all surprising that so many of Edgar Allan Poe’s works explore such themes as death, eyes, the power of the dead over the power of the living, retribution, the human conscience, and especially death and murder. From his disturbingly morbid short story â€Å"The Telltale Heart† to the mysteriously supernatural poem â€Å"The Raven†, Poe’s tales are a direct byproduct of the mayhem experienced in his life, as well as his (arguably) psychologically-tormented mind. Though all of this author’s piecesRead MoreEdgar Allan Poe s The Cask Of Amontillado1232 Words   |  5 PagesPoe’s Irony To develop the analytical paper about the text â€Å"The Cask of Amontillado† by Edgar Allan Poe, some sources will be used to support the thesis statement, which is â€Å"The author uses irony in the text to illustrate the murder of Fortunado by Montresor, who seeks salvation through death†. Also, there is going to be an analysis on the irony found in the text in relation with the story. To support this thesis, I am going to use some examples from some sources such as â€Å"Literary analysis: IronyRead MoreEdgar Allan Poes The Cask of the Amontillado Essay1520 Words   |  7 PagesSomething Unexpected Poe has written a several different stories relating to being buried alive, â€Å"The Premature Burial† and â€Å"The Cask of Amontillado† being the most popular. Edgar Allan Poe â€Å"was one of the seminal American poets and short story writers of the nineteenth century† he was an influencer for writers like Charles Baudelaire and Jules Verne. Poe lost both of his parents as a child and was raised with a foster family and lost his foster mom early, too. He lost many of his loved onesRead MoreThe Cask of Amontillado by Edgar Allan Poe888 Words   |  4 PagesThe Cask of Amontillado by Edgar Allan Poe In ?The Cask of Amontillado?, Edgar Allan Poe takes us on a trip into the mind of a mad man. Poe uses certain elements to convey an emotional impact. He utilizes irony, descriptive detail of setting, and dark character traits to create the search of sinful deceit. Poe also uses first person, where the narrator is the protagonist who is deeply involved. The purpose is to get the reader to no longer be the observer. He wants them to see with MontressorRead MoreTheme Of Young Goodman Brown And The Cask Of Amontillado970 Words   |  4 PagesHawthorne and Edgar Allan Poe compliment and counteract this goal in their works â€Å"Young Goodman Brown† and â€Å"The Cask of Amontillado†, respectively, is with irony. Their masterful use of irony engages the reader in the work and invites them to consider the story and the characters’ intentions. The irony presented in â€Å"Young Goodman Brown† by Nathaniel Hawthorne and â€Å"The Cask of Amontillado† by Edg ar Allan Poe allows us to understand the emotions of the characters and the mood of the work, however, Poe utilizesRead MoreThe Theme of Revenge in â€Å"The Cask of Amontillado† Essay1629 Words   |  7 PagesEdgar Allan Poe’s â€Å"The Cask of Amontillado† is a frightening and entertaining short story about the severe consequences that result from persistent mockery and an unforgiving heart. Poe’s excellent use of Gothicism within the story sets the perfect tone for a dark and sinister plot of murder to unfold. â€Å"The Cask of Amontillado† simply overflows with various themes and other literary elements that result from Poe’s Gothic style of writing. Of these various themes, one that tends to dominant the storyRead MoreAnalysis Of Edgar Allan Poe s The Cask Of Amontillado 945 Words   |  4 Pages2014 Revenge and Irony A friendship is based on trust, but do we truly know anyone in the way we think? In â€Å"The Cask of Amontillado† written by Edgar Allan Poe, a man named Fortunato is about to find out what kind of ‘friend’ Montresor really is. Montresor shows himself to be friendly with Fortunato, but deep down he feels nothing but hate for him. In different ways, both of these men are proud and appear upper class, yet both have faults which will be there undoing. Edgar Allan Poe uses languageRead MoreCask of Amontillado Thesis Theme1058 Words   |  5 PagesIn The Cask of Amontillado, Edgar Allen Poe displays the theme of revenge. In the story, Montressor narrates the story and feels he has been wronged by Fortunado and vows for vengeance against him. Montressor attempts to justify his future crime to the reader. â€Å"A wrong is unredressed when retribution overtakes its redresser. It is equally unredressed when the avenger fails to make himself felt as such to him who has done the wrong.† (Poe 101) Fortunado is unaware of the wrong he caused MontressorRead MoreThe Cask Of Amontillado By Edgar Allan Poe1575 Words   |  7 Pagestale, â€Å"The Cask of Amontillado.† Montresor plots and kills an unwary friend/foe during carnival time for motives that are unclear. The author of this tale, Edgar Allan Poe, influenced by his somewhat tragic life and one of the most influential Gothic writers, uses symbolism and irony to show the multitude of complicated motives of the narrator in his famous horror story. Upon examining Edgar Allan Poe’s life, one is not surprised that he chooses to write such gloomy and sinister stories. Poe’s lifeRead MoreHow The Cask of Amontillado Uses Symbolism and Irony1291 Words   |  6 Pagesstop, yellow means slow down, and the green means to proceed. Another technique used in â€Å"The Cask of Amontillado†is irony. Irony, (in literature), is when the writer uses words to emit a meaning that is usually the opposite of its literal meaning. It is used to catch the reader’s attention and to give the text more depth. In the short story, â€Å"The Cask of Amontillado†, there is verbal and dramatic irony. Irony is important because it allows the reader to transmit an intense meaning without having to

Crime Causation and Diversion Paper Free Essays

Crime Causation and Diversion Paper University of Phoenix Online Juvenile Justice Systems and Processes CJA/473 LeDetra Jones October 01, 2012 Crime Causation and Diversion Paper Today the public became more concern about youth crime rising within the community. The public also believes that some of juvenile delinquents do not belong behind bars whereas others do. In the concern of the juveniles who do not belong behind bars the public started creating community outreach programs, intervention, and prevention programs. We will write a custom essay sample on Crime Causation and Diversion Paper or any similar topic only for you Order Now These programs create an environment for the youth to understand the consequences of their actions, responsibility, and help. This paper will be examining two juvenile diversions, interventions, and prevention programs, which are Island Girl Power and Inafa’ Maolek. The following will be addressed in the paper: How do they work to reduce juvenile crime (Based on analysis). Programs major goals, objectives, and core beliefs? Who are the key participants? Services provided? Which program is most effective at reducing crime and why? How programs reduce juvenile crime and major goal, objectives, and core beliefs The Inafa’Maolek is Guam’s only organization that dedicates exclusively to peacemaking, especially in settling disputes such as mediation, restorative justice, and conflict resolution training of all ages (Inafa’Maolek, 2010). The trainings conducted by Inafa’Maolek helps establish peer mediation programs in more than 30 public schools ranging from elementary to high schools. These special programs currently in schools include Date Rape Workshops, Bullying Workshops, and Hate Crimes Workshops. The organization provides programs to all sectors in the community, including senior citizens (Manamko) as well as DYA families. The heart and souls of its work focuses on mediating conflicts, many referred by Superior Court Judges (Inafa’Maolek). Island Girl Power is a program on Guam that works to Empower, Encourage, and Inspire young ladies to make positive lifestyle choices. This program believes that if the island works together to empower, ncourage, and inspire the young ladies of Guam to make a positive lifestyle choice by promoting positive male and female role models it helps to prevent the abuse and neglect in the families for generations to come (Blaz, 2009). Island Girl Power is a local program, taken, and expanded from a national program Girl Power. Its prevention program focuses on offering young ladies a variety of classes, activities in hopes of expanding their goals. It is a safe place where people can volunteer at their leisure and is expanding into the community through volunteers and center willing to offer classes (Blas, 2009). This program is a clubhouse more like and located in Dededo, GU. Their hours of operations are from Monday through Friday 8a. m. -5p. m. , and Saturdays 9a. m. -3p. m. This clubhouse offers many activities such as dancing, self-defense, and big sister club, etc. The reason this club focuses on young ladies is that it helps them to gain self pride, become wiser, and make smarter choices in life. Young ladies are usually self conscious about themselves and rebellious than males. They are more vulnerable to the outside world once they step into it. While the two organizations/clubs works in many ways of preventing and interventions juvenile delinquency, here are the clubs/organizations major goals, objectives, and core beliefs of what it can provide for the community as well as juveniles. The mission statement for the Inafa’Maolek is a conflict resolution organization dedicated to reducing violence related litigations and foster peace and harmony in schools, Workplaces, and communities (Inafa’Maolek, 2009). The vision statement for the Inafa’Maolek is that it will enhance peacemaking and reduce violence related litigation through advocacy, mediation, and education (Inafa’Maolek, 2009). The mission statement for the Island Girl power is that we want the girls to know just how special they are here at Island Girl Power! We believe that each girl can create a positive change in her life. If every girl makes it her goal to do her best, how can go wrong? We want to give girls ages seven to 14 a safe and enjoyable place to learn and play (Blas, 2010). By making the girls wiser to the world around them girls will make smarter choices in life- and maybe even help a friend. By accepting all girls, regardless of the income or status, we help bridge the gap between the haves and the have-nots (Blas, 2010). When a girl joins a club it means so much to them, the acceptance, and the pride they feel when they are part of a group is irreplaceable. We as an organization help girls understand the importance of community service by showing them the example of the wonderful people who volunteer to create a place just for them (Blas, 2010). The clubhouse goal is to decrease the incidence of teenage pregnancy, suicide, sexual, and substance abuse. These problems are the most serious challenges facing our girls today. We know that we cannot change the island overnight, but we can make it better -One girl at a time! Blas, 2010). The two organizations help juvenile delinquents/youths in the community to improve themselves to make wiser decisions and to give a sense of direction to where they should be in the future. Knowing that the organizations/clubs are do their best to provide the community with the proper services to help the children to become better helps the people to get over that there are other outlets for their teens. With major goals, objectives, and core beliefs here are the key participants of the programs and the services the programs provide. The key participants of these programs and services provided The key participants of these programs are teens in intervention, juvenile delinquents, teens in prevention (joining so they do not commit the crime), and teen volunteers. These key participants help the organizations to better understand teens nowadays. Juvenile delinquents in the early days probably have committed more serious crimes than teens today. There was not enough services provided to the teen besides, juvenile correction facilities. The community is very limited on the help needed for their children, and some are forced to look elsewhere that type of help. Because the key participants are teens whether trouble or just interested in the program, there are services that the programs for them. The services that Inafa’Maolek provides are one, peace theater- where teens perform a situation and how to bring instead of conflict. Second, mediation- where two parties meet privately to work out a solution. Third, restorative justice- RJ sessions provide a context within which people can take responsibility for their actions, restitution are made to victims, offenders are reintegrated, and harmony are restored to a community. Fourth, conflict coaching (Inafa’Maolek, 2009). These are the main services that this program provides, other services include; volunteering in schools, socializing with other teens, restore the community, and helping others who need help. The services that Island Girl Power provides are encouraging girls on their personalities, social skills, looks, and abilities to please other rather than develop their own interests and aspirations. Island style dance classes so that they can learn about who they are and where they come from. Self-defense classes so that young ladies have that skill to protect themselves or another against harm. Occasional classes in Gef Pago as well as the big sister service where an older girl will help guide the younger ones. Of the services provided by the two programs the most effective program to reduce juvenile crime would be Inafa’Maolek. Most effective program The reason for this decision is the Inafa’Maolek provides services and outcomes used to for schools and became very popular to teens, the government, other programs. It also provides more services than other treatment programs or organizations on the island. There are no other program that provides these services than Inafa’Maolek. It has shown that when teens take these sessions it guides them into becoming better person not only them but for his or her families. Conclusion In conclusion, as the community starts to see more troubled teens/delinquents these organizations/programs are ready to fight these behaviors to make them a better person. These programs were created to help the children because they are the future leaders and so forth. By understanding what drives them to commit these crimes is a mystery and why these programs try to bring all teens and their families to help one another. How to cite Crime Causation and Diversion Paper, Essay examples