How to Find Degrees of Freedom in Statistics

How to Find Degrees of Freedom in Statistics Many statistical inference problems require us to find the number of degrees of freedom. The number of degrees of freedom selects a single probability distribution from among infinitely many. This step is an often overlooked but crucial detail in both the calculation of ​confidence intervals and the workings of hypothesis tests. There is not a single general formula for the number of degrees of freedom. However, there are specific formulas used for each type of procedure in inferential statistics. In other words, the setting that we are working in will determine the number of degrees of freedom. What follows is a partial list of some of the most common inference procedures, along with the number of degrees of freedom that are used in each situation. Standard Normal Distribution Procedures involving standard normal distribution  are listed for completeness and to clear up some misconceptions. These procedures do not require us to find the number of degrees of freedom. The reason for this is that there is a single standard normal distribution. These types of procedures encompass those involving a population mean when the population standard deviation is already known, and also procedures concerning population proportions. One Sample T Procedures Sometimes statistical practice requires us to use Student’s t-distribution. For these procedures, such as those dealing with a population mean with unknown population standard deviation, the number of degrees of freedom is one less than the sample size. Thus if the sample size is n, then there are n - 1 degrees of freedom. T Procedures With Paired Data Many times it makes sense to treat data as paired. The pairing is carried out typically due to a connection between the first and second value in our pair. Many times we would pair before and after measurements. Our sample of paired data is not independent; however, the difference between each pair is independent. Thus if the sample has a total of n pairs of data points, (for a total of 2n values) then there are n - 1 degrees of freedom. T Procedures for Two Independent Populations For these types of problems, we are still using a t-distribution. This time there is a sample from each of our populations. Although it is preferable to have these two samples be of the same size, this is not necessary for our statistical procedures. Thus we can have two samples of size n1 and n2. There are two ways to determine the number of degrees of freedom. The more accurate method is to use Welch’s formula, a computationally cumbersome formula involving the sample sizes and sample standard deviations. Another approach, referred to as the conservative approximation, can be used to quickly estimate the degrees of freedom. This is simply the smaller of the two numbers n1 - 1 and n2 - 1. Chi-Squarefor Independence One use of the chi-square test is to see if two categorical variables, each with several levels, exhibit independence. The information about these variables is logged in a two-way table with r rows and c columns. The number of degrees of freedom is the product (r - 1)(c - 1). Chi-Square Goodness of Fit Chi-square goodness of fit  starts with a single categorical variable with a total of n levels. We test the hypothesis that this variable matches a predetermined model. The number of degrees of freedom is one less than the number of levels. In other words, there are n - 1 degrees of freedom. One FactorANOVA One factor analysis of variance (ANOVA) allows us to make comparisons between several groups, eliminating the need for multiple pairwise hypothesis tests. Since the test requires us to measure both the variation between several groups as well as the variation within each group, we end up with two degrees of freedom. The F-statistic, which is used for one factor ANOVA, is a fraction. The numerator and denominator each have degrees of freedom. Let c be the number of groups and n is the total number of data values. The number of degrees of freedom for the numerator is one less than the number of groups, or c - 1. The number of degrees of freedom for the denominator is the total number of data values, minus the number of groups, or n - c. It is clear to see that we must be very careful to know which inference procedure we are working with. This knowledge will inform us of the correct number of degrees of freedom to use.

A Fight for Renaissance by Anne Bradstreet

A Fight for Renaissance by Anne Bradstreet Anne Dudley Bradstreet was Americas first published poet. Cotton Mather described her as: a gentlewoman whose extraction and estate were considerable. She was an intelligent, well-educated poet, wife, and mother, who contradicted almost all of the stereotypes about stiff, cold Puritans. She used her talents to promote womens rights, to describe life as a Puritan woman in colonial America, and to let her husband and children know how much she loved them. Some historians have said that Anne described her own work as lowly, meanly clad, poor, ragged, foolish, broken, and blemished to appease critical males. It was the support of her family and friends who encouraged her to continue the struggle despite incredible societal pressure and rigorous odds. Her poems dealt with the hardships of life in the early settlements, the Puritan religion, and in subtle ways, the role of women in those times. Because she was a woman, her work was strongly criticized, and some believed that she stole the ideas for her writing from men. In her earlier works, Bradstreet wrote in the style of male authors that she admired. She was careful about expressing her true feelings, and this limited her abilities. She wrote for her own satisfaction, and shared her poetry with family and friends. Without her knowledge, her brother-in-law, Rev. John Woodbridge, took a manuscript of her poems to England with him and had them published in a book called, The Tenth Muse Lately sprung up in America By a Gentlewoman in those parts, which Anne had dedicated to her father. Rev. Woodbridge wrote By a Gentlewoman in the title to stress that Anne Bradstreet was a virtuous Puritan who did not neglect her duties for her writing. These later poems were her claim to fame, bec ause they reflected actual experience (as a wife, as a mother, and a woman in seventeenth-century New England), combined with a poets imagination, warmth, and a straightforward humanitarian philosophy. Anne struggled to write poetry in a society that was hostile to imagination and to a woman writer. Seventeenth century Puritan women were expected to be deferential, and her education and her privileged status as a close relative of two governors could not completely protect her from the scorn and persecution that other women who stepped out of their role in Puritan society generally received. Anne wrote quite a bit about her experiences as a wife, mother, grandmother, and as a settler in colonial America. She also wrote about nature, science, religion, the social and political happenings of the time, and about her feelings towards the biases women of her time faced. Anne Bradstreet was, in some ways, an early feminist. Through her poetry, she asserted the right of women to learning and expression of thought. The stereotypical Puritan standards at that time indicated that a womans place was in the home attending to the family and her husbands needs. Women were generally considered intellectually inferior. The attitude of Annes day was accurately expressed by Reverend Thomas Parker, a minister in Newbury, Massachusetts, in a letter to his sister, Elizabeth Avery, in England: Your printing of a book, beyond the custom of your sex, doth rankly smell. As if the social pressure wasnt bad enough, many women faced crushing workloads and a severe lack of free time, as well. Some women suffered from the lack of an education. Others internalized the belief in intellectual inferiority Western society tried to push on them from nearly every authoritative voice. It was Annes personal situation such as an extensive education, support of friends and an influential family, which gave her the means to cope with some of these obstacles. One of her later works, In Honor of That High and Mighty Princess Queen Elizabeth of Happy Memory, defiantly proclaims her opinion that women are worth more than a mans servant. Anne was deeply interested in relating the arduous life of the early settlers in her poems. Her work provides an excellent view of the difficulties she and her fellow colonists encountered. From the loss of a house to fire, to the risks and difficulties of child-bearing, to the pain of losing children, Anne described such situations with deep emotion and faith. Her writing gives modern-day readers a glimpse into Puritan views of salvation and redemption, and reveals faith that continued even in the midst of doubt. The Puritans believed that suffering was Gods way of preparing the heart for accepting His grace. Anne had difficulty reconciling herself with this idea, and she wrote about how she struggled to do everything that she could to give into His will. Puritan wives were expected to defer to their husbands within the family structure, but they were treated as fully equal in the souls vocation and in church affairs and enjoyed extensive legal and social protection against husbandly abuse of power. The delicate complexity of this view was perhaps best expressed in the couplet which Anne Bradstreet addressed to men: Preeminence each and all is yours/Yet grant some small acknowledgment of ours. Puritans also abhorred any waste of time, energy, or talent as a sin against God; ultimately, this worked in favor of talented women such as Bradstreet and defined early indications of the womens movement and clearly questioned the role of women in Puritanical society. References Blackstock, Carrie Galloway. Anne Bradstreet and Performativity: Self-Cultivation, Self-Deployment. Early American Literature 32. 3 (1987): 222-48. Bush, Sargent, Jr. American Poetry Begins: The Confident Modesty of The Tenth Muse. Wisconsin Academy Review: A Journal of Wisconsin Culture 38. 1 (Winter 1981-1982): 8-12. Caldwell, Patricia. Why Our First Poet Was a Woman: Bradstreet and the Birth Of an American Poetic Voice. Prospects: An Annual Journal of American Cultural Studies 13 (1978): 1-35. Doriani, Beth M. Then have ISaid with David: Anne Bradstreets Andover Manuscript Poems and the Influence of the Psalm Tradition. Early American Literature 24:1 (1979): 52-69. Eberwein, Anne Bradstreet (c.1612-1672). Legacy: A Journal of American Women Writers 11:2 (1984): 161-69. Kopacz, Paula. To Finish whats Begun: Anne Bradstreets Last Words. Early American Literature 23:2 (1978): 175-187. Margerum, Eileen. Anne Bradstreets Public Poetry and the Tradition of Humility. Early American Literature 17:2 (fall 1982): 152-60. Salska, Agnieska. Puritan Poetry: Its Public and Private Strain. Early American Literature 19:2 (Fall 1984): 107-121. Schweitzer, Ivy. Anne Bradstreet Wrestles with the Renaissance. Early American Literature 23:2 (1978): 291-312. Sweet, Timothy. Gender, Genre, and Subjectivity in Anne Bradstreets Early Elegies. Early American Literature 23:2 (1978); 152-174.

Leadership Development Case Study Example | Topics and Well Written Essays - 500 words

Leadership Development - Case Study Example ermed as the major decision taken in the recent times and has been brought about in a forced way owing to the company performance and non satisfactory responses from the profit index. The global trends and the overall reduction in the profit as a result of it is another reason that has brought about such a move. The larger states such as Russia and its overall standing in the global economic market had its impact on the Ford’s overall performance leading to tougher decisions being made. Mr. Odell may have contributed on the structural function and strengthening of the Ford’s existence in the global innovations, however the domain and context of market capturing still desires to be gripped further in order to make most of the market potential. The experimental work on the Mustang comes as a challenge that has yet to be practically tested and determined with regard to its potential success. Mr. Farley has also got his work cut out in the form of fulfilling for the vacuum that is being created through the step wise retirement of the number of individuals who were long associated with the company. Replacing the expertise with relatively equal and effectively able individuals is a challenge that needs to be resolved. Bringing Ford to the previous top level of success and high profits is another challenge and goal that the two individuals must set before them in order to overcome the existing challenges. The job rotation helps the leadership in a way that it allows the individuals working in a different environment, meaning exposure to larger domain and coming up with improved performances. Rotation allows the employees working with freshness of mind and removes the element of redundancy and boredom by repeatedly working in a similar environment and similar surroundings. The impact of rotation can be either positive or negative for a given organization. It can be positive if it is handled properly as it promotes productivity and brings along diversity in the cause

Civil War Research Paper Example | Topics and Well Written Essays - 1750 words

Civil War - Research Paper Example Revolution is actually a change whereby legitimacy of one system is terminated and another originated within the same society, however, this change may not necessarily brought about by force or violence. History narrates the stories of several important revolutions e.g. revolutions in England and France of 1688 and 1848 respectively had not observed any military conflict. Scope of civil war is broad and it may accompany revolution, but in the great French Revolution, it only played a secondary part. Like revolution, civil war can also be distinguished from insurrection, which is a struggle from the bottom up, an uprising of a more or less politically unorganized group against an established authority. Civil war is horizontal, insurrection vertical, conflict which may result in huge numbers of fatalities and ineffective use of valuable resources (Hironaka, 2005, p.3). Classifications of Civil Wars The concept of war is as old as the human being is attached to religion, politics, and s ocial reforms. Likewise, civil wars may also be classified in terms of these three aspects i.e. religion, political or strategic objectives, and social reforms. The rise of Protestantism caused a whole series of religious civil wars between 1550 and 1648. The civil wars in England between during the years 1641 to 1651, in the United States from 1861 to 1865, and in China from 1921 to1928, were political. The history of ancient Greece and Rome shows a whole series of social civil wars between rich and poor, aristocrats and plebians. The Russian civil war from 1918 to1921was primarily a social war between the upper class on the one hand and the city proletariat aided by the peasants on the other. Religious civil wars have usually been very bloody and ruthless. Social civil wars tend to resemble them in this respect; while political civil wars are commonly humane, as years ago. The Thirty Years War (1618-1648) primarily fought in Germany was indescribably ferocious; the recent civil wa r in Russia was marked by much cruelty; while the American Civil War was comparatively well controlled (Hironaka, 2005). Characteristics of Different Civil Wars The character of civil war varies considerably according to the type of political organization in the country in which it occurs. In unitary states civil war is likely to be amateurish and bungling in its early stages. The old government is weakened by the withdrawal of large numbers of its trained personnel, who then proceed to improvise an opposition government which does not at first function very efficiently. The English civil war of 1641 to 1651 and the American Civil War are cases in point (Keegan, 2009). In federated states, civil war closely resembles international war. Here organized functional governments already exist and the task of generating a civil war between them is relatively simple, especially when the nature of the federal bond approximates a league rather than a closer union. The Thirty Years War, the Wa r of the Sonderbund in Switzerland in 1848, and the American Civil War afford varying instructions of the nature of the civil conflict in federated states. In his second inaugural address, Abraham Lincoln said â€Å"slavery was some how cause of the war† (Brook and Nurphy, 2009). Civil wars in colonial states are in general much like civil

Essay --

This short story starts out by setting the scene. The American and a girl sit at a table in front of a building where they were waiting on a train to arrive. It is very hot outside and the background is hills described to be long and white. â€Å"They look like white elephants,† she said. â€Å"I’ve never seen one,† the man drank his beer. â€Å"No you wouldn’t have.† â€Å"I might have,† the man said. â€Å"Just because you say I wouldn’t have doesn’t prove anything.† (Hemingway 6-10) These lines from Ernest Hemingway depict how a man can overpower a woman with his chosen words and tone. In this conversation between the American and the woman, you will see the woman become less and less sure of herself and eventually she can’t even make her own decisions. The girl is even unsure if she wants water with her drink. â€Å"We want two Anis del Toro.† â€Å"With water?† â€Å"I don’t know,† the girl said. â€Å"Is it good with water?† (Hemingway 19-21) Marsh 2 In the previous lines you can see the girl is skeptical. She is waiting for reassurance from the American. â€Å"The Huffington Post† featured an article which came from a study conducted by the University of Texas. Students observed the behavior of boys and girls in a room and how they responded to social cues. Each child was left alone with his mother and were told by their mothers not to touch a forbidden object. The boys not only touched the object more frequently than girls but they ignored the mother’s voice telling them no when they picked up the forbidden object. The girls touch the object less frequently and when they did they often looked at their mother for reassurance. The boys rarely paid attent... ... comforting the girl and telling her to come in the shade. This is him protecting her and giving the girl security which she doesn’t have on her own. The train finally arrives which seems to have been what the girl wanted because she did not wish to discuss the topic anymore. Marsh 7 Works Cited: Zweig, Robert. â€Å"Literature: An Introduction to Reading and Writing†: Hills are Like White Elephants(1927) Tenth Edition. Pearson Education 2004. 350-353. Print. Biddle, Tabby. â€Å"The Huffington Post† : Why Do Women Feel They Need Permission? Jan 30,2009 Hoplock, Lisa â€Å"Science of Relationships†: How You Doin’? Self-Esteem Affects How People Flirt (2014) www.scienceofrelationships.com

One of My Worst Days

I received unbelievable news that changed my life forever. While sitting at â€Å"Designing U† hair salon with my mother Lashed all morning, boredom soon kicked in. I logged onto Backbone and started reading many deviating posts that all mentioned a guy named Drew. As time went by, I started to wonder was everyone talking about my church friend Dander Johnson. Once realization set in, my biggest fear became true.While continuing to read the Backbone posts, I came across Dress cousin Davison Johnson status. Davison explained how he couldn't believe something this tragic appended, â€Å"Drew was the light of everyone eyes, he was always caring and helping anyone with anything†, says Davison. Not only was Drew his cousin they were like two peas in a pod. From going to the same school all their lives , to becoming stars on Bilabial High School football team. As minutes passed by my father Charles contacted my mother lashed and l.He informed us that Drew had been out all mor ning with two of his friends. The two other teenagers were a boy and a girl, whom I don't know personally till this day. The young lady was known to be the driver, according to her, while driving down highway 78, he swerved to dodge another vehicle and lost control of the car. With the vehicle flipping and neither of the teens wearing seat-belts it didn't make the situation better. The two teens were rushed to the RE and My church friend Drew was pronounced dead at the scene.I had many unanswered questions to why this occurred. For instance, â€Å"Why did Drew have to be the only one? † â€Å"Why couldn't he leave this world a peaceful way† and â€Å"Why couldn't his family and I see him walk across the stage this year? â€Å". Drew would've been a senior this year and would've had the chance to shine on the football like he Ovid doing. His football number, #52, was spray painted onto BBS football field as the team played in the playoffs last November.Their school al so recognized his family and framed his Jersey. This incident brought everyone closer. Till this day everyone still remembers him as the kid who dreamed to make it to the NFG one day and as the loving and caring person he was. I have realized that people's leave sooner than expected and no longer question God because I know he makes no mistakes. I always tell myself that Drew and I will reunite one day. One of My Worst Days By Closures

Martin Luther King - 975 Words

The month of May is set aside each year to celebrate African American History. When you think of Black History month, the first thing that we all think about is the historical speech, â€Å"I have a dream†. However, he did so much more than just present the speech that we all are familiar with had moral values that he stood for and was the leader of many civil right movements. This man is known as Martin Luther King. He was born on January 15, 1929 in Atlanta, Georgia. Martin Jr.’s parents were Reverend Martin Luther King, Sr. and Alberta Williams King. King Jr.’s father and his grandfather were both ministers and Martin’s mother was a school teacher. He had a sister by the name of Christine and a brother by the name of Alfred. His mother†¦show more content†¦Johnson. Throughout his efforts he was arrested up to twenty times and he was physically abused at least four times. In 1964, Martin Luther King was the youngest man to ever receive t he Noble Peace Prize. This was a high ranked award and was recognized worldwide. When was informed that he had been chosen for the prize money he stated that he was going to give a portion equally 54,123 to further the civil right movements. One evening on April 4, 1968, Martin Luther King was staying in a motel in Memphis, Tennessee. He was there to lead a protest march in sympathy of garbage workers who were on strike. He was standing on his balcony outside one early evening right outside his motel room when he was shot and assassinated by a single shot which hit his face and neck. Within an hour he was pronounced dead at 7:05 p.m. at St. Joseph’s Hospital. Not too long after the murder, a package was dropped off near the door of Canipes Amusement Co. close by the scene, and a white Mustang sped away. The Memphis police officers found the pack to contain a .30-06 rifle, ammunition, a pair of binoculars, and other items. In 1968, the national holiday Martin Luther Kin g Jr. Day was designated to honor this exceptional man and his efforts in the civil right movements. It is observed on the third Monday of January each year, which is around the time of Kings birthday, January 15. It was officially observed in all 50 states for the first time in 2000.Show MoreRelatedThe And Martin Luther King2263 Words   |  10 Pageshr and Martin Luther King were seekers of justice and embraced liberal protestant outlooks early on. The similarities in their theology, while not surprising as King derived much of his material from Niebuhr, proved to be uncanny in that they both concerned themselves with how the church should operate within society, the way love should be implemented in the ethics of individuals, and social change brought forth by nonviolence. Niebuhr’s quest for justice was in result to the horrific events heRead MoreMartin Luther King Jr.1078 Words   |  5 PagesMartin Luther King, Jr., was a very strong person, constantly fighting for w hat he believed in, which was equality for African Americans. He was not scared to stand up and tell the world what he wanted for society. He was fearless and did everything in his power to prove a point. Martin Luther King, Jr., was the strongest individual of his time, for he fought until death, which proves how much he was willing to risk his life to make the world an equal place. Growing up, he had a very interestingRead MoreMartin Luther King Jr.1144 Words   |  5 PagesMartin Luther King Jr. (January 15 1929-April 4, 1968) Brief Summary (of who MLK Jr. is): Martin Luther King Jr. was a Baptist minister and an activist who led the civil rights movement in the 1950. He was a fundamental force behind the civil rights movement that ended legal segregation. He was awarded the Nobel Peace Prize in 1964. But he was sadly assassinated in 1968 on a second floor balcony of Lorraine Motel in Memphis, Tennessee†¦ Childhood: Martin Luther was never poor. He lived with a middleRead MoreDr. Martin Luther King874 Words   |  4 PagesDr. Martin Luther King, Jr. writes this letter as a response to the clergymen, who criticized and impeded the nonviolent campaign led by King in Birmingham. In his long letter, Marin Luther King presents a good deal of rational reasons for why the nonviolent campaign should be done in Southern America. He also demonstrates his unmovable determination to accomplish the goal of this nonviolent campaign. Obviously, King intends to awake the clergymen and other opponents by this touching letter. FromRead MoreMartin Luther King Jr.2405 Words   |  10 PagesMartin Luther King Jr. was a Baptist minister and social activist, who led the Civil Rights Movement in the United States from the mid-1950s until his death by assassination in 1968. IN THESE GROUPS NOBEL PEACE PRIZE WINNERS FAMOUS PEOPLE WHO DIED IN 1968 FAMOUS PEOPLE WHO WENT TO PRISON FAMOUS CAPRICORNS Show All Groups 1 of 19  «  » QUOTES â€Å"But we come here tonight to be saved from that patience that makes us patient with anything less than freedom and justice.† —Martin Luther King Jr. Read MoreDr. Martin Luther King1101 Words   |  5 PagesDr. Martin Luther King is a very passionate, motivating and an inspiring speaker. His â€Å"I Have a Dream is a perfect example of pathos. His speech had so much passions that it filled the audience with so much emotions. Even though there is a strong presence of pathos, than logo and ethos. They are very much present in his speech. On August 28, 1963, on a Washington DC street filled with over 250,000 demonstrators [black and white, young and old] came together to witness Dr. Martin Luther King speaksRead MoreMartin Luther King Jr.881 Words   |  4 PagesMartin Luther King Jr. â€Å" If you can’t fly, then run, if you can’t run, then walk, if you can’t walk, then crawl, but whatever you do, you have to keep moving forward.† (King). Martin Luther King Jr. is a name many know. He was born on January 15, 1929 in Atlanta, Georgia. He grew up in a very religious family, with his father being a pastor, and all. He was galvanized by his father and became a Baptist minister and social minister after he attended Boston University at the age of 15. He, laterRead MoreMartin Luther King Jr.951 Words   |  4 PagesMartin Luther King Jr. is one of the heroes that made an enormous impact on society and the history of the United States. King was born in January 15, 1929 in Atlanta, Georgia. It was a difficult time in the world and he finds it very difficult to play with other boys in town. Their parents never let them play with poor Michael (which is his original name). He doesn’t realize it at the time, but the color of his skin is the cause of many injustices for the rest of his life. His family has alwaysRead MoreMartin Luther King And Gandhi910 Words   |  4 Pages Martin Luther King Jr. had illustrated civil disobedient to the world during a challenging time, by quoting inspirational words from Gandhi and Thoreau. Gandhi had also quoted Thoreau throughout his stimulating time. Before Martin Luther King and Gandhi, Thoreau exemplified civil disobedience in the 1800’s. The purpose of Thoreau’s civil disobedience was to make a different world. King and Gandhi had the same purpose. That is one of the main reasons why they connected to Thoreau’s essay. BornRead MoreDr. Martin Luther King1647 Words   |  7 PagesKing was born on January 15, 1929, in Atlanta, Georgia, to the Reverend Martin Luther King, Sr. (1899–1984) and Alberta Williams King (1904–1974).[1] King s legal name at birth was Michael King,[2] and his father was also born Michael King, but the elder King changed his and his son s names following a 1934 trip to Germany to attend the Fifth Baptist World Alliance Congress in Berlin. It was during this time he chose to be called Martin Luther King in honor of the German reformer Martin Luther