title: Rachel Riley

text: Her television debut came when she joined "Countdown" aged 22. With an interest in popularising mathematics and the sciences, she has since co-presented "The Gadget Show" on Channel 5 (2013–14) and "It's Not Rocket Science" on ITV (2016). She was also a contestant on the BBC celebrity dance show "Strictly Come Dancing" in 2013.


title: Rachel Riley

text: Riley was born in Rochford, Essex. She was raised in the Thorpe Bay area of Southend-on-Sea and was educated at the independent Thorpe Hall School, and Southend High School for Girls, a grammar school, where she obtained four As at A-Level. She then completed a master's degree in mathematics at the University of Oxford.


title: Rachel Riley

text: During a university holiday Riley considered a career in the financial sector and completed an internship at Deutsche Bank in the City of London. The experience put her off: she found the extreme behaviour of city traders wearing and she disliked the early-morning train commute.


title: Rachel Riley

text: On "Countdown", Riley replaced the long-serving Carol Vorderman. Like Vorderman, Riley's role is to handle the placement of tiles on the board for the letters and numbers rounds and to find an exact solution in the numbers rounds if the contestants are unable to do so. Riley's appointment to "Countdown" was announced at the same time as the announcement of a new main host, Jeff Stelling, replacing Des O'Connor; the duo of Stelling and Riley was in place for the new series beginning in January 2009. Although she had no ambition to be a television presenter, she was encouraged to apply by her mother, and decided to do so because she was interested in the numbers part of the game. Having beaten 1,000 applicants for the role, she commented, "There's only one cool maths job around and I was lucky enough to get it so I'm absolutely thrilled".


title: Rachel Riley

text: Since it was first broadcast on 2 January 2012, Riley has also performed her "Countdown" role on the comedy crossover spin-off version, "8 Out of 10 Cats Does Countdown", alongside comedian Jimmy Carr as host. While "Countdown" is seen as a straight light entertainment show, in explaining the difference between the two, Riley sees "Countdown" as the role she is happy for her grandmother to see, while "Cats Does Countdown" is the more risqué, cheeky role which she shows to her friends.


title: Rachel Riley

text: From September 2013, Riley appeared in the eleventh series of the BBC One ballroom dancing programme "Strictly Come Dancing" with professional dancing partner Pasha Kovalev. She was eliminated in week 6 of the show, on 3 November, after losing out in the dance-off against Abbey Clancy and Aljaž Škorjanec, who went on to win the series.


title: Rachel Riley

text: According to Riley she lacked a natural talent for performing, so instead sought to frame each dance as that of a character. For the first five weeks, Riley suffered from stage fright, commenting that "As soon as the music would start, I would have a fuzzy brain and it was like an out-of-body experience"; after seeing a cognitive behavioural therapist she was able to control her breathing, and so was only able to truly enjoy the show for what proved to be her final appearance.


title: Rachel Riley

text: From 2013 to 2014, Riley co-presented on the Channel 5 programme "The Gadget Show" with Jason Bradbury. She presented three series of the show and was later replaced by Amy Williams. In 2016, Riley was part of the three-person presenting team for ITV's six-part series, "It's Not Rocket Science", billed by the network as an entertainment series celebrating science. Her co-presenters, Ben Miller and Romesh Ranganathan, similarly had a background in science and maths.


title: Rachel Riley

text: In August 2016, it was announced that Riley had joined Sky Sports to present "Friday Night Football" alongside her former "Countdown" co-presenter Jeff Stelling, and "Fantasy Football Club" with Max Rushden and Paul Merson. She left "Friday Night Football" in 2017.


title: Rachel Riley

text: In August 2012, Riley married Jamie Gilbert, whom she had met while they were both studying at the University of Oxford. It was announced in November 2013 that they were separating. The split has been cited as an example of the "Strictly" curse. She began dating her "Strictly" dance partner, Pasha Kovalev, soon after the show ended in December 2013. In May 2019, Riley announced that she was pregnant with the couple's first child. On 28 June 2019, Riley and Kovalev married in Las Vegas. On 15 December 2019, Riley gave birth to a baby girl. In April 2021, Riley announced that she was pregnant with the couple's second child. On 5 November 2021, Riley gave birth to their second daughter.


title: Rachel Riley

text: Riley is a keen supporter of Manchester United, like her father who was originally from Salford; in October 2010, Riley presented a programme on the club's television channel MUTV that featured a tour of their Trafford Training Centre in Carrington. She has also hosted episodes of "An Audience with..." on the channel. To mark her 1,000th episode of "Countdown" (aired on 25 June 2013), United player Ryan Giggs presented her with a signed team shirt, Giggs himself having celebrated his 1,000th game for the club the same year. In her appearance as a contestant on the BBC quiz show "Celebrity Mastermind", broadcast on 4 January 2012, her specialist subject was a limited (13-year) history of the club; she eventually finished in joint second place.


title: Rachel Riley

text: Riley’s mother is Jewish. She stated that, "My family came over in the pogroms" from Tsarist Russia. She is an atheist.


title: Rachel Riley

text: In 2018, Riley began a campaign against the way the Labour Party under the leadership of Jeremy Corbyn had handled allegations of antisemitism. She said she decided to speak out after seeing "Israel is a racist endeavour" posters on London bus stops. In September 2018, after criticising Corbyn over the ongoing antisemitism row, she stated she did not have "any party loyalties". In January 2019, Riley made a speech at a Westminster reception for the Holocaust Educational Trust and addressed what she described as the "hideous abuse" she had received.


title: Rachel Riley

text: In "Jewish News", Riley was quoted:In the name of Labour I've been called a hypocrite, lying propagandist, a tits-teeth-and-arse clothes horse dolly bird, weaponiser of anti-Semitism, fascist, right-wing extremist, Nazi sympathiser, Twitter cancer, thick Tory, brainwashed, an anti-Semite, white supremacist, hate preacher, Zio political trollster, not a real Jew, a child bully, conspiracy theorist, a paedo-protector minion puppet who my dead grandfather would be disgusted by.


title: Rachel Riley

text: In February 2019, according to "The Times" and "i", Riley had been involved in talks to set up a centrist breakaway party from Labour. According to "Jewish News" in April, Riley backed the Stop Funding Fake News campaign. In November 2019, Riley posted an image on Twitter of herself wearing a shirt with an edited image of Corbyn carrying a sign bearing the caption "Jeremy Corbyn is a racist endeavour". The tweet was condemned by some for erasing the struggle against the apartheid regime in South Africa, the original subject of the sign, to make a political point, with some users calling for Riley to be fired. The professional photographer who took the original shot, Rob Scott, also declared his displeasure, stating she had "illegally manipulated and printed" the picture to "cynically promote her agenda", adding "I am appalled by the abuse of property, moral rights and change of anti-racist message to anti-Corbyn one."


title: Rachel Riley

text: In February 2019, Riley and fellow campaigner Tracy-Ann Oberman instructed a lawyer to take action against 70 individuals who had posted tweets which Riley and Oberman regarded as either libellous or harassment. As a result, Riley and Oberman sued one person who had retweeted a link to an article which had accused Oberman and Riley of harassing a young Labour activist who had commented on antisemitism in the Labour Party. In May 2019, a High Court judge ruled that the article that was linked in the tweet was defamatory. In July 2020, Riley and Oberman dropped their joint libel suit and contributed towards the defendant's legal costs.


title: Rachel Riley

text: In 2021 Riley was awarded £10,000 damages by a High Court judge after suing Laura Murray, then an aide of Corbyn, over comments made on Twitter.


title: Rachel Riley

text: On 16 November 2022, Riley was awarded £50,000 in damages after a libel action against Michael Sivier, a blogger who had accused Riley of abusing a teenager during a 2019 Twitter discussion. Sivier had previously been found guilty of 3 of the 4 charges against him before the UK Court of Appeals ordered a review of them; the High Court's decision confirmed both Sivier's guilt and his reparation judgment for Riley.


title: Rachel Riley

text: Riley has visited schools to enthuse pupils on the "joys of applied maths, quantum mechanics and time travel and so on".


title: Rachel Riley

text: In June 2019, Riley was criticised by environmental groups and accused of greenwashing for her promotion of the "future energy solutions" of Shell, an oil and gas company.


title: Rachel Riley

text: She is listed on the website of the Center for Countering Digital Hate (CCDH) as a patron. She participated in an April 2022 study by the CCDH, which found that Instagram failed to act on 90% of abusive direct messages sent to high-profile women.


title: Rachel Riley

text: In October 2021, Riley published her first book, "At Sixes and Sevens: How to Understand Numbers and Make Maths Easy".


title: Rachel Riley

text: She has also made brief appearances in "Dispatches", "Britain's Brightest" and "1001 Things You Should Know".


title: Aisha

text: Aisha (; , , ; ) was Muhammad's third and youngest wife. In Islamic writings, her name is thus often prefixed by the title "Mother of the Believers" (), referring to the description of Muhammad's wives in the Qur'an.


title: Aisha

text: Little is known about the early life of Aisha. A preponderance of classical sources converge on Aisha being six or seven years old at the time of her marriage, and nine at the consummation; her age has become a source of ideological friction in modern times. Aisha had an important role in early Islamic history, both during Muhammad's life and after his death. In Sunni tradition, Aisha is portrayed as scholarly and inquisitive. She contributed to the spread of Muhammad's message and served the Muslim community for 44 years after his death. She is also known for narrating 2,210 hadiths, not just on matters related to Muhammad's private life, but also on topics such as inheritance, pilgrimage, and eschatology. Her intellect and knowledge in various subjects, including poetry and medicine, were highly praised by early luminaries such as al-Zuhri and her student Urwa ibn al-Zubayr.


title: Aisha

text: Her father, Abu Bakr (), became the first caliph to succeed Muhammad, and after two years was succeeded by Umar (). During the time of the third caliph Uthman (), Aisha had a leading part in the opposition that grew against him, though she did not agree either with those responsible for his assassination or with the party of Ali (). During the reign of Ali, she wanted to avenge Uthman's death, which she attempted to do in the Battle of the Camel. She participated in the battle by giving speeches and leading troops on the back of her camel. She ended up losing the battle, but her involvement and determination left a lasting impression. Because of her involvement in this battle, Shia Muslims have a generally negative view of Aisha. Afterward, she lived quietly in Medina for more than twenty years, took no part in politics, became reconciled to Ali and did not oppose caliph Mu'awiya ().


title: Aisha

text: Biographical information on Muhammad and his companions are recorded in hadiths and sira. Hadiths were initially narrated orally before being collected and compiled by Hadith scholars. In Islam, hadiths are regarded as fundamental sources second only to the Quran. However, the historical reliability of both hadith and sira has been a topic of debate among some academic circles.


title: Aisha

text: Aisha was born in Mecca . She was the daughter of Abu Bakr and Umm Ruman, two of Muhammad's most trusted companions. No sources offer much more information about Aisha's childhood years.


title: Aisha

text: The idea to match Aisha with Muhammad was suggested by Khawlah bint Hakim after the death of Muhammad's first wife, Khadija bint Khuwaylid. After this, the previous agreement regarding the marriage of Aisha with Jubayr ibn Mut'im was put aside by common consent. Abu Bakr was uncertain at first "as to the propriety or even legality of marrying his daughter to his 'brother'." Muhammad responded that they were brothers only in religion. Orientalist William Montgomery Watt suggests that Muhammad hoped to strengthen his ties with Abu Bakr; the strengthening of ties commonly served as a basis for marriage in Arabian culture.


title: Aisha

text: All extant hadiths agree that Aisha was married to Muhammad in Mecca but the marriage was consummated only in the month of Shawwal after his "hijrah" to Medina (April 623). Some classical sources have Aisha speak of the marriage to have been executed in Medina itself without referencing to any delay.


title: Aisha

text: Islamic sources of the classical era list Aisha's age at the time of her marriage as six or seven and nine or ten at its consummation. In a hadith from Sahih al-Bukhari, Aisha recollects having been married at six years of age. Ibn Sa'd's biography holds her age at the time of marriage as between six and seven, and gives her age at consummation to be nine while Ibn Hisham's biography of Muhammad suggests she may have been ten years old at consummation. Al-Tabari notes Aisha to have stayed with her parents after the marriage and consummated the relationship at nine years of age since she was young and sexually immature at the time of marriage; however, elsewhere Tabari appears to suggest that she was born during the Jahiliyyah (before 610 C.E), which would translate to an age of about twelve or more at marriage.


title: Aisha

text: In Islamic literature, the young age of her marriage did not draw any significant discourse; nonetheless, Spellberg and Ali find the very mention of her age to be atypical of early Muslim biographers, and hypothesize a connotation to her virginity and religious purity. Her age did not interest later Muslim scholars either, and even went unremarked-upon by medieval and early-modern Christian polemicists. Early Orientalist writers—despite taking a condescending approach towards Muhammad and Islam—did not focus on Aisha's age but instead on Muhammad's engaging in polygamy, the ethics of marrying for political causes, etc. A few, however chose to explain the age-gap—passively and without any condemnation—, citing the contemporary understanding of the Orient as a "hot" place, that promulgated sexually deviant practices.


title: Aisha

text: Beginning in the late nineteenth century, with the East and its alleged immoralities subject to increasing opprobrium, the colonizing powers sought to regulate the age of consent. As such efforts ran into conflicts with local forms of "Sharia", pointers to Aisha's age at marriage (and the associated Prophetic precedent) proliferated across the archives in explaining the backwardness of Muslim societies and their reticence to reforms. In response, some Muslims chose to align themselves with the projects of modernization and re-calculated her age—using deft stratagems of omission and commission—to fix it at early adolescence, but conservatives rejected such revisionist readings since they flew in the face of "ʻilm al-ḥadīth".


title: Aisha

text: In the mid-20th century, amidst growing concerns of Islamic extremism, as Muslim societies and Islam itself came under scrutiny, pointed criticisms of Aisha's young age at marriage began to appear; this has since prompted many Muslim scholars to contextualize the traditionally accepted age of Aisha with renewed vigor, emphasizing cultural relativism, anachronism, the political dimensions of the marriage, Aisha's non-ordinary physique, etc. In the late-twentieth century and early twenty-first century, Aisha's age has become a tool of Islamophobic polemicists to accuse Muhammad of pedophilia—not as a diagnostic category but as the highest category of evil—and reason for the apparently higher prevalence of child marriage in Muslim societies, among other ills.


title: Aisha

text: In most Muslim traditions, Khadija bint Khuwaylid is described as Muhammad's most beloved and favored wife; Sunni tradition places Aisha as second only to Khadija. There are several hadiths, or stories or sayings of Muhammad, that support this belief. One relates that when a companion asked Muhammad, "who is the person you love most in the world?" he responded, "Aisha." Others relate that Muhammad built Aisha's apartment so that her door opened directly into the mosque, and that she was the only woman with whom Muhammad received revelations. They bathed in the same water and he prayed while she lay stretched out in front of him.


title: Aisha

text: Various traditions reveal the mutual affection between Muhammad and Aisha. He would often just sit and watch her and her friends play with dolls, and on occasion, he would even join them. Additionally, they were close enough that each was able to discern the mood of the other, as many stories relate. It is also important to note that there exists evidence that Muhammad did not view himself as entirely superior to Aisha, at least not enough to prevent Aisha from speaking her mind, even at the risk of angering Muhammad. On one such instance, Muhammad's "announcement of a revelation permitting him to enter into marriages disallowed to other men drew from her [Aisha] the retort, 'It seems to me your Lord hastens to satisfy your desire!'" Furthermore, Muhammad and Aisha had a strong intellectual relationship. Muhammad valued her keen memory and intelligence and so instructed his companions to draw some of their religious practices from her.


title: Aisha

text: Aisha was jealous of Khadija bint Khuwaylid, Muhammad's first wife, saying, "I did not feel jealous of any of the wives of the Prophet as much as I did of Khadija though I did not see her, the Prophet used to mention her very often, and whenever he slaughtered a sheep, he would cut its parts and send them to the women friends of Khadija. When I sometimes said to him, "(You treat Khadija in such a way) as if there is no woman on earth except Khadija," he would say, "Khadija was such-and-such, and from her I had children."


title: Aisha

text: Aisha and Muhammad would often have races with each other, "I had a race with him (the Prophet) and I outstripped him on my feet. When I became fleshy, (again) I raced with him (the Prophet) and he outstripped me. He said: This is for that outstripping."


title: Aisha

text: The story of the accusation of adultery levied against Aisha, also known as the Event of Ifk, can be traced to "surah" (chapter) "An-Nur" of the Qur'an. As the story goes, Aisha left her "howdah" in order to search for a missing necklace. Her slaves mounted the "howdah" and prepared it for travel without noticing any difference in weight without Aisha's presence. Hence the caravan accidentally departed without her. She remained at the camp until the next morning, when Safwan ibn al-Mu‘attal, a nomad and member of Muhammad's army, found her and brought her back to Muhammad at the army's next camp. Rumours that Aisha and Safwan had committed adultery were spread, particularly by Abd-Allah ibn Ubayy, Hassan ibn Thabit, Mistah ibn Uthatha and Hammanah bint Jahsh (sister of Zaynab bint Jahsh, another of Muhammad's wives). Usama ibn Zayd, son of Zayd ibn Harithah, defended Aisha's reputation; while Ali ibn Abi Talib advised: "Women are plentiful, and you can easily change one for another." Muhammad came to speak directly with Aisha about the rumours. He was still sitting in her house when he announced that he had received a revelation from God confirming Aisha's innocence. Surah 24 details the Islamic laws and punishment regarding adultery and slander. Aisha's accusers were subjected to punishments of 80 lashes.


title: Aisha

text: After the daily "Asr" prayer, Muhammad would visit each of his wives' apartments to inquire about their well-being. Muhammad was just in the amount of time he spent with them and attention he gave to them. Once, Muhammad's fifth wife, Zaynab bint Jahsh, received some honey from a relative which Muhammad took a particular liking to. As a result, every time Zaynab offered some of this honey to him he would spend a long time in her apartment. This did not sit well with Aisha and Hafsa bint Umar.


title: Aisha

text: Soon after this event, Muhammad reported that he had received a revelation in which he was told that he could eat anything permitted by God. Some Sunni commentators on the Qur'an sometimes give this story as the "occasion of revelation" for At-Tahrim, which opens with the following verses: Word spread to the small Muslim community that Muhammad's wives were speaking sharply to him and conspiring against him. Muhammad, saddened and upset, separated from his wives for a month. ‘Umar, Hafsa's father, scolded his daughter and also spoke to Muhammad of the matter. By the end of this time, his wives were humbled; they agreed to "speak correct and courteous words" and to focus on the afterlife.


title: Aisha

text: Aisha remained Muhammad's favorite wife throughout his life. When he became ill and suspected that he was probably going to die, he began to ask his wives whose apartment he was to stay in next. They eventually figured out that he was trying to determine when he was due with Aisha, and they then allowed him to retire there. He remained in Aisha's apartment until his death, and his last breath was taken as he lay in the arms of Aisha, his second most beloved wife.


title: Aisha

text: After Muhammad's death, which ended Aisha and Muhammad's 14-year-long marriage, Aisha lived fifty more years in and around Medina. Much of her time was spent learning and acquiring knowledge of the Quran and the "sunnah" of Muhammad. Aisha was one of three wives (the other two being Hafsa bint Umar and Umm Salama) who memorized the Qur'an. Like Hafsa, Aisha had her script of the Quran written after Muhammad's death. During Aisha's life many prominent customs of Islam, such as veiling of women, began.


title: Aisha

text: Aisha's importance to revitalizing the Arab tradition and leadership among the Arab women highlights her magnitude within Islam. Aisha became involved in the politics of early Islam and the first three caliphate reigns: Abu Bakr, ‘Umar, and ‘Uthman. During a time in Islam when women were not expected or wanted, to contribute outside the household, Aisha delivered public speeches, became directly involved in a war and even battles, and helped both men and women to understand the practices of Muhammad.


title: Aisha

text: After Muhammad's death in 632, Abu Bakr was appointed as the first caliph. This matter of succession to Muhammad is extremely controversial to the Shia who believe that Ali had been appointed by Muhammad to lead while Sunni maintain that the public elected Abu Bakr. Abu Bakr had two advantages in achieving his new role: his long personal friendship with Muhammad and his role as a father-in-law. As caliph, Abu Bakr was the first to set guidelines for the new position of authority.


title: Aisha

text: Aisha garnered more special privileges in the Islamic community for being known as both a wife of Muhammad and the daughter of the first caliph. Being the daughter of Abu Bakr tied Aisha to honorable titles earned from her father's strong dedication to Islam. For example, she was given the title of "al-siddiqa bint al-Siddiq", meaning 'the truthful woman, daughter of the truthful man', a reference to Abu Bakr's support of the Isra and Mi'raj.


title: Aisha

text: In 634 Abu Bakr fell sick and was unable to recover. Before his death, he appointed ‘Umar, one of his chief advisers, as the second caliph. Throughout ‘Umar's time in power Aisha continued to play the role of a consultant in political matters.


title: Aisha

text: After ‘Umar died, ‘Uthmān was chosen to be the third caliph. He wanted to promote the interests of the Umayyads. Aisha had little involvement with ‘Uthmān for the first couple years, but eventually, she found a way into the politics of his reign. She eventually grew to despise ‘Uthmān, and many are unsure of what specifically triggered her eventual opposition towards him. A prominent opposition that arose towards him was when ‘Uthmān mistreated ‘Ammar ibn Yasir (companion of Muhammad) by beating him. Aisha became enraged and spoke out publicly, saying, "How soon indeed you have forgotten the practice (sunnah) of your prophet and these, his hairs, a shirt, and sandal have not yet perished!".


title: Aisha

text: As time continued issues of antipathy towards ‘Uthmān continued to arise. Another instance of opposition arose when the people came to Aisha after Uthmān ignored the rightful punishment for Walid ibn Uqbah (Uthmān's brother). Aisha and Uthmān argued with each other, Uthmān eventually commented on why Aisha had come and how she was "ordered to stay at home". Arising from this comment, was the question of whether Aisha and for that matter women, still could be involved in public affairs. The Muslim community became split: "some sided with Uthmān, but others demanded to know who indeed had a better right than Aisha in such matters".


title: Aisha

text: The caliphate took a turn for the worse when Egypt was governed by Abdullah ibn Saad. Abbott reports that Muhammad ibn Abi Hudhayfa of Egypt, an opponent of ‘Uthmān, forged letters in the Mothers of the Believers' names to the conspirators against ‘Uthmān. The people cut off ‘Uthmān's water and food supply. When Aisha realized the behavior of the crowd, Abbott notes, Aisha could not believe the crowd "would offer such indignities to a widow of Mohammad". This refers to when Safiyya bint Huyayy (one of Muhammad's wives) tried to help ‘Uthmān and was taken by the crowd. Malik al-Ashtar then approached her about killing Uthmān and the letter, and she claimed she would never want to "command the shedding of the blood of the Muslims and the killing of their Imām"; she also claimed she did not write the letters. The city continued to oppose ‘Uthmān, but as for Aisha, her journey to Mecca was approaching. With the journey to Mecca approaching at this time, she wanted to rid herself of the situation. ‘Uthmān heard of her not wanting to hurt him, and he asked her to stay because she influenced the people, but this did not persuade Aisha, and she continued on her journey.


title: Aisha

text: In 655, Uthman's house was put under siege by about 1000 rebels. Eventually the rebels broke into the house and murdered Uthman, provoking the First Fitna. After killing Uthman, the rebels asked Ali to be the new caliph, although Ali was not involved in the murder of Uthman according to many reports. Ali reportedly initially refused the caliphate, agreeing to rule only after his followers persisted.


title: Aisha

text: When Ali could not execute those merely accused of Uthman's murder, Aisha delivered a fiery speech against him for not avenging the death of Uthman. The first to respond to Aisha was Abdullah ibn Aamar al-Hadhrami, the governor of Mecca during the reign of Uthman, and prominent members of the Banu Umayya. With the funds from the "Yemeni Treasury" Aisha set out on a campaign against the Rashidun Caliphate of Ali.


title: Aisha

text: Aisha, along with an army including Zubayr ibn al-Awwam and Talha ibn Ubayd Allah, confronted Ali's army, demanding the prosecution of Uthman's killers who had mingled with his army outside the city of Basra. When her forces captured Basra she ordered the execution of 600 Muslims and 40 others, including Hakim ibn Jabala, who were put to death in the Grand Mosque of Basra. Aisha's forces are also known to have tortured and imprisoned Uthman ibn Hunaif a Sahabi and the governor of Basra appointed by Ali.


title: Aisha

text: Ali rallied supporters and fought Aisha's forces near Basra in 656. The battle is known as the Battle of the Camel, after the fact that Aisha directed her forces from a howdah on the back of a large camel. Aisha's forces were defeated and an estimated 10,000 Muslims were killed in the battle, considered the first engagement where Muslims fought Muslims.


title: Aisha

text: After 110 days of the conflict, Ali met Aisha with reconciliation. He sent her back to Medina under military escort headed by her brother Muhammad ibn Abi Bakr, one of Ali's commanders. She subsequently retired to Medina with no more interference with the affairs of the state. She was also awarded a pension by Ali.


title: Aisha

text: Although she retired to Medina, her forsaken efforts against the Rashidun Caliphate of Ali did not end the First Fitna.


title: Aisha

text: After 25 years of a monogamous relationship with his first wife, Khadija bint Khuwaylid, Muhammad participated in nine years of polygyny, marrying at least nine further wives. Muhammad's subsequent marriages were depicted purely as political matches rather than unions of sexual indulgence. In particular, Muhammad's unions with Aisha and Hafsa bint Umar associated him with two of the most significant leaders of the early Muslim community, Aisha's and Hafsa's fathers, Abu Bakr and ‘Umar ibn al-Khattāb, respectively.


title: Aisha

text: Aisha's marriage has given her significance among many within Islamic culture, becoming known as the most learned woman of her time. Being Muhammad's favorite wife, Aisha occupied an important position in his life. When Muhammad married Aisha in her youth, she was accessible "...to the values needed to lead and influence the sisterhood of Muslim women." After the death of Muhammad, Aisha was discovered to be a renowned source of hadiths, due to her qualities of intelligence and memory. Aisha conveyed ideas expressing Muhammad's practice (sunnah). She expressed herself as a role model to women, which can also be seen within some traditions attributed to her. The traditions regarding Aisha habitually opposed ideas unfavorable to women in efforts to elicit social change.


title: Aisha

text: Not only was Aisha supportive of Muhammad, but she contributed scholarly intellect to the development of Islam. She was given the title "al-Siddiqah", meaning 'the one who affirms the truth'. Aisha was known for her "...expertise in the Quran, shares of inheritance, lawful and unlawful matters, poetry, Arabic literature, Arab history, genealogy, and general medicine." Her intellectual contributions regarding the verbal texts of Islam were in time transcribed into written form, becoming the official history of Islam. After the death of Muhammad, Aisha was regarded as the most reliable source in the teachings of hadith. Aisha's authentication of Muhammad's ways of prayer and his recitation of the Qur'an allowed for the development of knowledge of his sunnah of praying and reading verses of the Quran.


title: Aisha

text: During Aisha's entire life she was a strong advocate for the education of Islamic women, especially in law and the teachings of Islam. She was known for establishing the first "madrasa" for women in her home. Attending Aisha's classes were various family relatives and orphaned children. Men also attended Aisha's classes, with a simple curtain separating the male and female students.


title: Aisha

text: Spellberg argues that Aisha's political influence helped promote her father, Abu Bakr, to the caliphate after Muhammad's death.


title: Aisha

text: After the defeat at the Battle of the Camel, Aisha retreated to Medina and became a teacher. Upon her arrival in Medina, Aisha retired from her public role in politics. Her discontinuation of public politics did not stop her political influence completely. Privately, Aisha continued influencing those intertwined in the Islamic political sphere. Among the Islamic community, she was known as an intelligent woman who debated law with male companions. Aisha was also considered to be the embodiment of proper rituals while partaking in the pilgrimage to Mecca, a journey she made with several groups of women. For the last two years of her life, Aisha spent much of her time telling the stories of Muhammad, hoping to correct false passages that had become influential in formulating Islamic law. Due to this, Aisha's political influence continues to impact those in Islam.


title: Aisha

text: Aisha died at her home in Medina on 17 Ramadan 58 AH (16 July 678). She was 67 years old. Abu Hurairah led her funeral prayer after the "tahajjud" (night) prayer, and she was buried at Jannat al-Baqi‘.


title: Aisha

text: Sunnis believe she was Muhammad's favorite wife after Khadija bint Khuwaylid. They consider her (among other wives) to be "Umm al-Mu’minin" and among the members of the Ahl al-Bayt, or Muhammad's family. According to Sunni hadith reports, Muhammad saw Aisha in two dreams in which he was shown that he would marry her.


title: Aisha

text: The Shia view Aisha is different than Sunni. They criticize her for opposing Ali during his caliphate in the Battle of the Camel, when she fought men from Ali's army in Basra.


title: Slaughterhouse-Five

text: Slaughterhouse-Five, or, The Children's Crusade: A Duty-Dance with Death is a 1969 semi-autobiographic science fiction-infused anti-war novel by Kurt Vonnegut. It follows the life and experiences of Billy Pilgrim, from his early years, to his time as an American soldier and chaplain's assistant during World War II, to the post-war years, with Billy occasionally traveling through time. The text centers on Billy's capture by the German Army and his survival of the Allied firebombing of Dresden as a prisoner of war, an experience which Vonnegut himself lived through as an American serviceman. The work has been called an example of "unmatched moral clarity" and "one of the most enduring anti-war novels of all time".


title: Slaughterhouse-Five

text: The story is told in a non-linear order by an unreliable narrator (he begins the novel by telling the reader, "All of this happened, more or less"). Events become clear through flashbacks and descriptions of his time travel experiences. In the first chapter, the narrator describes his writing of the book, his experiences as a University of Chicago anthropology student and a Chicago City News Bureau correspondent, his research on the Children's Crusade and the history of Dresden, and his visit to Cold War-era Europe with his wartime friend Bernard V. O'Hare. He then writes about Billy Pilgrim, an American man from the fictional town of Ilium, New York, who believes that he was held at one time in an alien zoo on a planet he calls Tralfamadore, and that he has experienced time travel.


title: Slaughterhouse-Five

text: As a chaplain's assistant in the United States Army during World War II, Billy is an ill-trained, disoriented, and fatalistic American soldier who discovers that he does not like war and refuses to fight. He is transferred from a base in South Carolina to the front line in Luxembourg during the Battle of the Bulge. He narrowly escapes death as the result of a string of events. He also meets Roland Weary, a patriot, warmonger, and sadistic bully who derides Billy's cowardice. The two of them are captured in 1944 by the Germans, who confiscate all of Weary's belongings and force him to wear wooden clogs that cut painfully into his feet; the resulting wounds become gangrenous, which eventually kills him. While Weary is dying in a rail car full of prisoners, he convinces a fellow soldier, Paul Lazzaro, that Billy is to blame for his death. Lazzaro vows to avenge Weary's death by killing Billy, because revenge is "the sweetest thing in life".


title: Slaughterhouse-Five

text: At this exact time, Billy becomes "unstuck in time" and has flashbacks from his former and future life. Billy and the other prisoners are transported into Germany. By 1945, the prisoners have arrived in the German city of Dresden to work in "contract labor" (forced labor). The Germans hold Billy and his fellow prisoners in an empty slaughterhouse called "Schlachthof-fünf" ("slaughterhouse five"). During the extensive bombing of Dresden by the Allies, German guards hide with the prisoners in the slaughterhouse, which is partially underground and well-protected from the damage on the surface. As a result, they are among the few survivors of the firestorm that rages in the city between February 13 and 15, 1945. After V-E Day in May 1945, Billy is transferred to the United States and receives an honorable discharge in July 1945.


title: Slaughterhouse-Five

text: Soon, Billy is hospitalized with symptoms similar to post-traumatic stress disorder and placed under psychiatric care at a Veterans Affairs hospital in Lake Placid. There, he shares a room with Eliot Rosewater, who introduces Billy to the novels of an obscure science fiction author, Kilgore Trout. After his release, Billy marries Valencia Merble, whose father owns the Ilium School of Optometry that Billy later attends. Billy becomes a successful and wealthy optometrist. In 1947, Billy and Valencia conceive their first child, Robert, on their honeymoon in Cape Ann, Massachusetts. Two years later their second child, Barbara, is born. On Barbara's wedding night, Billy is abducted by a flying saucer and taken to a planet many light-years away from Earth called Tralfamadore. The Tralfamadorians are described as being able to see in four dimensions, simultaneously observing all points in the space-time continuum. They universally adopt a fatalistic worldview: death means nothing to them, and their common response to hearing about death is "so it goes".


title: Slaughterhouse-Five

text: On Tralfamadore, Billy is put in a transparent geodesic dome exhibit in a zoo; the dome represents a house on Earth. The Tralfamadorians later abduct a pornographic film star named Montana Wildhack, who had disappeared on Earth and was believed to have drowned in San Pedro Bay. They intend to have her mate with Billy. She and Billy fall in love and have a child together. Billy is instantaneously sent back to Earth in a time warp to re-live past or future moments of his life.


title: Slaughterhouse-Five

text: In 1968, Billy and a co-pilot are the only survivors of a plane crash in Vermont. While driving to visit Billy in the hospital, Valencia crashes her car and dies of carbon monoxide poisoning. Billy shares a hospital room with Bertram Rumfoord, a Harvard University history professor researching an official history of the war. They discuss the bombing of Dresden, which the professor initially refuses to believe Billy witnessed; the professor claims that the bombing of Dresden was justified despite the great loss of civilian lives and the complete destruction of the city.


title: Slaughterhouse-Five

text: Billy's daughter takes him home to Ilium. He escapes and flees to New York City. In Times Square he visits a pornographic book store, where he discovers books written by Kilgore Trout and reads them. Among the books he discovers a book entitled "The Big Board", about a couple abducted by aliens and tricked into managing the aliens' investments on Earth. He also finds a number of magazine covers noting the disappearance of Montana Wildhack, who happens to be featured in a pornographic film being shown in the store. Later in the evening, when he discusses his time travels to Tralfamadore on a radio talk show, he is ejected from the studio. He returns to his hotel room, falls asleep, and time-travels back to 1945 in Dresden. Billy and his fellow prisoners are tasked with locating and burying the dead. After a Maori New Zealand soldier working with Billy dies of dry heaves the Germans begin cremating the bodies en masse with flamethrowers. Billy's friend Edgar Derby is shot for stealing a teapot. Eventually all of the German soldiers leave to fight on the Eastern Front, leaving Billy and the other prisoners alone with tweeting birds as the war ends.


title: Slaughterhouse-Five

text: Through non-chronological storytelling, other parts of Billy's life are told throughout the book. After Billy is evicted from the radio studio, Barbara treats Billy as a child and often monitors him. Robert becomes starkly anti-communist, enlists as a Green Beret and fights in the Vietnam War. Billy eventually dies in 1976, at which point the United States has been partitioned into twenty separate countries and attacked by China with thermonuclear weapons. He gives a speech in a baseball stadium in Chicago in which he predicts his own death and proclaims that "if you think death is a terrible thing, then you have not understood a word I've said." Billy soon after is shot with a laser gun by an assassin commissioned by the elderly Lazzaro.


title: Slaughterhouse-Five

text: In keeping with Vonnegut's signature style, the novel's syntax and sentence structure are simple, and irony, sentimentality, black humor, and didacticism are prevalent throughout the work. Like much of his oeuvre, "Slaughterhouse-Five" is broken into small pieces, and in this case, into brief experiences, each focused on a specific point in time. Vonnegut has noted that his books "are essentially mosaics made up of a whole bunch of tiny little chips...and each chip is a joke." Vonnegut also includes hand-drawn illustrations in "Slaughterhouse-Five", and also in his next novel, "Breakfast of Champions" (1973). Characteristically, Vonnegut makes heavy use of repetition, frequently using the phrase, "So it goes". He uses it as a refrain when events of death, dying, and mortality occur or are mentioned; as a narrative transition to another subject; as a "memento mori"; as comic relief; and to explain the unexplained. The phrase appears 106 times.


title: Slaughterhouse-Five

text: The book has been categorized as a postmodern, meta-fictional novel. The first chapter of "Slaughterhouse-Five" is written in the style of an author's preface about how he came to write the novel. The narrator introduces the novel's genesis by telling of his connection to the Dresden bombing, and why he is recording it. He provides a description of himself and of the book-saying that it is a desperate attempt at creating a scholarly work. He ends the first chapter by discussing the beginning and end of the novel. He then segues to the story of Billy Pilgrim: "Listen: Billy Pilgrim has come unstuck in time", thus the transition from the writer's perspective to that of the third-person, omniscient narrator. (The use of "Listen" as an opening interjection has been said to mimic the opening “Hwaet!” of the medieval epic poem "Beowulf".) The fictional "story" appears to begin in Chapter Two, although there is no reason to presume that the first chapter is not also fiction. This technique is common in postmodern meta-fiction.


title: Slaughterhouse-Five

text: The narrator explains that Billy Pilgrim experiences his life discontinuously, so that he randomly lives (and re-lives) his birth, youth, old age, and death, rather than experiencing them in the normal linear order. There are two main narrative threads: a description of Billy's World War II experience, which, though interrupted by episodes from other periods and places in his life, is mostly linear; and a description of his discontinuous pre-war and post-war lives. A main idea is that Billy's existential perspective had been compromised by his having witnessed Dresden's destruction (although he had come "unstuck in time" before arriving in Dresden). "Slaughterhouse-Five" is told in short, declarative sentences, which create the impression that one is reading a factual report.


title: Slaughterhouse-Five

text: The first sentence says, "All this happened, more or less." (In 2010 this was ranked No. 38 on the "American Book Review"s list of "100 Best First Lines from Novels.") The opening sentences of the novel have been said to contain the aesthetic "method statement" of the entire novel.


title: Slaughterhouse-Five

text: In "Slaughterhouse-Five", Kurt Vonnegut attempts to come to terms with war through the narrator's eyes, Billy Pilgrim. An example within the novel, showing Kurt Vonnegut's aim to accept his past war experiences, occurs in chapter one, when he states that "All this happened, more or less. The war parts, anyway, are pretty much true. One guy I knew really was shot in Dresden for taking a teapot that wasn't his. Another guy I knew really did threaten to have his personal enemies killed by hired gunmen after the war. And so on. I've changed all the names."


title: Slaughterhouse-Five

text: "Slaughterhouse-Five" focuses on human imagination while interrogating the novel's overall theme, which is the catastrophe and impact that war leaves behind.


title: Slaughterhouse-Five

text: Death is something that happens fairly often in "Slaughterhouse-Five." When a death occurs in the novel, Vonnegut marks the occasion with the saying "so it goes." Bergenholtz and Clark write about what Vonnegut actually means when he uses that saying: "Presumably, readers who have not embraced Tralfamadorian determinism will be both amused and disturbed by this indiscriminate use of 'So it goes.' Such humor is, of course, black humor."


title: Slaughterhouse-Five

text: Christian philosophy is present in Vonnegut's "Slaughterhouse-Five" but it is not very well-regarded. When God and Christianity is brought up in the work, it is mentioned in a bitter or disregarding tone. One only has to look at how the soldiers react to the mention of it. Though Billy Pilgrim had adopted some part of Christianity, he did not ascribe to all of them. JC Justus summarizes it the best when he mentions that, "'Tralfamadorian determinism and passivity' that Pilgrim later adopts as well as Christian fatalism wherein God himself has ordained the atrocities of war...". Following Justus's argument, Pilgrim was a character that had been through war and traveled through time. Having experienced all of these horrors in his lifetime, Pilgrim ended up adopting the Christian ideal that God had everything planned and he had given his approval for the war to happen.


title: Slaughterhouse-Five

text: As Billy Pilgrim becomes "unstuck in time", he is faced with a new type of philosophy. When Pilgrim becomes acquainted with the Tralfamadorians, he learns a different viewpoint concerning fate and free will. While Christianity may state that fate and free will are matters of God's divine choice and human interaction, Tralfamadorianism would disagree. According to Tralfamadorian philosophy, things are and always will be, and there is nothing that can change them. When Billy asks why they had chosen "him", the Tralfamadorians reply, "Why "you"? Why "us" for that matter? Why "anything"? Because this moment simply is." The mindset of the Tralfamadorian is not one in which free will exists. Things happen because they were always destined to be happening. The narrator of the story explains that the Tralfamadorians see time all at once. This concept of time is best explained by the Tralfamadorians themselves, as they speak to Billy Pilgrim on the matter stating, "I am a Tralfamadorian, seeing all time as you might see a stretch of the Rocky Mountains. All time is all time. It does not change. It does not lend itself to warnings or explanations. It simply "is."" After this particular conversation on seeing time, Billy makes the statement that this philosophy does not seem to evoke any sense of free will. To this, the Tralfamadorian reply that free will is a concept that, out of the "visited thirty-one inhabited planets in the universe" and "studied reports on one hundred more," "only on Earth is there any talk of free will.”


title: Slaughterhouse-Five

text: Using the Tralfamadorian passivity of fate, Billy Pilgrim learns to overlook death and the shock involved with death. Pilgrim claims the Tralfamadorian philosophy on death to be his most important lesson:The most important thing I learned on Tralfamadore was that when a person dies he only "appears" to die. He is still very much alive in the past, so it is very silly for people to cry at his funeral. All moments, past, present, and future, always have existed, always will exist. ... When a Tralfamadorian sees a corpse, all he thinks is that the dead person is in bad condition in that particular moment, but that the same person is just fine in plenty of other moments. Now, when I myself hear that somebody is dead, I simply shrug and say what the Tralfamadorians say about dead people, which is "So it goes."


title: Slaughterhouse-Five

text: The significance of postmodernism is a reoccurring theme in Kurt Vonnegut's novel. In fact, it is said that post-modernism emerged from the modernist movement. This idea has appeared on various platforms such as music, art, fashion and film. In Slaughterhouse-Five, Kurt Vonnegut uses postmodernism in order to challenge modernist ideas. This novel is oftentimes referred to as an "anti-war book". Vonnegut uses his personal war knowledge to unmask the real horrors behind closed doors. Postmodernism brings to light the heart-wrenching truth caused by wars. Throughout the years, postmodernists argue that the world is a meaningless place with no universal morals. Everything happens simply by chance.


title: Slaughterhouse-Five

text: Some have argued that Kurt Vonnegut is speaking out for veterans, many of whose post-war states are untreatable. Pilgrim's symptoms have been identified as what is now called post-traumatic stress disorder, which didn't exist as a term when the novel was written. In the words of one writer, "perhaps due to the fact that PTSD was not officially recognized as a mental disorder yet, the establishment fails Billy by neither providing an accurate diagnosis nor proposing any coping mechanisms." Billy found life meaningless simply because of the things that he saw in the war. War desensitized and forever changed him.


title: Slaughterhouse-Five

text: Vonnegut was in the city of Dresden when it was bombed; he came home traumatized and unable to properly communicate the horror of what happened there. "Slaughterhouse-Five" is the product of the twenty years of work it took for him to communicate it in a way that satisfied him. William Allen notices this when he says, "Precisely because the story was so hard to tell, and because Vonnegut was willing to take two decades necessary to tell it – to speak the unspeakable – "Slaughterhouse-Five" is a great novel, a masterpiece sure to remain a permanent part of American literature." Vonnegut's claim of a death toll of 135,000 people was based on Holocaust denier David Irving's claim; the real number was closer to 25,000, but Vonnegut's response was, “Does it matter?” Historians claim that Vonnegut's inflated number, and his false comparison to the Hiroshima atomic bombing propagates a false historical awareness.


title: Slaughterhouse-Five

text: Billy Pilgrim ended up owning "half of three Tastee-Freeze stands. Tastee-Freeze was a sort of frozen custard. It gave all the pleasure that ice cream could give, without the stiffness and bitter coldness of ice cream" (61). Throughout "Slaughterhouse-Five", when Billy is eating or near food, he thinks of food in positive terms. This is partly because food is both a status symbol and comforting to people in Billy's situation. "Food may provide nourishment, but its more important function is to soothe... Finally, food also functions as a status symbol, a sign of wealth. For instance, en route to the German prisoner-of-war camp, Billy gets a glimpse of the guards' boxcar and is impressed by its contents... In sharp contrast, the Americans' boxcar proclaims their dependent prisoner-of-war status."


title: Slaughterhouse-Five

text: Throughout the novel, the bird sings "Poo-tee-weet?” After the Dresden firebombing, the bird breaks out in song. The bird also sings outside of Billy's hospital window. The song is a symbol of a loss of words. There are no words big enough to describe a war massacre.


title: Slaughterhouse-Five

text: As in other novels by Vonnegut, certain characters cross over from other stories, making cameo appearances and connecting the discrete novels to a greater opus. Fictional novelist Kilgore Trout, often an important character in other Vonnegut novels, is a social commentator and a friend to Billy Pilgrim in "Slaughterhouse-Five". In one case, he is the only non-optometrist at a party; therefore, he is the odd man out. He ridicules everything the Ideal American Family holds true, such as Heaven, Hell, and Sin. In Trout's opinion, people do not know if the things they do turn out to be good or bad, and if they turn out to be bad, they go to Hell, where "the burning never stops hurting." Other crossover characters are Eliot Rosewater, from "God Bless You, Mr. Rosewater"; Howard W. Campbell Jr., from "Mother Night"; and Bertram Copeland Rumfoord, relative of Winston Niles Rumfoord, from "The Sirens of Titan". While Vonnegut re-uses characters, the characters are frequently rebooted and do not necessarily maintain the same biographical details from appearance to appearance. Trout in particular is palpably a different person (although with distinct, consistent character traits) in each of his appearances in Vonnegut's work.


title: Slaughterhouse-Five

text: In the "Twayne's United States Authors" series volume on Kurt Vonnegut, about the protagonist's name, Stanley Schatt says:


title: Slaughterhouse-Five

text: By naming the unheroic hero Billy Pilgrim, Vonnegut contrasts John Bunyan's "Pilgrim's Progress" with Billy's story. As Wilfrid Sheed has pointed out, Billy's solution to the problems of the modern world is to "invent a heaven, out of 20th century materials, where Good Technology triumphs over Bad Technology. His scripture is Science Fiction, Man's last, good fantasy".


title: Slaughterhouse-Five

text: "Slaughterhouse-Five" makes numerous cultural, historical, geographical, and philosophical allusions. It tells of the bombing of Dresden in World War II, and refers to the Battle of the Bulge, the Vietnam War, and the civil rights protests in American cities during the 1960s. Billy's wife, Valencia, has a "Reagan for President!" bumper sticker on her Cadillac, referring to Ronald Reagan's failed 1968 Republican presidential nomination campaign. Another bumper sticker is mentioned, reading "Impeach Earl Warren," referencing a real-life campaign by the far-right John Birch Society.


title: Slaughterhouse-Five

text: The Serenity Prayer appears twice. Critic Tony Tanner suggested that it is employed to illustrate the contrast between Billy Pilgrim's and the Tralfamadorians' views of fatalism. Richard Hinchcliffe contends that Billy Pilgrim could be seen at first as typifying the Protestant work ethic, but he ultimately converts to evangelicalism.


title: Slaughterhouse-Five

text: The reviews of "Slaughterhouse-Five" have been largely positive since the March 31, 1969 review in "The New York Times" newspaper that stated: "you'll either love it, or push it back in the science-fiction corner." It was Vonnegut's first novel to become a bestseller, staying on the "New York Times" bestseller list for sixteen weeks and peaking at No. 4. In 1970, "Slaughterhouse-Five" was nominated for best-novel Nebula and Hugo Awards. It lost both to "The Left Hand of Darkness" by Ursula K. Le Guin. It has since been widely regarded as a classic anti-war novel, and has appeared in "Time" magazine's list of the 100 best English-language novels written since 1923.


title: Slaughterhouse-Five

text: "Slaughterhouse-Five" has been the subject of many attempts at censorship due to its irreverent tone, purportedly obscene content and depictions of sex, American soldiers' use of profanity, and perceived heresy. It was one of the first literary acknowledgments that homosexual men, referred to in the novel as "fairies", were among the victims of the Holocaust.


title: Slaughterhouse-Five

text: In the United States it has at times been banned from literature classes, removed from school libraries, and struck from literary curricula. In 1972, following the ruling of "Todd v. Rochester Community Schools", it was banned from Rochester Community Schools in Oakland County, Michigan. The circuit judge described the book as "depraved, immoral, psychotic, vulgar and anti-Christian." It was later reinstated.


title: Slaughterhouse-Five

text: The U.S. Supreme Court considered the First Amendment implications of the removal of the book, among others, from public school libraries in the case of "Island Trees School District v. Pico", and concluded that "local school boards may not remove books from school library shelves simply because they dislike the ideas contained in those books and seek by their removal to 'prescribe what shall be orthodox in politics, nationalism, religion, or other matters of opinion.'" "Slaughterhouse-Five" is the sixty-seventh entry to the American Library Association's list of the "Most Frequently Challenged Books of 1990–1999" and number forty-six on the ALA's "Most Frequently Challenged Books of 2000–2009". In August 2011, the novel was banned at the Republic High School in Missouri. The Kurt Vonnegut Memorial Library countered by offering 150 free copies of the novel to Republic High School students on a first-come, first-served basis.


title: Slaughterhouse-Five

text: Critics have accused "Slaughterhouse-Five" of being a quietist work, because Billy Pilgrim believes that the notion of free will is a quaint Earthling illusion. The problem, according to Robert Merrill and Peter A. Scholl, is that "Vonnegut's critics seem to think that he is saying the same thing [as the Tralfamadorians]." For Anthony Burgess, ""Slaughterhouse" is a kind of evasion—in a sense, like J. M. Barrie's "Peter Pan"—in which we're being told to carry the horror of the Dresden bombing, and everything it implies, up to a level of fantasy..." For Charles Harris, "The main idea emerging from "Slaughterhouse-Five" seems to be that the proper response to life is one of resigned acceptance." For Alfred Kazin, "Vonnegut deprecates any attempt to see tragedy, that day, in Dresden...He likes to say, with arch fatalism, citing one horror after another, 'So it goes.'" For Tanner, "Vonnegut has...total sympathy with such quietistic impulses." The same notion is found throughout "The Vonnegut Statement", a book of original essays written and collected by Vonnegut's most loyal academic fans.


title: Slaughterhouse-Five

text: When confronted with the question of how the desire to improve the world fits with the notion of time presented in "Slaughterhouse-Five", Vonnegut himself responded "you understand, of course, that everything I say is horseshit."


title: A Time to Kill (1996 film)

text: A Time to Kill is a 1996 American legal drama film. It is based on John Grisham's 1989 novel of the same name. Sandra Bullock, Samuel L. Jackson, Matthew McConaughey, and Kevin Spacey star with Donald and Kiefer Sutherland appearing in supporting roles. The film received mixed to positive reviews and was a commercial success, making $152 million at the worldwide box office. It is the second of two films based on Grisham's novels directed by Joel Schumacher, with the other being "The Client" released two years prior.


title: A Time to Kill (1996 film)

text: In Canton, Mississippi, ten-year-old African American girl Tonya Hailey is abducted, raped, and beaten by two local white men, Billy Ray Cobb and James Willard, while on her way home getting groceries. The duo dump her in a nearby river after a failed attempt to hang her. Tonya survives, and the two men are arrested by Sheriff Ozzie Walls.


title: A Time to Kill (1996 film)

text: Tonya's father, Carl Lee Hailey, contacts Jake Brigance, a white lawyer who previously defended his brother Lester. Brigance admits the possibility that the rapists will walk free. Carl Lee goes to the county courthouse and opens fire with an automatic rifle, killing both rapists and unintentionally wounding Deputy Dwayne Looney, whose leg is later amputated. Carl Lee is arrested and Brigance agrees to defend him.


title: A Time to Kill (1996 film)

text: As the rape and subsequent revenge killing gain national media attention, district attorney Rufus Buckley decides to take the case in hopes of furthering his political career. He seeks the death penalty, and presiding Judge Omar Noose denies Brigance a change of venue to a more ethnically diverse county, meaning that Carl Lee will have an all-White jury. Brigance seeks help from his defense team: law student Ellen Roark, close friend Harry Rex Vonner, and former mentor and longtime activist Lucien Wilbanks, a once-great civil rights lawyer. Meanwhile, Billy Ray's brother, Freddie Lee Cobb, plans to avenge his brother's death by joining and enlisting the help of the Mississippi branch of the Ku Klux Klan and its Grand Dragon, Stump Sisson, to ensure Carl Lee's conviction and death sentence by any means necessary.


title: A Time to Kill (1996 film)

text: On the first day of the trial, the Klan rallies, only to be outnumbered by counter-protesters consisting of the area's minority residents and whites who support Carl Lee. The protest erupts into a violent brawl that results in dozens of injuries and the death of Stump Sisson. The Klan also begins to target Brigance, assaulting his elderly secretary and her husband, who dies of a heart attack brought on by the assault. They also burn a cross on his lawn and threaten his wife and daughter. When Brigance refuses to back down, the Klan then increases their attacks, including burning Brigance's house. Soon after Cobb kidnaps and assaults Roark.


title: A Time to Kill (1996 film)

text: Brigance is able to discredit the state's psychiatrist, Dr. Wilbert Rodeheaver. However, Buckley in turn discredits Brigance's psychiatrist, Dr. Willard Tyrell Bass, by revealing his prior conviction of statutory rape. Dispirited, Brigance tells Carl Lee that there is little hope for an acquittal. Carl Lee replies that he had chosen Brigance as an attorney because he is a white man and has insight into how the jury sees Carl Lee. During closing arguments, a deeply-shaken Brigance tells the jury to close their eyes and listen to a story. He describes, in slow and painful detail, the entire ordeal of Tonya, in which some of the jurors shed tears. Brigance then asks the jury, in his final comment, to "now imagine she's white."


title: A Time to Kill (1996 film)

text: After deliberation, a black child runs out of the courthouse and screams, "He's innocent!" Jubilation ensues amongst the supporters while the Klan becomes enraged over their defeat. Meanwhile, Sheriff Walls arrests Freddie Lee for his crimes, as well as a corrupt deputy who is also revealed to be a Klan member.


title: A Time to Kill (1996 film)

text: Sometime later, Brigance brings his wife and daughter to a family cookout at Carl Lee's house to celebrate his freedom, challenging Carl Lee's previous statement that their children would "never play together".


title: A Time to Kill (1996 film)

text: The film was mainly produced in and around Canton, Mississippi, using a soundstage built specifically for the production in the city's industrial park. Most location filming took place around the Madison County Courthouse and former county jail on the courthouse grounds. Other location filming took place in the Jackson, Mississippi, metro area, including the Jackson-Evers International Airport and Hinds County Medical Center (now Merit Health Central).


title: A Time to Kill (1996 film)

text: Grisham had apparently not wanted to sell the film rights to the book. He sold the rights for a record $6 million. He received casting approval for the film and overruled the director's choice of Woody Harrelson as the lead role, which was based on Grisham himself. Val Kilmer was also an early contender for the role. Sandra Bullock also received $6 million for five weeks of work.


title: A Time to Kill (1996 film)

text: "A Time to Kill" was released in the U.S. on July 24, 1996. It reached number one during its first two weeks and grossed over $108 million domestically.


title: A Time to Kill (1996 film)

text: On Rotten Tomatoes, the film has an approval rating of 67% based on 58 reviews, with an average rating of 6.2/10. The critics' consensus reads: "Overlong and superficial, "A Time to Kill" nonetheless succeeds on the strength of its skillful craftsmanship and top-notch performances". It has a score of 54 out of 100 on Metacritic, based on 21 reviews. Audiences surveyed by CinemaScore gave the film a grade of "A" on a scale of A+ to F.


title: A Time to Kill (1996 film)

text: Roger Ebert gave the film three stars out of four, saying: "I was absorbed by "A Time to Kill", and found the performances strong and convincing," and added that "this is the best of the film versions of Grisham novels, I think, and it has been directed with skill by Joel Schumacher."


title: A Time to Kill (1996 film)

text: The film was not without its detractors. Anthony Puccinelli gave the film one star, calling it "worthless" and remarking: ""A Time to Kill" argues for vigilantism but disguises its message by making the vigilante black, allowing viewers to think their blood lust and thirst for revenge is actually empathy for the oppressed." Peter Travers felt that "they [Schumacher and screenwriter Akiva Goldsman] cram[med] in too much," adding, "This distracts from the heart of the picture, which is in the bond between Carl Lee (the brilliant [Samuel L.] Jackson is quietly devastating) and Jake, a husband and father who knows he, too, would have shot anyone who raped his little girl." Gene Siskel remarked it was "An overwrought, contrived courtroom thriller", "cornball" and concluded "This story has been recycled out of countless better movies."


title: A Time to Kill (1996 film)

text: Grisham enjoyed the film, remarking: "When all was said and done I was happy with it, happy we were able to find a kid like Matthew McConaughey. It wasn't a great movie, but it was a good one."


title: A Time to Kill (1996 film)

text: In France, the film has been the subject of controversy. Critics have accused the movie of making an apology for the death penalty and right of self-defense. A question mark was added at the end of the title ("Le Droit de tuer ?"/"The Right to Kill ?") so as not to shock the audience. Amnesty International France uses the word "disturbing" when referring to the film in one of its documents. "Les Inrockuptibles" described the film as "nauseating", "stinking", almost "fascist", with an "ultra-populist" script that makes one want to "vomit". "Libération" criticized the script, calling it "extremely dirty": the movie, says the newspaper, "militates in favour of the Black cause only to legitimize, after many plot buckles (resurrection of the Ku Klux Klan, the deceits of court, threats of many kinds) the mentally ill gesture of the avenging father". According to "Libération", the movie "justifies the indefensible" with a "dripping sentimentalism".


title: A Time to Kill (1996 film)

text: Elliot Goldenthal scored the film. AllMusic gave the soundtrack two and a half stars out of five, commenting that it "doesn't work particularly well when it's separated from the film itself."


title: Statistics

text: Statistics (from German: "Statistik", "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.


title: Statistics

text: When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation.


title: Statistics

text: Two main statistical methods are used in data analysis: descriptive statistics, which summarize data from a sample using indexes such as the mean or standard deviation, and inferential statistics, which draw conclusions from data that are subject to random variation (e.g., observational errors, sampling variation). Descriptive statistics are most often concerned with two sets of properties of a "distribution" (sample or population): "central tendency" (or "location") seeks to characterize the distribution's central or typical value, while "dispersion" (or "variability") characterizes the extent to which members of the distribution depart from its center and each other. Inferences on mathematical statistics are made under the framework of probability theory, which deals with the analysis of random phenomena.


title: Statistics

text: A standard statistical procedure involves the collection of data leading to a test of the relationship between two statistical data sets, or a data set and synthetic data drawn from an idealized model. A hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis of no relationship between two data sets. Rejecting or disproving the null hypothesis is done using statistical tests that quantify the sense in which the null can be proven false, given the data that are used in the test. Working from a null hypothesis, two basic forms of error are recognized: Type I errors (null hypothesis is falsely rejected giving a "false positive") and Type II errors (null hypothesis fails to be rejected and an actual relationship between populations is missed giving a "false negative"). Multiple problems have come to be associated with this framework, ranging from obtaining a sufficient sample size to specifying an adequate null hypothesis.


title: Statistics

text: Measurement processes that generate statistical data are also subject to error. Many of these errors are classified as random (noise) or systematic (bias), but other types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also occur. The presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems.


title: Statistics

text: Statistics is a mathematical body of science that pertains to the collection, analysis, interpretation or explanation, and presentation of data, or as a branch of mathematics. Some consider statistics to be a distinct mathematical science rather than a branch of mathematics. While many scientific investigations make use of data, statistics is concerned with the use of data in the context of uncertainty and decision making in the face of uncertainty.


title: Statistics

text: In applying statistics to a problem, it is common practice to start with a population or process to be studied. Populations can be diverse topics such as "all people living in a country" or "every atom composing a crystal". Ideally, statisticians compile data about the entire population (an operation called census). This may be organized by governmental statistical institutes. "Descriptive statistics" can be used to summarize the population data. Numerical descriptors include mean and standard deviation for continuous data (like income), while frequency and percentage are more useful in terms of describing categorical data (like education).


title: Statistics

text: When a census is not feasible, a chosen subset of the population called a sample is studied. Once a sample that is representative of the population is determined, data is collected for the sample members in an observational or experimental setting. Again, descriptive statistics can be used to summarize the sample data. However, drawing the sample contains an element of randomness; hence, the numerical descriptors from the sample are also prone to uncertainty. To draw meaningful conclusions about the entire population, "inferential statistics" is needed. It uses patterns in the sample data to draw inferences about the population represented while accounting for randomness. These inferences may take the form of answering yes/no questions about the data (hypothesis testing), estimating numerical characteristics of the data (estimation), describing associations within the data (correlation), and modeling relationships within the data (for example, using regression analysis). Inference can extend to forecasting, prediction, and estimation of unobserved values either in or associated with the population being studied. It can include extrapolation and interpolation of time series or spatial data, and data mining.


title: Statistics

text: Mathematical statistics is the application of mathematics to statistics. Mathematical techniques used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure-theoretic probability theory.


title: Statistics

text: Formal discussions on inference date back to Arab mathematicians and cryptographers, during the Islamic Golden Age between the 8th and 13th centuries. Al-Khalil (717–786) wrote the "Book of Cryptographic Messages", which contains one of the first uses of permutations and combinations, to list all possible Arabic words with and without vowels. Al-Kindi's "Manuscript on Deciphering Cryptographic Messages" gave a detailed description of how to use frequency analysis to decipher encrypted messages, providing an early example of statistical inference for decoding. Ibn Adlan (1187–1268) later made an important contribution on the use of sample size in frequency analysis.


title: Statistics

text: The earliest writing containing statistics in Europe dates back to 1663, with the publication of "Natural and Political Observations upon the Bills of Mortality" by John Graunt. Early applications of statistical thinking revolved around the needs of states to base policy on demographic and economic data, hence its "stat-" etymology. The scope of the discipline of statistics broadened in the early 19th century to include the collection and analysis of data in general. Today, statistics is widely employed in government, business, and natural and social sciences.


title: Statistics

text: The mathematical foundations of statistics developed from discussions concerning games of chance among mathematicians such as Gerolamo Cardano, Blaise Pascal, Pierre de Fermat, and Christiaan Huygens. Although the idea of probability was already examined in ancient and medieval law and philosophy (such as the work of Juan Caramuel), probability theory as a mathematical discipline only took shape at the very end of the 17th century, particularly in Jacob Bernoulli's posthumous work "Ars Conjectandi". This was the first book where the realm of games of chance and the realm of the probable (which concerned opinion, evidence, and argument) were combined and submitted to mathematical analysis. The method of least squares was first described by Adrien-Marie Legendre in 1805, though Carl Friedrich Gauss presumably made use of it a decade earlier in 1795.


title: Statistics

text: The modern field of statistics emerged in the late 19th and early 20th century in three stages. The first wave, at the turn of the century, was led by the work of Francis Galton and Karl Pearson, who transformed statistics into a rigorous mathematical discipline used for analysis, not just in science, but in industry and politics as well. Galton's contributions included introducing the concepts of standard deviation, correlation, regression analysis and the application of these methods to the study of the variety of human characteristics—height, weight, eyelash length among others. Pearson developed the Pearson product-moment correlation coefficient, defined as a product-moment, the method of moments for the fitting of distributions to samples and the Pearson distribution, among many other things. Galton and Pearson founded "Biometrika" as the first journal of mathematical statistics and biostatistics (then called biometry), and the latter founded the world's first university statistics department at University College London.


title: Statistics

text: The second wave of the 1910s and 20s was initiated by William Sealy Gosset, and reached its culmination in the insights of Ronald Fisher, who wrote the textbooks that were to define the academic discipline in universities around the world. Fisher's most important publications were his 1918 seminal paper "The Correlation between Relatives on the Supposition of Mendelian Inheritance" (which was the first to use the statistical term, variance), his classic 1925 work "Statistical Methods for Research Workers" and his 1935 "The Design of Experiments", where he developed rigorous design of experiments models. He originated the concepts of sufficiency, ancillary statistics, Fisher's linear discriminator and Fisher information. He also coined the term null hypothesis during the Lady tasting tea experiment, which "is never proved or established, but is possibly disproved, in the course of experimentation". In his 1930 book "The Genetical Theory of Natural Selection", he applied statistics to various biological concepts such as Fisher's principle (which A. W. F. Edwards called "probably the most celebrated argument in evolutionary biology") and Fisherian runaway, a concept in sexual selection about a positive feedback runaway effect found in evolution.


title: Statistics

text: The final wave, which mainly saw the refinement and expansion of earlier developments, emerged from the collaborative work between Egon Pearson and Jerzy Neyman in the 1930s. They introduced the concepts of "Type II" error, power of a test and confidence intervals. Jerzy Neyman in 1934 showed that stratified random sampling was in general a better method of estimation than purposive (quota) sampling.


title: Statistics

text: Today, statistical methods are applied in all fields that involve decision making, for making accurate inferences from a collated body of data and for making decisions in the face of uncertainty based on statistical methodology. The use of modern computers has expedited large-scale statistical computations and has also made possible new methods that are impractical to perform manually. Statistics continues to be an area of active research for example on the problem of how to analyze big data.


title: Statistics

text: When full census data cannot be collected, statisticians collect sample data by developing specific experiment designs and survey samples. Statistics itself also provides tools for prediction and forecasting through statistical models.


title: Statistics

text: To use a sample as a guide to an entire population, it is important that it truly represents the overall population. Representative sampling assures that inferences and conclusions can safely extend from the sample to the population as a whole. A major problem lies in determining the extent that the sample chosen is actually representative. Statistics offers methods to estimate and correct for any bias within the sample and data collection procedures. There are also methods of experimental design for experiments that can lessen these issues at the outset of a study, strengthening its capability to discern truths about the population.


title: Statistics

text: Sampling theory is part of the mathematical discipline of probability theory. Probability is used in mathematical statistics to study the sampling distributions of sample statistics and, more generally, the properties of statistical procedures. The use of any statistical method is valid when the system or population under consideration satisfies the assumptions of the method. The difference in point of view between classic probability theory and sampling theory is, roughly, that probability theory starts from the given parameters of a total population to deduce probabilities that pertain to samples. Statistical inference, however, moves in the opposite direction—inductively inferring from samples to the parameters of a larger or total population.


title: Statistics

text: A common goal for a statistical research project is to investigate causality, and in particular to draw a conclusion on the effect of changes in the values of predictors or independent variables on dependent variables. There are two major types of causal statistical studies: experimental studies and observational studies. In both types of studies, the effect of differences of an independent variable (or variables) on the behavior of the dependent variable are observed. The difference between the two types lies in how the study is actually conducted. Each can be very effective.


title: Statistics

text: An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation. Instead, data are gathered and correlations between predictors and response are investigated. While the tools of data analysis work best on data from randomized studies, they are also applied to other kinds of data—like natural experiments and observational studies—for which a statistician would use a modified, more structured estimation method (e.g., Difference in differences estimation and instrumental variables, among many others) that produce consistent estimators.


title: Statistics

text: Experiments on human behavior have special concerns. The famous Hawthorne study examined changes to the working environment at the Hawthorne plant of the Western Electric Company. The researchers were interested in determining whether increased illumination would increase the productivity of the assembly line workers. The researchers first measured the productivity in the plant, then modified the illumination in an area of the plant and checked if the changes in illumination affected productivity. It turned out that productivity indeed improved (under the experimental conditions). However, the study is heavily criticized today for errors in experimental procedures, specifically for the lack of a control group and blindness. The Hawthorne effect refers to finding that an outcome (in this case, worker productivity) changed due to observation itself. Those in the Hawthorne study became more productive not because the lighting was changed but because they were being observed.


title: Statistics

text: An example of an observational study is one that explores the association between smoking and lung cancer. This type of study typically uses a survey to collect observations about the area of interest and then performs statistical analysis. In this case, the researchers would collect observations of both smokers and non-smokers, perhaps through a cohort study, and then look for the number of cases of lung cancer in each group. A case-control study is another type of observational study in which people with and without the outcome of interest (e.g. lung cancer) are invited to participate and their exposure histories are collected.


title: Statistics

text: Various attempts have been made to produce a taxonomy of levels of measurement. The psychophysicist Stanley Smith Stevens defined nominal, ordinal, interval, and ratio scales. Nominal measurements do not have meaningful rank order among values, and permit any one-to-one (injective) transformation. Ordinal measurements have imprecise differences between consecutive values, but have a meaningful order to those values, and permit any order-preserving transformation. Interval measurements have meaningful distances between measurements defined, but the zero value is arbitrary (as in the case with longitude and temperature measurements in Celsius or Fahrenheit), and permit any linear transformation. Ratio measurements have both a meaningful zero value and the distances between different measurements defined, and permit any rescaling transformation.


title: Statistics

text: Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically, sometimes they are grouped together as categorical variables, whereas ratio and interval measurements are grouped together as quantitative variables, which can be either discrete or continuous, due to their numerical nature. Such distinctions can often be loosely correlated with data type in computer science, in that dichotomous categorical variables may be represented with the Boolean data type, polytomous categorical variables with arbitrarily assigned integers in the integral data type, and continuous variables with the real data type involving floating-point arithmetic. But the mapping of computer science data types to statistical data types depends on which categorization of the latter is being implemented.


title: Statistics

text: Other categorizations have been proposed. For example, Mosteller and Tukey (1977) distinguished grades, ranks, counted fractions, counts, amounts, and balances. Nelder (1990) described continuous counts, continuous ratios, count ratios, and categorical modes of data. (See also: Chrisman (1998), van den Berg (1991).)


title: Statistics

text: The issue of whether or not it is appropriate to apply different kinds of statistical methods to data obtained from different kinds of measurement procedures is complicated by issues concerning the transformation of variables and the precise interpretation of research questions. "The relationship between the data and what they describe merely reflects the fact that certain kinds of statistical statements may have truth values which are not invariant under some transformations. Whether or not a transformation is sensible to contemplate depends on the question one is trying to answer."


title: Statistics

text: A descriptive statistic (in the count noun sense) is a summary statistic that quantitatively describes or summarizes features of a collection of information, while descriptive statistics in the mass noun sense is the process of using and analyzing those statistics. Descriptive statistics is distinguished from inferential statistics (or inductive statistics), in that descriptive statistics aims to summarize a sample, rather than use the data to learn about the population that the sample of data is thought to represent.


title: Statistics

text: Statistical inference is the process of using data analysis to deduce properties of an underlying probability distribution. Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population. Inferential statistics can be contrasted with descriptive statistics. Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population.


title: Statistics

text: Consider independent identically distributed (IID) random variables with a given probability distribution: standard statistical inference and estimation theory defines a random sample as the random vector given by the column vector of these IID variables. The population being examined is described by a probability distribution that may have unknown parameters.


title: Statistics

text: A statistic is a random variable that is a function of the random sample, but . The probability distribution of the statistic, though, may have unknown parameters. Consider now a function of the unknown parameter: an estimator is a statistic used to estimate such function. Commonly used estimators include sample mean, unbiased sample variance and sample covariance.


title: Statistics

text: A random variable that is a function of the random sample and of the unknown parameter, but whose probability distribution "does not depend on the unknown parameter" is called a pivotal quantity or pivot. Widely used pivots include the z-score, the chi square statistic and Student's t-value.


title: Statistics

text: Between two estimators of a given parameter, the one with lower mean squared error is said to be more efficient. Furthermore, an estimator is said to be unbiased if its expected value is equal to the true value of the unknown parameter being estimated, and asymptotically unbiased if its expected value converges at the limit to the true value of such parameter.


title: Statistics

text: Other desirable properties for estimators include: UMVUE estimators that have the lowest variance for all possible values of the parameter to be estimated (this is usually an easier property to verify than efficiency) and consistent estimators which converges in probability to the true value of such parameter.


title: Statistics

text: This still leaves the question of how to obtain estimators in a given situation and carry the computation, several methods have been proposed: the method of moments, the maximum likelihood method, the least squares method and the more recent method of estimating equations.


title: Statistics

text: Interpretation of statistical information can often involve the development of a null hypothesis which is usually (but not necessarily) that no relationship exists among variables or that no change occurred over time.


title: Statistics

text: The best illustration for a novice is the predicament encountered by a criminal trial. The null hypothesis, H, asserts that the defendant is innocent, whereas the alternative hypothesis, H, asserts that the defendant is guilty. The indictment comes because of suspicion of the guilt. The H (status quo) stands in opposition to H and is maintained unless H is supported by evidence "beyond a reasonable doubt". However, "failure to reject H" in this case does not imply innocence, but merely that the evidence was insufficient to convict. So the jury does not necessarily "accept" H but "fails to reject" H. While one can not "prove" a null hypothesis, one can test how close it is to being true with a power test, which tests for type II errors.


title: Statistics

text: What statisticians call an alternative hypothesis is simply a hypothesis that contradicts the null hypothesis.


title: Statistics

text: Standard deviation refers to the extent to which individual observations in a sample differ from a central value, such as the sample or population mean, while Standard error refers to an estimate of difference between sample mean and population mean.


title: Statistics

text: A statistical error is the amount by which an observation differs from its expected value. A residual is the amount an observation differs from the value the estimator of the expected value assumes on a given sample (also called prediction).


title: Statistics

text: Mean squared error is used for obtaining efficient estimators, a widely used class of estimators. Root mean square error is simply the square root of mean squared error.


title: Statistics

text: Many statistical methods seek to minimize the residual sum of squares, and these are called "methods of least squares" in contrast to Least absolute deviations. The latter gives equal weight to small and big errors, while the former gives more weight to large errors. Residual sum of squares is also differentiable, which provides a handy property for doing regression. Least squares applied to linear regression is called ordinary least squares method and least squares applied to nonlinear regression is called non-linear least squares. Also in a linear regression model the non deterministic part of the model is called error term, disturbance or more simply noise. Both linear regression and non-linear regression are addressed in polynomial least squares, which also describes the variance in a prediction of the dependent variable (y axis) as a function of the independent variable (x axis) and the deviations (errors, noise, disturbances) from the estimated (fitted) curve.


title: Statistics

text: Measurement processes that generate statistical data are also subject to error. Many of these errors are classified as random (noise) or systematic (bias), but other types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also be important. The presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems.


title: Statistics

text: Most studies only sample part of a population, so results don't fully represent the whole population. Any estimates obtained from the sample only approximate the population value. Confidence intervals allow statisticians to express how closely the sample estimate matches the true value in the whole population. Often they are expressed as 95% confidence intervals. Formally, a 95% confidence interval for a value is a range where, if the sampling and analysis were repeated under the same conditions (yielding a different dataset), the interval would include the true (population) value in 95% of all possible cases. This does "not" imply that the probability that the true value is in the confidence interval is 95%. From the frequentist perspective, such a claim does not even make sense, as the true value is not a random variable. Either the true value is or is not within the given interval. However, it is true that, before any data are sampled and given a plan for how to construct the confidence interval, the probability is 95% that the yet-to-be-calculated interval will cover the true value: at this point, the limits of the interval are yet-to-be-observed random variables. One approach that does yield an interval that can be interpreted as having a given probability of containing the true value is to use a credible interval from Bayesian statistics: this approach depends on a different way of interpreting what is meant by "probability", that is as a Bayesian probability.


title: Statistics

text: In principle confidence intervals can be symmetrical or asymmetrical. An interval can be asymmetrical because it works as lower or upper bound for a parameter (left-sided interval or right sided interval), but it can also be asymmetrical because the two sided interval is built violating symmetry around the estimate. Sometimes the bounds for a confidence interval are reached asymptotically and these are used to approximate the true bounds.


title: Statistics

text: Statistics rarely give a simple Yes/No type answer to the question under analysis. Interpretation often comes down to the level of statistical significance applied to the numbers and often refers to the probability of a value accurately rejecting the null hypothesis (sometimes referred to as the p-value).


title: Statistics

text: The standard approach is to test a null hypothesis against an alternative hypothesis. A critical region is the set of values of the estimator that leads to refuting the null hypothesis. The probability of type I error is therefore the probability that the estimator belongs to the critical region given that null hypothesis is true (statistical significance) and the probability of type II error is the probability that the estimator doesn't belong to the critical region given that the alternative hypothesis is true. The statistical power of a test is the probability that it correctly rejects the null hypothesis when the null hypothesis is false.


title: Statistics

text: Referring to statistical significance does not necessarily mean that the overall result is significant in real world terms. For example, in a large study of a drug it may be shown that the drug has a statistically significant but very small beneficial effect, such that the drug is unlikely to help the patient noticeably.


title: Statistics

text: Although in principle the acceptable level of statistical significance may be subject to debate, the significance level is the largest p-value that allows the test to reject the null hypothesis. This test is logically equivalent to saying that the p-value is the probability, assuming the null hypothesis is true, of observing a result at least as extreme as the test statistic. Therefore, the smaller the significance level, the lower the probability of committing type I error.


title: Statistics

text: Exploratory data analysis (EDA) is an approach to analyzing data sets to summarize their main characteristics, often with visual methods. A statistical model can be used or not, but primarily EDA is for seeing what the data can tell us beyond the formal modeling or hypothesis testing task.


title: Statistics

text: Misuse of statistics can produce subtle but serious errors in description and interpretation—subtle in the sense that even experienced professionals make such errors, and serious in the sense that they can lead to devastating decision errors. For instance, social policy, medical practice, and the reliability of structures like bridges all rely on the proper use of statistics.


title: Statistics

text: Even when statistical techniques are correctly applied, the results can be difficult to interpret for those lacking expertise. The statistical significance of a trend in the data—which measures the extent to which a trend could be caused by random variation in the sample—may or may not agree with an intuitive sense of its significance. The set of basic statistical skills (and skepticism) that people need to deal with information in their everyday lives properly is referred to as statistical literacy.