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Analysis of variance

Analysis of variance is a collection of statistical models and their associated estimation procedures used to analyze the differences among group means in a sample. ANOVA was developed by statistician and evolutionary biologist Ronald Fisher; the ANOVA is based on the law of total variance, where the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether two or more population means are equal, therefore generalizes the t-test beyond two means. While the analysis of variance reached fruition in the 20th century, antecedents extend centuries into the past according to Stigler; these include hypothesis testing, the partitioning of sums of squares, experimental techniques and the additive model. Laplace was performing hypothesis testing in the 1770s; the development of least-squares methods by Laplace and Gauss circa 1800 provided an improved method of combining observations.

It initiated much study of the contributions to sums of squares. Laplace knew. By 1827, Laplace was using least squares methods to address ANOVA problems regarding measurements of atmospheric tides. Before 1800, astronomers had isolated observational errors resulting from reaction times and had developed methods of reducing the errors; the experimental methods used in the study of the personal equation were accepted by the emerging field of psychology which developed strong experimental methods to which randomization and blinding were soon added. An eloquent non-mathematical explanation of the additive effects model was available in 1885. Ronald Fisher introduced the term variance and proposed its formal analysis in a 1918 article The Correlation Between Relatives on the Supposition of Mendelian Inheritance, his first application of the analysis of variance was published in 1921. Analysis of variance became known after being included in Fisher's 1925 book Statistical Methods for Research Workers.

Randomization models were developed by several researchers. The first was published in Polish by Jerzy Neyman in 1923. One of the attributes of ANOVA that ensured its early popularity was computational elegance; the structure of the additive model allows solution for the additive coefficients by simple algebra rather than by matrix calculations. In the era of mechanical calculators this simplicity was critical; the determination of statistical significance required access to tables of the F function which were supplied by early statistics texts. The analysis of variance can be used as an exploratory tool to explain observations. A dog show provides an example. A dog show is not a random sampling of the breed: it is limited to dogs that are adult, pure-bred, exemplary. A histogram of dog weights from a show might plausibly be rather complex, like the yellow-orange distribution shown in the illustrations. Suppose we wanted to predict the weight of a dog based on a certain set of characteristics of each dog.

One way to do, to explain the distribution of weights by dividing the dog population into groups based on those characteristics. A successful grouping will split dogs such that each group has a low variance of dog weights and the mean of each group is distinct. In the illustrations to the right, groups are identified as X1, X2, etc. In the first illustration, the dogs are divided according to the product of two binary groupings: young vs old, short-haired vs long-haired. Since the distributions of dog weight within each of the groups has a large variance, since the means are similar across groups, grouping dogs by these characteristics does not produce an effective way to explain the variation in dog weights: knowing which group a dog is in doesn't allow us to predict its weight much better than knowing the dog is in a dog show. Thus, this grouping fails to explain the variation in the overall distribution. An attempt to explain the weight distribution by grouping dogs as pet vs working breed and less athletic vs more athletic would be somewhat more successful.

The heaviest show dogs are to be big, working breeds, while breeds kept as pets tend to be smaller and thus lighter. As shown by the second illustration, the distributions have variances that are smaller than in the first case, the means are more distinguishable. However, the significant overlap of distributions, for example, means that we cannot distinguish X1 and X2 reliably. Grouping dogs according to a coin flip might produce distributions that look similar. An attempt to explain weight by breed is to produce a good fit. All Chihuahuas are light and all St Bernards are heavy; the difference in weights between Setters and Pointers does not justify separate breeds. The analysis of variance provides the formal tools to justify these intuitive judgments. A common use of the method is the development of models; the method has some advantages over correlation: not all of the data must be numeric and one result of the method is a judgment in the confidence in an explanatory relationship. ANOVA is a form of statistical hypothesis testing used in the analysis of experimental data.


Chuchura railway station

Chuchura railway station is a Kolkata Suburban Railway station on the Howrah-Bardhaman main line. It is located in Hooghly district in the Indian state of West Bengal, it is under the jurisdiction of Eastern Railway zone. Chuchura railway station is a small railway stations of Howrah railway division, it serves surrounding areas. It is 36 km. from Howrah Station. East Indian Railway Company started construction of a line out of Howrah for the proposed link with Delhi via Rajmahal and Mirzapur in 1851; the first passenger train in eastern India ran from Howrah to Hooghly on 15 August 1854. The track was extended to Raniganj by 1855. Electrification of Howrah—Burdwan main line was completed with 25 kV AC overhead system in 1958

Francesco Baccini

Francesco Baccini is an Italian singer-songwriter. Born in Genoa, Baccini made his official debut in 1988 with the stage name Espressione Musica, with "Mamma dammi i soldi", the closing theme song of the 38th edition of the Sanremo Music Festival. Put under contract by Caterina Caselli, in 1989 he released his first album, both a critical and commercial success. In 1990 he won the Festivalbar competition and peaked the Italian hit parade with the song "Sotto questo sole", recorded together with the band Ladri di biciclette. In 1997 he entered the competition at the Sanremo Music Festival, ranking eleventh with the song "Senza tu". In 2004 he toured with "Orco Loco", subtitled as “A Clipcomedy with Songs”, a recital in which he performed both as a singer and, for the first time, as an actor. Album1989 - Cartoons 1990 - Il pianoforte non è il mio forte 1992 - Nomi e cognomi 1993 - Nudo 1996 - Baccini a colori 1997 - Baccini and Best Friends 1999 - Nostra signora degli autogrill 2001 - Forza Francesco!

2005 - Stasera teatro 2006 - 2007 - Dalla parte di Caino 2008 - Uniti 2011 - Baccini canta Tenco 2017 - Chewing-gum Blues Official website Francesco Baccini on IMDb Francesco Baccini discography at Discogs

Bobby Graham (footballer)

Bobby Graham is a Scottish retired professional footballer who played for Liverpool during the 1960s. Born in Motherwell, North Lanarkshire, Graham played for Motherwell Bridge Works as an amateur before Bill Shankly signed him for Liverpool as 17-year-old in November 1961. A forward, Graham scored on his full debut, a 6-1 victory over KR Reykjavik on 14 September 1964 in a European Cup preliminary round 2nd leg tie at Anfield, he scored a hat-trick in his first league game against Aston Villa 12 days on 26 September, the game finished 5-1 to the Reds with Graham's goals coming in the 6th, 64th and 86th minutes. Graham was at Liverpool at an unfortunate time for himself as he found it difficult to dislodge the successful strike partnership of Ian St John and Roger Hunt and found first team appearances hard to come by; such was the dominance of both St John and Hunt he missed out on the 1965 FA Cup Final win and only made 1 appearance during the Reds run to the league title the following season not enough to gain him a medal.

The 1969–70 season was the most successful for him in a red shirt, with Hunt and St John both pensioned off he made 54 first-team appearances and scored 21 goals which included a stunning strike in the Merseyside derby at Goodison Park, the same game that saw Everton's Sandy Brown score'that' infamous own goal. Shortly afterwards, two new strikers arrived in the form of Kevin Keegan from Scunthorpe United and John Toshack from Cardiff City, Graham lost his place once again. In March 1972 he was allowed to leave Anfield and moved to Highfield Road and Coventry City where he linked up with former teammate St John once more, again he struggled to get 1st team recognition going out on loan to Tranmere Rovers, when St John was in charge, for 10 games. Graham returned to Scotland. Graham moved to his home town club Motherwell. Ian St John again signed him for the Fir Park club and by the end of his first season he had shown why'The Saint' had shown such faith, he finished top scorer. A young Willie Pettigrew was added to the side the following season and the pair formed a lethal partnership that terrorised Scottish defences for four seasons.

When Crawford Boyd was interviewed for the Queen of the South F. C. website, Boyd listed Bobby Graham as the best player that he played against in his time at Queens. After 132 games and 37 goals Graham joined Hamilton Academical in 1977 for a record transfer fee of £15,000, he, made over 100 appearances scoring 42 times, he left Hamilton and senior football when he ended his playing days at Shotts Bon Accord in the Scottish junior football scene. Player profile at Former players at Bobby Graham at Post War English & Scottish Football League A–Z Player's Database

Naomi Duguid

Naomi Duguid is a food writer and photographer from Canada. Duguid is based in Toronto and has coauthored six cookbooks, well as Burma: Rivers of Flavor in 2012, her first solo publication, she is best known for her cookbooks co-written with her ex-husband Jeffrey Alford. Duguid attended Queen's University in Kingston and proceeded through law school. After travelling around the world Naomi met Jeffrey Alford in Tibet in 1985 and the two were soon married, she quit her job as a lawyer and went into writing cookbooks in 1995. She has jointly put out five books with her husband on world cooking. All five books have gone on to be major successes and have won Cookbook of the Year from the James Beard Foundation in 1996 and 2001 as well as Cuisine Canada Cookbook Award in 1999 and 2004. Alford and Duguid have two sons together, lived in Toronto, Canada until they separated in 2009. Naomi Duguid continues to live in Toronto, Jeffrey Alford now lives in Thailand. Flatbreads and Flavors: A Culinary Atlas Home Baking: Sweet and Savory Traditions from Around the World Hot Sour Salty Sweet Seductions of Rice Mangoes and Curry Leaves: Culinary Travels Through the Great Subcontinent Beyond the Great Wall: Recipes and Travels in the Other China Burma: Rivers of Flavor Taste of Persia Kramer, Jane.

"Profiles: The Hungry Travellers". The New Yorker. 84: 100–106. Hot Sour Salty Sweet: Official website of Jeffrey Alford + Naomi Duguid

Marilyn Hickey

Marilyn Allene Hickey is an American Christian minister and televangelist who teaches Bible studies both nationally and internationally. Marilyn Allene Hickey was born on July 1931, in Dalhart, Texas; when she was a young girl, Hickey's parents were professing Methodists and attended church only casually. Her family suffered from hereditary mental disorders according to one of her telecasts, her father had it, after her grandfather and her great-grandfather that had it before the "devil and his imps" got to Marilyn, at the age of 36, she was the only one in her family not to suffer a mental disorder. In her family, she said that her family had a history of heart diseases Hickey herself, that at age 11, she was told by her doctors she had an enlarged heart, progressively got worse until she had surgery, she became. In college, she studied Spanish, she met Wallace Hickey at an Assemblies of God Church, where Wallace served as a pastor, together on December 26, 1954, the couple were married. Around the same time and Wallace met Dr. T.

L. Osborn, a Pentecostal evangelist, 8 years Hickey's senior, when she and Wallace both had traveled around in her husband's car, doing tent revival meetings, in town, she became lifelong friends with him, until she lost him, only 4 months, after she lost Wallace; the most coincidental thing is she was a guest-speaker at one of the conferences in which Dr. Osborn held. After a short time in Texas, they moved to Colorado to found Full Gospel Chapel; the church known as Orchard Road Christian Center, became one of the largest churches in the Denver area. They turned over the pastorate to their daughter Sarah Bowling and son-in-law Reece Bowling; the church meets in Centennial, Colorado. Hickey holds a Bachelor of Arts in Collective Foreign Languages from the University of Northern Colorado and an Honorary Doctorate of Divinity from Oral Roberts University. In 2015, Hickey was honored at Oral Roberts University with a Lifetime Global Achievement Award. Hickey has four grandchildren. Hickey's husband of 57 years, died after a long battle of Alzheimer's disease, in the care center of Denver, Colorado, on October 19, 2012, at age 87.

Hickey has aired a television program since 1973 and, since 1996, has co-hosted it with her daughter Sarah Bowling. Today with Marilyn and Sarah can be seen on various Christian networks such as the DayStar Network, Channel C, independent stations in both the U. S. and internationally, as well as through her YouTube Channel. She has been seen on the Trinity Broadcasting Network. In 2012, Hickey held a three-day prayer and faith healing rally in Karachi, Pakistan, attended by over 400,000 people. On 12 November 2016 with her 7th trip to Pakistan she aimed at reaching 1,000,000 people in a single meeting in Karachi. Hickey has served as a member of the Board of Regents of Oral Roberts University. Hickey preaches a Charismatic Word of Faith message. Apologetics Charismatics Faith healing Full Gospel Glossolalia Pentecostalism Official website