|
Type III Error
In statistical hypothesis testing, there are various notions of so-called type III errors (or errors of the third kind), and sometimes type IV errors or higher, by analogy with the type I and type II errors of Jerzy Neyman and Egon Pearson. Fundamentally, type III errors occur when researchers provide the right answer to the wrong question, i.e. when the correct hypothesis is rejected but for the wrong reason. Since the paired notions of type I errors (or "false positives") and type II errors (or "false negatives") that were introduced by Neyman and Pearson are now widely used, their choice of terminology ("errors of the first kind" and "errors of the second kind"), has led others to suppose that certain sorts of mistakes that they have identified might be an "error of the third kind", "fourth kind", etc. None of these proposed categories have been widely accepted. The following is a brief account of some of these proposals. Systems theory In systems theory an additi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Hypothesis Testing
A statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis. Hypothesis testing allows us to make probabilistic statements about population parameters. History Early use While hypothesis testing was popularized early in the 20th century, early forms were used in the 1700s. The first use is credited to John Arbuthnot (1710), followed by Pierre-Simon Laplace (1770s), in analyzing the human sex ratio at birth; see . Modern origins and early controversy Modern significance testing is largely the product of Karl Pearson ( ''p''-value, Pearson's chi-squared test), William Sealy Gosset ( Student's t-distribution), and Ronald Fisher ("null hypothesis", analysis of variance, "significance test"), while hypothesis testing was developed by Jerzy Neyman and Egon Pearson (son of Karl). Ronald Fisher began his life in statistics as a Bayesian (Zabell 1992), but Fisher soon grew disenchanted with t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oak Ridge National Laboratory
Oak Ridge National Laboratory (ORNL) is a U.S. multiprogram science and technology national laboratory sponsored by the U.S. Department of Energy (DOE) and administered, managed, and operated by UT–Battelle as a federally funded research and development center (FFRDC) under a contract with the DOE, located in Oak Ridge, Tennessee. Established in 1943, ORNL is the largest science and energy national laboratory in the Department of Energy system (by size) and third largest by annual budget. It is located in the Roane County section of Oak Ridge, Tennessee. Its scientific programs focus on materials, nuclear science, neutron science, energy, high-performance computing, systems biology and national security, sometimes in partnership with the state of Tennessee, universities and other industries. ORNL has several of the world's top supercomputers, including Frontier, ranked by the TOP500 as the world's most powerful. The lab is a leading neutron and nuclear power research f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type I And Type II Errors
In statistical hypothesis testing, a type I error is the mistaken rejection of an actually true null hypothesis (also known as a "false positive" finding or conclusion; example: "an innocent person is convicted"), while a type II error is the failure to reject a null hypothesis that is actually false (also known as a "false negative" finding or conclusion; example: "a guilty person is not convicted"). Much of statistical theory revolves around the minimization of one or both of these errors, though the complete elimination of either is a statistical impossibility if the outcome is not determined by a known, observable causal process. By selecting a low threshold (cut-off) value and modifying the alpha (α) level, the quality of the hypothesis test can be increased. The knowledge of type I errors and type II errors is widely used in medical science, biometrics and computer science. Intuitively, type I errors can be thought of as errors of ''commission'', i.e. the researcher unluck ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ethics In Mathematics
Ethics in mathematics is an emerging field of applied ethics, the inquiry into ethical aspects of the practice and applications of mathematics. It deals with the professional responsibilities of mathematicians whose work influences decisions with major consequences, such as in law, finance, the military, and environmental science. Although many research mathematicians see no ethical implications in their pure research, assumptions made in mathematical approaches can have real consequences. A very instrumental interpretation of the impact of mathematics makes it difficult to see ethical consequences, but it is easier to see how all branches of mathematics serve to structure and conceptualise solutions to real problems. These structures can set up perverse incentives, where targets can be met without improving services, or league table positions are gamed. While the assumptions written into metrics often reflect the world view of the groups who are responsible for designing them, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abraham Silvers
Abraham Silvers (born 29 April 1934 in Bronx, New York) is an American mathematician and statistician who has written extensively on research methods and approaches to clinical trials, medical studies and environmental risk assessment. Silvers received his PhD under the supervision of Leo Sario from the University of California, Los Angeles in 1964. He was elected a Fellow of the American Statistical Association (ASA) in 1988 for his contributions to clinical trial and health risk assessment methodology, and in 1993, ASA awarded him a Distinguished Medal for his work in environmental statistics. Publications He has co-authored and published over 100 articles including: * 1964: Dissertation: Differential Geometric Methods in the Study of Mappings into Abstract Riemann Surfaces * 1968: Insulin delivery rate into plasma in normal and diabetic subjects * 1978: A prospective evaluation of the leukocyte adherence inhibition test in colorectal cancer and its correlation with carcinoembr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ian I
Ian or Iain is a name of Scottish Gaelic origin, derived from the Hebrew given name (Yohanan, ') and corresponding to the English name John. The spelling Ian is an Anglicization of the Scottish Gaelic forename ''Iain''. It is a popular name in Scotland, where it originated, as well as other English-speaking countries. The name has fallen out of the top 100 male baby names in the United Kingdom, having peaked in popularity as one of the top 10 names throughout the 1960s. In 1900, Ian was the 180th most popular male baby name in England and Wales. , the name has been in the top 100 in the United States every year since 1982, peaking at 65 in 2003. Other Gaelic forms of "John" include "Seonaidh" ("Johnny" from Lowland Scots), "Seon" (from English), "Seathan", and "Seán" and "Eoin" (from Irish). Its Welsh counterpart is Ioan, its Cornish equivalent is Yowan and Breton equivalent is Yann. Notable people named Ian As a first name (alphabetical by family name) *Ian Agol (born 19 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dirty Rotten Strategies
Dirt is an unclean matter, especially when in contact with a person's clothes, skin, or possessions. In such cases, they are said to become dirty. Common types of dirt include: * Debris: scattered pieces of waste or remains * Dust: a general powder of Organic matter, organic or Mineral, mineral matter * wikt:filth, Filth: foul matter such as excrement * wikt:grime, Grime: a black, ingrained dust such as soot * Soil: the mix of clay, sand, and humus which lies on top of bedrock. The term 'soil' may be used to refer to unwanted substances or dirt that are deposited onto surfaces such as clothing. Exhibitions and studies A season of artworks and exhibits on the theme of dirt was sponsored by the Wellcome Trust in 2011. The centrepiece was an exhibition at the Wellcome Collection showing pictures and histories of notable dirt such as the great dust heaps at Euston railway station, Euston and London King's Cross railway station, King's Cross in the 19th century and the Fresh Ki ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Tukey
John Wilder Tukey (; June 16, 1915 – July 26, 2000) was an American mathematician and statistician, best known for the development of the fast Fourier Transform (FFT) algorithm and box plot. The Tukey range test, the Tukey lambda distribution, the Tukey test of additivity, and the Teichmüller–Tukey lemma all bear his name. He is also credited with coining the term 'bit' and the first published use of the word 'software'. Biography Tukey was born in New Bedford, Massachusetts in 1915, to a Latin teacher father and a private tutor. He was mainly taught by his mother and attended regular classes only for certain subjects like French. Tukey obtained a BA in 1936 and MSc in 1937 in chemistry, from Brown University, before moving to Princeton University, where in 1939 he received a PhD in mathematics after completing a doctoral dissertation titled "On denumerability in topology". During World War II, Tukey worked at the Fire Control Research Office and collaborated wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Howard Raiffa
Howard Raiffa (; January 24, 1924 – July 8, 2016) was an American academic who was the Frank P. Ramsey Professor (Emeritus) of Managerial Economics, a joint chair held by the Business School and Harvard Kennedy School at Harvard University. He was an influential Bayesian decision theorist and pioneer in the field of decision analysis, with works in statistical decision theory, game theory, behavioral decision theory, risk analysis, and negotiation analysis. He helped found and was the first director of the International Institute for Applied Systems Analysis. Early life After service in the Army Air Forces during World War II, Raiffa received a bachelor's degree in mathematics in 1946, a master's degree in statistics in 1947 and a PhD in mathematics in 1951, all from the University of Michigan. Career *His book ''Applied Statistical Decision Theory'' with Robert Schlaifer introduced the idea of conjugate prior distributions. *A lecture of his in the 1960s concerning the use o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard Hamming
Richard Wesley Hamming (February 11, 1915 – January 7, 1998) was an American mathematician whose work had many implications for computer engineering and telecommunications. His contributions include the Hamming code (which makes use of a Hamming matrix), the Hamming window, Hamming numbers, sphere-packing (or Hamming bound), Hamming graph concepts, and the Hamming distance. Born in Chicago, Hamming attended University of Chicago, University of Nebraska and the University of Illinois at Urbana–Champaign, where he wrote his doctoral thesis in mathematics under the supervision of Waldemar Trjitzinsky (1901–1973). In April 1945 he joined the Manhattan Project at the Los Alamos Laboratory, where he programmed the IBM calculating machines that computed the solution to equations provided by the project's physicists. He left to join the Bell Telephone Laboratories in 1946. Over the next fifteen years he was involved in nearly all of the Laboratories' most prominent achievements ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gettier Problems
The Gettier problem, in the field of epistemology, is a landmark philosophical problem concerning the understanding of descriptive knowledge. Attributed to American philosopher Edmund Gettier, Gettier-type counterexamples (called "Gettier-cases") challenge the long-held justified true belief (JTB) account of knowledge. The JTB account holds that knowledge is equivalent to justified true belief; if all three conditions (justification, truth, and belief) are met of a given claim, then we have knowledge of that claim. In his 1963 three-page paper titled "Is Justified True Belief Knowledge?", Gettier attempts to illustrate by means of two counterexamples that there are cases where individuals can have a justified, true belief regarding a claim but still fail to know it because the reasons for the belief, while justified, turn out to be false. Thus, Gettier claims to have shown that the JTB account is inadequate because it does not account for all of the necessary and sufficient conditio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type I And Type II Errors
In statistical hypothesis testing, a type I error is the mistaken rejection of an actually true null hypothesis (also known as a "false positive" finding or conclusion; example: "an innocent person is convicted"), while a type II error is the failure to reject a null hypothesis that is actually false (also known as a "false negative" finding or conclusion; example: "a guilty person is not convicted"). Much of statistical theory revolves around the minimization of one or both of these errors, though the complete elimination of either is a statistical impossibility if the outcome is not determined by a known, observable causal process. By selecting a low threshold (cut-off) value and modifying the alpha (α) level, the quality of the hypothesis test can be increased. The knowledge of type I errors and type II errors is widely used in medical science, biometrics and computer science. Intuitively, type I errors can be thought of as errors of ''commission'', i.e. the researcher unluck ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
