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In Sanskrit, rasa translates to "mercury", and Nāgārjuna Siddha was said to have developed a method of converting mercury into gold. Scholarship on Indian alchemy is in the publication of The Alchemical Body by David Gordon White. A modern bibliography on Indian alchemical studies has been written by White. The content... | [
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Platonic and Aristotelian thought, which had already been somewhat appropriated into hermetical science, continued to be assimilated during the late 7th and early 8th centuries through Syriac translations and scholarship. In the late ninth and early tenth centuries, the Arabic works attributed to Jābir ibn Hayyān (Lati... | [
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His original system consisted of seven elements, which included the five classical elements (aether, air, earth, fire, and water) in addition to two chemical elements representing the metals: sulphur, "the stone which burns", which characterized the principle of combustibility, and mercury, which contained the idealize... | [
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It is said that the Chinese invented gunpowder while trying to find a potion for eternal life. Described in 9th-century texts and used in fireworks in China by the 10th century, it was used in cannons by 1290. From China, the use of gunpowder spread to Japan, the Mongols, the Muslim world, and Europe. Gunpowder was use... | [
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The translation of Arabic texts concerning numerous disciplines including alchemy flourished in 12th-century Toledo, Spain, through contributors like Gerard of Cremona and Adelard of Bath. Translations of the time included the Turba Philosophorum, and the works of Avicenna and Muhammad ibn Zakariya al-Razi. These broug... | [
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Albertus Magnus, a Dominican friar, is known to have written works such as the Book of Minerals where he observed and commented on the operations and theories of alchemical authorities like Hermes and Democritus and unnamed alchemists of his time. Albertus critically compared these to the writings of Aristotle and Avic... | [
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The practical confirmed the theoretical, and Bacon advocated its uses in natural science and medicine. In later European legend, he became an archmage. In particular, along with Albertus Magnus, he was credited with the forging of a brazen head capable of answering its owner's questions. Soon after Bacon, the influenti... | [
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In the 14th century, alchemy became more accessible to Europeans outside the confines of Latin speaking churchmen and scholars. Alchemical discourse shifted from scholarly philosophical debate to an exposed social commentary on the alchemists themselves. Dante, Piers Plowman, and Chaucer all painted unflattering pictur... | [
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Most of 'his' work was aimed at gathering alchemical knowledge that had existed before him, especially as regarded the philosopher's stone. Through the 14th and 15th centuries, alchemists were much like Flamel: they concentrated on looking for the philosophers' stone. Bernard Trevisan and George Ripley made similar con... | [
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Paracelsus pioneered the use of chemicals and minerals in medicine and wrote, "Many have said of Alchemy, that it is for the making of gold and silver. For me such is not the aim, but to consider only what virtue and power may lie in medicines." His hermetical views were that sickness and health in the body relied on t... | [
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Alchemists were contracted by the elite for practical purposes related to mining, medical services, and the production of chemicals, medicines, metals, and gemstones. Rudolf II, Holy Roman Emperor, in the late 16th century, famously received and sponsored various alchemists at his court in Prague, including Dee and his... | [
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Michael Sendivogius (Michał Sędziwój, 1566–1636), a Polish alchemist, philosopher, medical doctor and pioneer of chemistry wrote mystical works but is also credited with distilling oxygen in a lab sometime around 1600. Sendivogious taught his technique to Cornelius Drebbel who, in 1621, applied this in a submarine. Isa... | [
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Boyle would note the place in which the experiment was carried out, the wind characteristics, the position of the Sun and Moon, and the barometer reading, all just in case they proved to be relevant. This approach eventually led to the founding of modern chemistry in the 18th and 19th centuries, based on revolutionary ... | [
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This interpretation further forwarded the view that alchemy is an art primarily concerned with spiritual enlightenment or illumination, as opposed to the physical manipulation of apparatus and chemicals, and claims that the obscure language of the alchemical texts were an allegorical guise for spiritual, moral or mysti... | [
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Michael Maier names Mary the Jewess, Cleopatra the Alchemist, Medera, and Taphnutia as the four women who knew how to make the philosopher's stone. Zosimos' sister Theosebia (later known as Euthica the Arab) and Isis the Prophetess also played a role in early alchemical texts. The first alchemist whose name we know was... | [
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Modern historical research
The history of alchemy has become a significant and recognized subject of academic study. As the language of the alchemists is analyzed, historians are becoming more aware of the intellectual connections between that discipline and other facets of Western cultural history, such as the evolut... | [
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The concepts of prima materia and anima mundi are central to the theory of the philosopher's stone. Magnum opus
The Great Work of Alchemy is often described as a series of four stages represented by colors. nigredo, a blackening or melanosis
albedo, a whitening or leucosis
citrinitas, a yellowing or xanthosis
rubedo,... | [
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Esoteric interpretations of historical texts
In the eyes of a variety of modern esoteric and Neo-Hermeticist practitioners, alchemy is fundamentally spiritual. In this interpretation, transmutation of lead into gold is presented as an analogy for personal transmutation, purification, and perfection. According to this v... | [
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In texts that are held to have been written according to this view, the cryptic alchemical symbols, diagrams, and textual imagery of late alchemical works are supposed to contain multiple layers of meanings, allegories, and references to other equally cryptic works; which must be laboriously decoded to discover their t... | [
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The volumes of work he wrote brought new light into understanding the art of transubstantiation and renewed alchemy's popularity as a symbolic process of coming into wholeness as a human being where opposites brought into contact and inner and outer, spirit and matter are reunited in the hieros gamos or divine marriag... | [
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In the last hundred years, alchemists have been portrayed in a magical and spagyric role in fantasy fiction, film, television, novels, comics and video games. Science
One goal of alchemy, the transmutation of base substances into gold, is now known to be impossible by chemical means but possible by physical means. Al... | [
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), Les alchimistes grecs, t. 4.1 : Zosime de Panopolis. Mémoires authentiques, Paris, Les Belles Lettres, 1995. Andrée Collinet and Henri-Dominique Saffrey (ed. ), Les alchimistes grecs, t. 10 : L'Anonyme de Zuretti ou l'Art sacré and divin de la chrysopée par un anonyme, Paris, Les Belles Lettres, 2000. Andrée Colline... | [
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Philippe Derchain, "L'Atelier des Orfèvres à Dendara et les origines de l'alchimie," Chronique d'Égypte, vol. 65, no 130, 1990, p. 219–242. Korshi Dosoo, « A History of the Theban Magical Library », Bulletin of the American Society of Papyrologists 53 (2016), p. 251–274. Olivier Dufault, Early Greek Alchemy, Patronage ... | [
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Shannon Grimes, Becoming Gold: Zosimos of Panopolis and the Alchemical Arts in Roman Egypt, Auckland, Rubedo Press, 2018,
Paul T. Keyser, « Greco-Roman Alchemy and Coins of Imitation Silver », American Journal of Numismatics 7–8 (1995–1996), p. 209–234. Paul Keyser, « The Longue Durée of Alchemy », in John Scarboroug... | [
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Daniel Stolzenberg, « Unpropitious Tinctures: Alchemy, Astrology & Gnosis According to Zosimos of Panopolis », Archives internationales d'histoire des sciences 49 (1999), p. 3–31. Cristina Viano, « Byzantine Alchemy, or the Era of Systematization », in John Scarborough and Paul Keyser (eds. ), Oxford Handbook of Scienc... | [
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ASCII ( ), abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices. Most modern character-encoding schemes are based on ASCII, although they support many a... | [
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In addition, the original ASCII specification included 33 non-printing control codes which originated with Teletype machines; most of these are now obsolete, although a few are still commonly used, such as the carriage return, line feed, and tab codes. For example, lowercase i would be represented in the ASCII encoding... | [
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Locating the lowercase letters in sticks 6 and 7 caused the characters to differ in bit pattern from the upper case by a single bit, which simplified case-insensitive character matching and the construction of keyboards and printers. The X3 committee made other changes, including other new characters (the brace and ver... | [
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Before ASCII was developed, the encodings in use included 26 alphabetic characters, 10 numerical digits, and from 11 to 25 special graphic symbols. To include all these, and control characters compatible with the Comité Consultatif International Téléphonique et Télégraphique (CCITT) International Telegraph Alphabet No.... | [
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Eight-bit machines (with octets as the native data type) that did not use parity checking typically set the eighth bit to 0. Internal organization
The code itself was patterned so that most control codes were together and all graphic codes were together, for ease of identification. The first two so-called ASCII sticks ... | [
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2 (1878), the first typewriter with a shift key, and the shifted values of 23456789- were "#$%_&'() early typewriters omitted 0 and 1, using O (capital letter o) and l (lowercase letter L) instead, but 1! and 0) pairs became standard once 0 and 1 became common. Thus, in ASCII ! "#$% were placed in the second stick, pos... | [
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(full stop) so they could be used in uppercase without unshifting). However, ASCII split the ;: pair (dating to No. 2), and rearranged mathematical symbols (varied conventions, commonly -* =+) to :* ;+ -=. Some then-common typewriter characters were not included, notably ½ ¼ ¢, while ^ ` ~ were included as diacritics ... | [
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The main deviations in ASCII order are:
All uppercase come before lowercase letters; for example, "Z" precedes "a"
Digits and many punctuation marks come before letters
An intermediate order converts uppercase letters to lowercase before comparing ASCII values. Character groups
Control characters
ASCII reserves th... | [
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-0.... |
Paper tape was a very popular medium for long-term program storage until the 1980s, less costly and in some ways less fragile than magnetic tape. In particular, the Teletype Model 33 machine assignments for codes 17 (Control-Q, DC1, also known as XON), 19 (Control-S, DC3, also known as XOFF), and 127 (Delete) became de... | [
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The 33 ASR also could be configured to employ Control-R (DC2) and Control-T (DC4) to start and stop the tape punch; on some units equipped with this function, the corresponding control character lettering on the keycap above the letter was TAPE and TAPE respectively. Delete vs Backspace
The Teletype could not move its ... | [
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The assumption that no key sent a BS code allowed Control+H to be used for other purposes, such as the "help" prefix command in GNU Emacs. Escape
Many more of the control codes have been assigned meanings quite different from their original ones. The "escape" character (ESC, code 27), for example, was intended original... | [
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The best example of this is the newline problem on various operating systems. Teletype machines required that a line of text be terminated with both "Carriage Return" (which moves the printhead to the beginning of the line) and "Line Feed" (which advances the paper one line without moving the printhead). The name "Carr... | [
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IBM's PC DOS (also marketed as MS-DOS by Microsoft) inherited the convention by virtue of being loosely based on CP/M, and Windows in turn inherited it from MS-DOS. Unfortunately, requiring two characters to mark the end of a line introduces unnecessary complexity and ambiguity as to how to interpret each character whe... | [
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-0.9599609375,
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The File Transfer Protocol adopted the Telnet protocol, including use of the Network Virtual Terminal, for use when transmitting commands and transferring data in the default ASCII mode. This adds complexity to implementations of those protocols, and to other network protocols, such as those used for E-mail and the Wor... | [
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Printable characters
Codes 20hex to 7Ehex, known as the printable characters, represent letters, digits, punctuation marks, and a few miscellaneous symbols. There are 95 printable characters in total. Code 20hex, the "space" character, denotes the space between words, as produced by the space bar of a keyboard. Since ... | [
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0.0943603516,
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-1.3125,
-0.375,
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-1.1083984375,
0.81... |
On March 11, 1968, US President Lyndon B. Johnson mandated that all computers purchased by the United States Federal Government support ASCII, stating:
I have also approved recommendations of the Secretary of Commerce [Luther H. Hodges] regarding standards for recording the Standard Code for Information Interchange on ... | [
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-0.419433593... |
Other international standards bodies have ratified character encodings such as ISO 646 (1967) that are identical or nearly identical to ASCII, with extensions for characters outside the English alphabet and symbols used outside the United States, such as the symbol for the United Kingdom's pound sterling (£); e.g. with... | [
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-0... |
Escape codes were defined to indicate which national variant applied to a piece of text, but they were rarely used, so it was often impossible to know what variant to work with and, therefore, which character a code represented, and in general, text-processing systems could cope with only one variant anyway. Because th... | [
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... |
In Japan and Korea, still a variation of ASCII is used, in which the backslash (5C hex) is rendered as ¥ (a Yen sign, in Japan) or ₩ (a Won sign, in Korea). This means that, for example, the file path C:\Users\Smith is shown as C:¥Users¥Smith (in Japan) or C:₩Users₩Smith (in Korea). 8-bit codes
Eventually, as 8-, 16-... | [
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-... |
The IBM PC defined code page 437, which replaced the control characters with graphic symbols such as smiley faces, and mapped additional graphic characters to the upper 128 positions. Operating systems such as DOS supported these code pages, and manufacturers of IBM PCs supported them in hardware. Digital Equipment Cor... | [
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0.4... |
While ASCII is limited to 128 characters, Unicode and the UCS support more characters by separating the concepts of unique identification (using natural numbers called code points) and encoding (to 8-, 16-, or 32-bit binary formats, called UTF-8, UTF-16, and UTF-32, respectively). ASCII was incorporated into the Unicod... | [
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The Austroasiatic languages , also known as Mon–Khmer , are a large language family in Mainland Southeast Asia and South Asia. These languages are scattered throughout parts of Thailand, India, Bangladesh, Nepal, and southern China. There are around 117 million speakers of Austroasiatic languages. Of these languages, ... | [
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Etymology
The name Austroasiatic comes from a combination of the Latin words for "South" and "Asia", hence "South Asia". Typology
Regarding word structure, Austroasiatic languages are well known for having an iambic "sesquisyllabic" pattern, with basic nouns and verbs consisting of an initial, unstressed, reduced minor... | [
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Little work has been done on the Munda languages, which are not well documented. With their demotion from a primary branch, Proto-Mon–Khmer becomes synonymous with Proto-Austroasiatic. Paul Sidwell (2005) reconstructs the consonant inventory of Proto-Mon–Khmer as follows:
This is identical to earlier reconstructions e... | [
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... |
Munda
North Munda
Korku
Kherwarian
South Munda
Kharia–Juang
Koraput Munda
Mon–Khmer
Eastern Mon–Khmer
Khmer (Cambodian)
Pearic
Bahnaric
Katuic
Vietic (Vietnamese, Muong)
Northern Mon–Khmer
Khasi (Meghalaya, India)
Palaungic
Khmuic
Southern Mon–Khmer
Mon
Aslian (Malaya)
Nicobarese (Nicobar Islands)
... | [
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Vietic: 10 languages of Vietnam and Laos, including the Vietnamese language, which has the most speakers of any Austroasiatic language. Katuic: 19 languages of Laos, Vietnam, and Thailand. Khmero-Bahnaric languages
Bahnaric: 40 languages of Vietnam, Laos, and Cambodia. Khmeric languages
The Khmer dialects of Cambodia... | [
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Sidwell & Blench (2011) suggest Shompen as an additional branch, and believe that a Vieto-Katuic connection is worth investigating. In general, however, the family is thought to have diversified too quickly for a deeply nested structure to have developed, since Proto-Austroasiatic speakers are believed by Sidwell to ha... | [
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Austroasiatic would have had two possible dispersal routes from the western periphery of the Pearl River watershed of Lingnan, which would have been either a coastal route down the coast of Vietnam, or downstream through the Mekong River via Yunnan. Both the reconstructed lexicon of Proto-Austroasiatic and the archaeol... | [
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during the arrival of rice agriculture in Indochina, but notes that the origin of Proto-Austroasiatic itself is older than that date. The lexicon of Proto-Austroasiatic can be divided into an early and late stratum. The early stratum consists of basic lexicon including body parts, animal names, natural features, and pr... | [
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-0.0344848633,
-0.36889... |
Khmuic, Palaungic, and Khasic resulted from a westward dispersal that ultimately came from the Red Valley valley. Based on their current distributions, about half of all Austroasiatic branches (including Nicobaric and Munda) can be traced to coastal maritime dispersals. Hence, this points to a relatively late riverine ... | [
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-0.0168... |
Acehnese has many basic words that are of Austroasiatic origin, suggesting that either Austronesian speakers have absorbed earlier Austroasiatic residents in northern Sumatra, or that words might have been borrowed from Austroasiatic languages in southern Vietnam – or perhaps a combination of both. Sidwell (2006) argue... | [
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-0.591796875,
-0.3166503... |
Kerinci: van Reijn (1974) notes that Kerinci, a Malayic language of central Sumatra, shares many phonological similarities with Austroasiatic languages, such as sesquisyllabic word structure and vowel inventory. John Peterson (2017) suggests that "pre-Munda" ("proto-" in regular terminology) languages may have once dom... | [
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... |
Hmong-Mien
Several lexical resemblances are found between the Hmong-Mien and Austroasiatic language families (Ratliff 2010), some of which had earlier been proposed by Haudricourt (1951). This could imply a relation or early language contact along the Yangtze. According to Cai (et al. 2011), Hmong–Mien is at least par... | [
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From Mainland Southeast Asia, the Austroasiatic-speakers expanded into the Indian-subcontinent and Maritime Southeast Asia. There is evidence that later back migration from more northerly East Asian groups (such as Kra-Dai-speakers) merged with indigenous Southeast Asians, contributing to the fragmentation observed amo... | [
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found that modern East-Eurasians can be modeled from four ancestry components, which descended from a common ancestor in Mainland Southeast Asia, one being the "Ancestral Austroasiatic" component (AAA), which is more prevalent among modern Southeast Asians, and making up the exclusive ancestry among Austroasiatic-speak... | [
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-0.2326660156,
-0.4238281... |
of Linguistics, Research School of Pacific Studies, Australian National University. Alves, Mark J. (2015). Morphological functions among Mon-Khmer languages: beyond the basics. In N. J. Enfield & Bernard Comrie (eds. ), Languages of Mainland Southeast Asia: the state of the art. Berlin: de Gruyter Mouton, 531–557. Brad... | [
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-0.... |
Shorto, Harry L. edited by Sidwell, Paul, Cooper, Doug and Bauer, Christian (2006). A Mon–Khmer comparative dictionary. Canberra: Australian National University. Pacific Linguistics. Shorto, H. L. Bibliographies of Mon–Khmer and Tai Linguistics. London oriental bibliographies, v. 2. London: Oxford University Press, 196... | [
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External links
Swadesh lists for Austro-Asiatic languages (from Wiktionary's Swadesh-list appendix)
Austro-Asiatic at the Linguist List MultiTree Project (not functional as of 2014): Genealogical trees attributed to Sebeok 1942, Pinnow 1959, Diffloth 2005, and Matisoff 2006
Mon–Khmer.com: Lectures by Paul Sidwell
... | [
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Afroasiatic (Afro-Asiatic), also known as Afrasian or Hamito-Semitic, Semito-Hamitic, or Erythraean, is a large language family of about 300 languages that are spoken predominantly in Western Asia, North Africa, the Horn of Africa and parts of the Sahel. With the exception of Semitic, all branches of the Afroаsiatic fa... | [
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Etymology
In the early 19th century, linguists grouped the Berber, Cushitic and Egyptian languages within a "Hamitic" phylum, in acknowledgement of these languages' genetic relation with each other and with those in the Semitic phylum. The terms "Hamitic" and "Semitic" were etymologically derived from the Book of Genes... | [
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Distribution and branches
Scholars generally treat the Afroasiatic language family as including the following five branches, whereas Omotic is disputed:
Berber
Chadic
Cushitic
Egyptian
Semitic
Although there is general agreement on these six families, linguists who study Afroasiatic raise some points of disagree... | [
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This situation is not unusual, even among long-established language families: scholars also frequently disagree on the internal classification of the Indo-European languages, for instance. The extinct Meroitic language has been proposed (Bruce Trigger, 1964, 1977) as an unclassified Afroasiatic language, because it sha... | [
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Shilha (Berber), spoken by around 7 million people in Morocco. Kabyle (Berber), spoken by around 5.6 million people in Algeria. Hebrew (Semitic), spoken by around 5 million native speakers, and additionally by 4 million second-language speakers in Israel and the Jewish diaspora; premodern Hebrew is the liturgical langu... | [
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In 1844, Theodor Benfey proposed a language family consisting of Semitic, Berber, and Cushitic (he called the latter "Ethiopic"). In the same year T.N. Newman suggested a relationship between Semitic and Hausa, but this would long remain a topic of dispute and uncertainty. Friedrich Müller named the traditional Hamito-... | [
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Meinhof's system of classification of the Hamitic languages was based on a belief that "speakers of Hamitic became largely coterminous with cattle herding peoples with essentially Caucasian origins, intrinsically different from and superior to the 'Negroes of Africa'." However, in the case of the so-called Nilo-Hamitic... | [
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Almost all scholars have accepted this classification as the new and continued consensus. Greenberg developed his model fully in his book The Languages of Africa (1963), in which he reassigned most of Meinhof's additions to Hamitic to other language families, notably Nilo-Saharan. Following Isaac Schapera and rejecting... | [
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Most scholars, however, reject this proposal, and continue to group Beja as the sole member of a Northern branch within Cushitic. Glottolog does not accept that the inclusion or even unity of Omotic has been established, nor that of Ongota or the unclassified Kujarge. It therefore splits off the following groups as sma... | [
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He divides Erythrean into Cushitic, comprising Beja, Agaw, and East-South Cushitic, and North Erythrean, comprising Chadic and "Boreafrasian." According to his classification, Boreafrasian consists of Egyptian, Berber, and Semitic. Vladimir Orel and Olga Stolbova (1995) group Berber with Semitic and Chadic with Egyptia... | [
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The best-known of these are the following:
Hermann Möller (1906) argued for a relation between Semitic and the Indo-European languages. This proposal was accepted by a few linguists (e.g. Holger Pedersen and Louis Hjelmslev). (For a fuller account, see Indo-Semitic languages.) However, the theory has little currency t... | [
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Date of Afroasiatic
The earliest written evidence of an Afroasiatic language is an Ancient Egyptian inscription dated to c. 3400 BC (5,400 years ago). Symbols on Gerzean (Naqada II) pottery resembling Egyptian hieroglyphs date back to c. 4000 BC, suggesting an earlier possible dating. This gives us a minimum date for ... | [
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While there is no definitive agreement on when or where the original homeland of this language family existed, many link the first speakers to the first farmers in the Levant who would later spread to North and East Africa. Others argue the first speakers were pre-agricultural and based in North East Africa. Similariti... | [
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alternative feminine endings *-ay/*-āy; corresponding vowel templates for verbal conjugations) which can be reconstructed for a higher-order proto-language (provisionally called "Proto-Berbero-Semitic" by Kossmann & Suchard (2018) and Putten (2018)). Whether this proto-language is ancestral to Berber and Semitic only, ... | [
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* indicates reconstructed forms based on comparison of related languages. There are two etymological dictionaries of Afroasiatic, one by Christopher Ehret, and one by Vladimir Orel and Olga Stolbova. The two dictionaries disagree on almost everything. The following table contains the thirty roots or so (out of thousand... | [
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Diakonoff, Igor M. 1996. "Some reflections on the Afrasian linguistic macrofamily." Journal of Near Eastern Studies 55, 293. Diakonoff, Igor M. 1998. "The earliest Semitic society: Linguistic data." Journal of Semitic Studies 43, 209. Dimmendaal, Gerrit, and Erhard Voeltz. 2007. "Africa". In Christopher Moseley, ed., E... | [
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0.2922363281,
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-0.... |
Greenberg, Joseph H. 1966. The Languages of Africa (2nd ed. with additions and corrections). Bloomington: Indiana University. Greenberg, Joseph H. 1981. "African linguistic classification." General History of Africa, Volume 1: Methodology and African Prehistory, edited by Joseph Ki-Zerbo, 292–308. Berkeley and Los Ange... | [
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In Orientalia et Classica: Papers of the Institute of Oriental and Classical Studies, Issue 5. Moscow. (Forthcoming.) Newman, Paul. 1980. The Classification of Chadic within Afroasiatic. Leiden: Universitaire Pers Leiden. Theil, R. 2006. Is Omotic Afro-Asiatic? Proceedings from the David Dwyer retirement symposium, Mic... | [
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Root Extension And Root Formation In Semitic And Afrasian, by Alexander Militarev in "Proceedings of the Barcelona Symposium on comparative Semitic", 19-20/11/2004. Aula Orientalis 23/1-2, 2005, pp. 83–129. Akkadian-Egyptian lexical matches, by Alexander Militarev in "Papers on Semitic and Afroasiatic Linguistics in Ho... | [
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In mathematics and statistics, the arithmetic mean ( ) or arithmetic average, or simply just the mean or the average (when the context is clear), is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results of an experiment or an observational study, ... | [
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The arithmetic mean is the most commonly used and readily understood measure of central tendency in a data set. In statistics, the term average refers to any of the measures of central tendency. The arithmetic mean of a set of observed data is defined as being equal to the sum of the numerical values of each and every ... | [
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Motivating properties
The arithmetic mean has several properties that make it useful, especially as a measure of central tendency. These include:
If numbers have mean , then . Since is the distance from a given number to the mean, one way to interpret this property is as saying that the numbers to the left of the ... | [
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However, when we consider a sample that cannot be arranged so as to increase arithmetically, such as , the median and arithmetic average can differ significantly. In this case, the arithmetic average is 6.2, while the median is 4. In general, the average value can vary significantly from most values in the sample, and ... | [
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Continuous probability distributions
If a numerical property, and any sample of data from it, could take on any value from a continuous range, instead of, for example, just integers, then the probability of a number falling into some range of possible values can be described by integrating a continuous probability dis... | [
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Secondly, in this situation, 0° (equivalently, 360°) is geometrically a better average value: there is lower dispersion about it (the points are both 1° from it, and 179° from 180°, the putative average). In general application, such an oversight will lead to the average value artificially moving towards the middle of ... | [
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See also
Fréchet mean
Generalized mean
Geometric mean
Harmonic mean
Inequality of arithmetic and geometric means
Mode
Sample mean and covariance
Standard deviation
Standard error of the mean
Summary statistics
References
Further reading
External links
Calculations and comparisons between arithmetic mean ... | [
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Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among means. ANOVA was developed by the statistician Ronald Fisher. ANOVA is based on the law of total variance, where the obse... | [
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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... | [
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In the first illustration, the dogs are divided according to the product (interaction) of two binary groupings: young vs old, and short-haired vs long-haired (e.g., group 1 is young, short-haired dogs, group 2 is young, long-haired dogs, etc.). Since the distributions of dog weight within each of the groups (shown in b... | [
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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 analysis of experimental data or the development of models. The method has some advantages over correlation:... | [
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The random-effects model would determine whether important differences exist among a list of randomly selected texts. The mixed-effects model would compare the (fixed) incumbent texts to randomly selected alternatives. Defining fixed and random effects has proven elusive, with competing definitions arguably leading tow... | [
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This design-based analysis was discussed and developed by Francis J. Anscombe at Rothamsted Experimental Station and by Oscar Kempthorne at Iowa State University. Kempthorne and his students make an assumption of unit treatment additivity, which is discussed in the books of Kempthorne and David R. Cox. Unit-treatment a... | [
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In the randomization-based analysis, there is no assumption of a normal distribution and certainly no assumption of independence. On the contrary, the observations are dependent! The randomization-based analysis has the disadvantage that its exposition involves tedious algebra and extensive time. Since the randomizatio... | [
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There are no necessary assumptions for ANOVA in its full generality, but the F-test used for ANOVA hypothesis testing has assumptions and practical
limitations which are of continuing interest. Problems which do not satisfy the assumptions of ANOVA can often be transformed to satisfy the assumptions. The property of u... | [
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Logic
The calculations of ANOVA can be characterized as computing a number of means and variances, dividing two variances and comparing the ratio to a handbook value to determine statistical significance. Calculating a treatment effect is then trivial: "the effect of any treatment is estimated by taking the difference ... | [
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The number of degrees of freedom DF can be partitioned in a similar way: one of these components (that for error) specifies a chi-squared distribution which describes the associated sum of squares, while the same is true for "treatments" if there is no treatment effect. See also Lack-of-fit sum of squares. The F-test
... | [
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The computer method calculates the probability (p-value) of a value of F greater than or equal to the observed value. The null hypothesis is rejected if this probability is less than or equal to the significance level (α). The ANOVA F-test is known to be nearly optimal in the sense of minimizing false negative errors f... | [
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