The Faculty Scholarly Productivity Index ( FSPI ), a product of Academic Analytics, is a metric designed to create benchmark standards for the measurement of academic and scholarly quality within and among United States research universities .
128-436: The index is based on a set of statistical algorithms developed by Lawrence B. Martin and Anthony Olejniczak . It measures the annual amount and impact of faculty scholarly work in several areas, including: The FSPI analysis creates, by academic field of study, a statistical score and a ranking based on the cumulative scoring of a program's faculty using these quantitative measures compared against national standards within
256-460: A de facto official language of Namibia after the end of German colonial rule alongside English and Afrikaans , and had de jure co-official status from 1984 until its independence from South Africa in 1990. However, the Namibian government perceived Afrikaans and German as symbols of apartheid and colonialism, and decided English would be the sole official language upon independence, stating that it
384-469: 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. Consider independent identically distributed (IID) random variables with
512-402: A second language , and 75–100 million as a foreign language . This would imply the existence of approximately 175–220 million German speakers worldwide. German sociolinguist Ulrich Ammon estimated a number of 289 million German foreign language speakers without clarifying the criteria by which he classified a speaker. As of 2012 , about 90 million people, or 16% of
640-587: A "commonly used" language and the Pan South African Language Board is obligated to promote and ensure respect for it. Cameroon was also a colony of the German Empire from the same period (1884 to 1916). However, German was replaced by French and English, the languages of the two successor colonial powers, after its loss in World War I . Nevertheless, since the 21st century, German has become
768-418: A decade earlier in 1795. 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
896-458: 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. A statistic is a random variable that is a function of the random sample, but not a function of unknown parameters . The probability distribution of
1024-484: 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 . 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
1152-471: 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 . 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. The best illustration for
1280-556: A greater need for regularity in written conventions. While the major changes of the MHG period were socio-cultural, High German was still undergoing significant linguistic changes in syntax, phonetics, and morphology as well (e.g. diphthongization of certain vowel sounds: hus (OHG & MHG "house") → haus (regionally in later MHG)→ Haus (NHG), and weakening of unstressed short vowels to schwa [ə]: taga (OHG "days")→ tage (MHG)). A great wealth of texts survives from
1408-548: 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
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#17328514907601536-1028: 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. 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
1664-453: A native tongue today, mostly descendants of German colonial settlers . The period of German colonialism in Namibia also led to the evolution of a Standard German-based pidgin language called " Namibian Black German ", which became a second language for parts of the indigenous population. Although it is nearly extinct today, some older Namibians still have some knowledge of it. German remained
1792-499: A novice is the predicament encountered by a criminal trial. The null hypothesis, H 0 , asserts that the defendant is innocent, whereas the alternative hypothesis, H 1 , asserts that the defendant is guilty. The indictment comes because of suspicion of the guilt. The H 0 (status quo) stands in opposition to H 1 and is maintained unless H 1 is supported by evidence "beyond a reasonable doubt". However, "failure to reject H 0 " in this case does not imply innocence, but merely that
1920-679: A popular foreign language among pupils and students, with 300,000 people learning or speaking German in Cameroon in 2010 and over 230,000 in 2020. Today Cameroon is one of the African countries outside Namibia with the highest number of people learning German. In the United States, German is the fifth most spoken language in terms of native and second language speakers after English, Spanish , French , and Chinese (with figures for Cantonese and Mandarin combined), with over 1 million total speakers. In
2048-404: A population, so results do not 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
2176-412: 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 a census ). This may be organized by governmental statistical institutes. Descriptive statistics can be used to summarize
2304-475: A result, the surviving texts are written in highly disparate regional dialects and exhibit significant Latin influence, particularly in vocabulary. At this point monasteries, where most written works were produced, were dominated by Latin, and German saw only occasional use in official and ecclesiastical writing. While there is no complete agreement over the dates of the Middle High German (MHG) period, it
2432-460: 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 . The basic steps of a statistical experiment are: Experiments on human behavior have special concerns. The famous Hawthorne study examined changes to the working environment at the Hawthorne plant of
2560-637: 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. 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
2688-399: A transformation is sensible to contemplate depends on the question one is trying to answer." 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
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#17328514907602816-419: A value accurately rejecting the null hypothesis (sometimes referred to as the p-value ). 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
2944-688: Is a West Germanic language in the Indo-European language family , mainly spoken in Western and Central Europe . It is the most spoken native language within the European Union . It is the most widely spoken and official (or co-official) language in Germany , Austria , Switzerland , Liechtenstein , and the Italian autonomous province of South Tyrol . It is also an official language of Luxembourg , Belgium and
3072-580: Is a recognized minority language in the following countries: In France, the High German varieties of Alsatian and Moselle Franconian are identified as " regional languages ", but the European Charter for Regional or Minority Languages of 1998 has not yet been ratified by the government. Namibia also was a colony of the German Empire, from 1884 to 1915. About 30,000 people still speak German as
3200-596: Is also notable for its broad spectrum of dialects , with many varieties existing in Europe and other parts of the world. Some of these non-standard varieties have become recognized and protected by regional or national governments. Since 2004, heads of state of the German-speaking countries have met every year, and the Council for German Orthography has been the main international body regulating German orthography . German
3328-546: Is an Indo-European language that belongs to the West Germanic group of the Germanic languages . The Germanic languages are traditionally subdivided into three branches: North Germanic , East Germanic , and West Germanic . The first of these branches survives in modern Danish , Swedish , Norwegian , Faroese , and Icelandic , all of which are descended from Old Norse . The East Germanic languages are now extinct, and Gothic
3456-575: 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. 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
3584-465: 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
3712-834: 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. 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. Most studies only sample part of
3840-472: Is called the "German Sprachraum ". German is the official language of the following countries: German is a co-official language of the following countries: Although expulsions and (forced) assimilation after the two World wars greatly diminished them, minority communities of mostly bilingual German native speakers exist in areas both adjacent to and detached from the Sprachraum. Within Europe, German
3968-430: Is complicated by the existence of several varieties whose status as separate "languages" or "dialects" is disputed for political and linguistic reasons, including quantitatively strong varieties like certain forms of Alemannic and Low German . With the inclusion or exclusion of certain varieties, it is estimated that approximately 90–95 million people speak German as a first language , 10–25 million speak it as
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4096-428: 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. Statistical inference is the process of using data analysis to deduce properties of an underlying probability distribution . Inferential statistical analysis infers properties of
4224-520: Is generally seen as ending when the 1346–53 Black Death decimated Europe's population. Modern High German begins with the Early New High German (ENHG) period, which Wilhelm Scherer dates 1350–1650, terminating with the end of the Thirty Years' War . This period saw the further displacement of Latin by German as the primary language of courtly proceedings and, increasingly, of literature in
4352-595: Is generally seen as lasting from 1050 to 1350. This was a period of significant expansion of the geographical territory occupied by Germanic tribes, and consequently of the number of German speakers. Whereas during the Old High German period the Germanic tribes extended only as far east as the Elbe and Saale rivers, the MHG period saw a number of these tribes expanding beyond this eastern boundary into Slavic territory (known as
4480-559: Is less closely related to languages based on Low Franconian dialects (e.g., Dutch and Afrikaans), Low German or Low Saxon dialects (spoken in northern Germany and southern Denmark ), neither of which underwent the High German consonant shift. As has been noted, the former of these dialect types is Istvaeonic and the latter Ingvaeonic, whereas the High German dialects are all Irminonic; the differences between these languages and standard German are therefore considerable. Also related to German are
4608-435: Is one of the major languages of the world . German is the second-most widely spoken Germanic language , after English, both as a first and as a second language . German is also widely taught as a foreign language , especially in continental Europe (where it is the third most taught foreign language after English and French), and in the United States. Overall, German is the fourth most commonly learned second language, and
4736-587: Is one of the three biggest newspapers in Namibia and the only German-language daily in Africa. An estimated 12,000 people speak German or a German variety as a first language in South Africa, mostly originating from different waves of immigration during the 19th and 20th centuries. One of the largest communities consists of the speakers of "Nataler Deutsch", a variety of Low German concentrated in and around Wartburg . The South African constitution identifies German as
4864-418: 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
4992-401: Is partly derived from Latin and Greek , along with fewer words borrowed from French and Modern English . English, however, is the main source of more recent loanwords . German is a pluricentric language ; the three standardized variants are German , Austrian , and Swiss Standard German . Standard German is sometimes called High German , which refers to its regional origin. German
5120-451: Is proposed for the statistical relationship between the two data sets, 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
5248-408: Is rejected when it is in fact true, giving a "false positive") and Type II errors (null hypothesis fails to be rejected when it is in fact false, 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. Statistical measurement processes are also prone to error in regards to
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5376-510: Is the Sachsenspiegel , the first book of laws written in Middle Low German ( c. 1220 ). The abundance and especially the secular character of the literature of the MHG period demonstrate the beginnings of a standardized written form of German, as well as the desire of poets and authors to be understood by individuals on supra-dialectal terms. The Middle High German period
5504-566: Is the only language in this branch which survives in written texts. The West Germanic languages, however, have undergone extensive dialectal subdivision and are now represented in modern languages such as English, German, Dutch , Yiddish , Afrikaans , and others. Within the West Germanic language dialect continuum, the Benrath and Uerdingen lines (running through Düsseldorf - Benrath and Krefeld - Uerdingen , respectively) serve to distinguish
5632-402: Is true ( statistical significance ) and the probability of type II error is the probability that the estimator does not 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. Referring to statistical significance does not necessarily mean that
5760-481: Is understood in all areas where German is spoken. Approximate distribution of native German speakers (assuming a rounded total of 95 million) worldwide: As a result of the German diaspora , as well as the popularity of German taught as a foreign language , the geographical distribution of German speakers (or "Germanophones") spans all inhabited continents. However, an exact, global number of native German speakers
5888-449: Is widely employed in government, business, and natural and social sciences. 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
6016-673: The Ostsiedlung ). With the increasing wealth and geographic spread of the Germanic groups came greater use of German in the courts of nobles as the standard language of official proceedings and literature. A clear example of this is the mittelhochdeutsche Dichtersprache employed in the Hohenstaufen court in Swabia as a standardized supra-dialectal written language. While these efforts were still regionally bound, German began to be used in place of Latin for certain official purposes, leading to
6144-644: The U.S. News & World Report annual survey, the FSPI focuses on research institutions as defined by the Carnegie Classification of Institutions of Higher Education . It draws on the approach used by the United States National Research Council (NRC), which publishes a ranking of U.S.-based graduate programs approximately every ten years, but focuses on providing a more frequently-gathered set of benchmark measurements that do not include
6272-627: The Alamanni , Bavarian, and Thuringian groups, all belonging to the Elbe Germanic group ( Irminones ), which had settled in what is now southern-central Germany and Austria between the second and sixth centuries, during the great migration. In general, the surviving texts of Old High German (OHG) show a wide range of dialectal diversity with very little written uniformity. The early written tradition of OHG survived mostly through monasteries and scriptoria as local translations of Latin originals; as
6400-760: 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. 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). ) The issue of whether or not it
6528-522: The Early Middle Ages . German is an inflected language , with four cases for nouns, pronouns, and adjectives (nominative, accusative, genitive, dative); three genders (masculine, feminine, neuter) and two numbers (singular, plural). It has strong and weak verbs . The majority of its vocabulary derives from the ancient Germanic branch of the Indo-European language family, while a smaller share
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#17328514907606656-417: The European Union 's population, spoke German as their mother tongue, making it the second most widely spoken language on the continent after Russian and the second biggest language in terms of overall speakers (after English), as well as the most spoken native language. The area in central Europe where the majority of the population speaks German as a first language and has German as a (co-)official language
6784-514: The German states . While these states were still part of the Holy Roman Empire , and far from any form of unification, the desire for a cohesive written language that would be understandable across the many German-speaking principalities and kingdoms was stronger than ever. As a spoken language German remained highly fractured throughout this period, with a vast number of often mutually incomprehensible regional dialects being spoken throughout
6912-724: The Holy Roman Emperor Maximilian I , and the other being Meißner Deutsch , used in the Electorate of Saxony in the Duchy of Saxe-Wittenberg . Alongside these courtly written standards, the invention of the printing press led to the development of a number of printers' languages ( Druckersprachen ) aimed at making printed material readable and understandable across as many diverse dialects of German as possible. The greater ease of production and increased availability of written texts brought about increased standardisation in
7040-644: The Old High German language in several Elder Futhark inscriptions from as early as the sixth century AD (such as the Pforzen buckle ), the Old High German period is generally seen as beginning with the Abrogans (written c. 765–775 ), a Latin-German glossary supplying over 3,000 Old High German words with their Latin equivalents. After the Abrogans , the first coherent works written in Old High German appear in
7168-640: The Sprachraum in Europe. German is used in a wide variety of spheres throughout the country, especially in business, tourism, and public signage, as well as in education, churches (most notably the German-speaking Evangelical Lutheran Church in Namibia (GELK) ), other cultural spheres such as music, and media (such as German language radio programs by the Namibian Broadcasting Corporation ). The Allgemeine Zeitung
7296-536: The Standard German language in its written form, and the Duden Handbook was declared its standard definition. Punctuation and compound spelling (joined or isolated compounds) were not standardized in the process. The Deutsche Bühnensprache ( lit. ' German stage language ' ) by Theodor Siebs had established conventions for German pronunciation in theatres , three years earlier; however, this
7424-503: The Upper German dialects spoken in the southern German-speaking countries , such as Swiss German ( Alemannic dialects ) and the various Germanic dialects spoken in the French region of Grand Est , such as Alsatian (mainly Alemannic, but also Central–and Upper Franconian dialects) and Lorraine Franconian (Central Franconian). After these High German dialects, standard German
7552-477: 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
7680-546: The 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 , as well as data mining . 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 . Formal discussions on inference date back to
7808-432: The limit to the true value of such parameter. 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. This still leaves the question of how to obtain estimators in
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#17328514907607936-707: The mathematicians and cryptographers of 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
8064-464: 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
8192-462: The pagan Germanic tradition. Of particular interest to scholars, however, has been the Hildebrandslied , a secular epic poem telling the tale of an estranged father and son unknowingly meeting each other in battle. Linguistically, this text is highly interesting due to the mixed use of Old Saxon and Old High German dialects in its composition. The written works of this period stem mainly from
8320-714: The Empire. Its use indicated that the speaker was a merchant or someone from an urban area, regardless of nationality. Prague (German: Prag ) and Budapest ( Buda , German: Ofen ), to name two examples, were gradually Germanized in the years after their incorporation into the Habsburg domain; others, like Pressburg ( Pozsony , now Bratislava), were originally settled during the Habsburg period and were primarily German at that time. Prague, Budapest, Bratislava, and cities like Zagreb (German: Agram ) or Ljubljana (German: Laibach ), contained significant German minorities. In
8448-1409: The FSPI has major flaws. It fails to adequately differentiate among and apply appropriate measures to evaluating the very distinct academic fields represented in most colleges and universities. Furthermore, a number of specific objections have been raised about how the FSPI measures scholarly productivity. Among them are: 1) inadequate—or inconsistent—weighting of quality of journals in which publications appear; 2) failure to differentiate labor involved in producing different types of publications (publications based on secondary sources and those based on tedious and deep research are not differentiated—hence departments with many faculty members who write much but research little are better rated; 3) failure to differentiate between scholarly concentrations of departments. Departments with faculty who are more involved in obscure, non-mainstream research are less cited than those involved in fashionable, mainstream areas of research and scholarship; 4) citation indexes, extensively used in scholarly productivity indexes, do not measure citations in books; 5) citation indexes are more appropriate for hard science disciplines and less appropriate for humanities disciplines; 6) non-conventional publications, which are increasing in number (e.g. - Web sites and on-line publications, audio and media productions) are ignored; 7) use of such indexes promotes "researching and publishing to
8576-718: The Frisian languages— North Frisian (spoken in Nordfriesland ), Saterland Frisian (spoken in Saterland ), and West Frisian (spoken in Friesland )—as well as the Anglic languages of English and Scots. These Anglo-Frisian dialects did not take part in the High German consonant shift, and the Anglic languages also adopted much vocabulary from both Old Norse and the Norman language . The history of
8704-524: The German language begins with the High German consonant shift during the Migration Period , which separated Old High German dialects from Old Saxon . This sound shift involved a drastic change in the pronunciation of both voiced and voiceless stop consonants ( b , d , g , and p , t , k , respectively). The primary effects of the shift were the following below. While there is written evidence of
8832-447: The German states; the invention of the printing press c. 1440 and the publication of Luther's vernacular translation of the Bible in 1534, however, had an immense effect on standardizing German as a supra-dialectal written language. The ENHG period saw the rise of several important cross-regional forms of chancery German, one being gemeine tiutsch , used in the court of
8960-675: The Germanic dialects that were affected by the High German consonant shift (south of Benrath) from those that were not (north of Uerdingen). The various regional dialects spoken south of these lines are grouped as High German dialects, while those spoken to the north comprise the Low German and Low Franconian dialects. As members of the West Germanic language family, High German, Low German, and Low Franconian have been proposed to be further distinguished historically as Irminonic , Ingvaeonic , and Istvaeonic , respectively. This classification indicates their historical descent from dialects spoken by
9088-646: The Irminones (also known as the Elbe group), Ingvaeones (or North Sea Germanic group), and Istvaeones (or Weser–Rhine group). Standard German is based on a combination of Thuringian - Upper Saxon and Upper Franconian dialects, which are Central German and Upper German dialects belonging to the High German dialect group. German is therefore closely related to the other languages based on High German dialects, such as Luxembourgish (based on Central Franconian dialects ) and Yiddish . Also closely related to Standard German are
9216-845: The Italian autonomous region of Friuli-Venezia Giulia , as well as a recognized national language in Namibia . There are also notable German-speaking communities in France ( Alsace ), the Czech Republic ( North Bohemia ), Poland ( Upper Silesia ), Slovakia ( Košice Region , Spiš , and Hauerland ), Denmark ( North Schleswig ), Romania and Hungary ( Sopron ). Overseas, sizeable communities of German-speakers are found in Brazil ( Blumenau and Pomerode ), South Africa ( Kroondal ), Namibia , among others, some communities have decidedly Austrian German or Swiss German characters (e.g. Pozuzo , Peru). German
9344-507: The MHG period. Significantly, these texts include a number of impressive secular works, such as the Nibelungenlied , an epic poem telling the story of the dragon -slayer Siegfried ( c. thirteenth century ), and the Iwein , an Arthurian verse poem by Hartmann von Aue ( c. 1203 ), lyric poems , and courtly romances such as Parzival and Tristan . Also noteworthy
9472-439: 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 generally concerned with the use of data in the context of uncertainty and decision-making in the face of uncertainty. In applying statistics to
9600-442: 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
9728-535: 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 and 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
9856-538: 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
9984-425: The data that they generate. 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. Statistics is a mathematical body of science that pertains to
10112-430: The development of non-local forms of language and exposed all speakers to forms of German from outside their own area. With Luther's rendering of the Bible in the vernacular, German asserted itself against the dominance of Latin as a legitimate language for courtly, literary, and now ecclesiastical subject-matter. His Bible was ubiquitous in the German states: nearly every household possessed a copy. Nevertheless, even with
10240-452: The dialect so as to make the work as natural and accessible to German speakers as possible. Copies of Luther's Bible featured a long list of glosses for each region, translating words which were unknown in the region into the regional dialect. Luther said the following concerning his translation method: One who would talk German does not ask the Latin how he shall do it; he must ask the mother in
10368-507: The eastern provinces of Banat , Bukovina , and Transylvania (German: Banat, Buchenland, Siebenbürgen ), German was the predominant language not only in the larger towns—like Temeschburg ( Timișoara ), Hermannstadt ( Sibiu ), and Kronstadt ( Brașov )—but also in many smaller localities in the surrounding areas. In 1901, the Second Orthographic Conference ended with a (nearly) complete standardization of
10496-406: 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. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements with different levels using
10624-495: The evidence was insufficient to convict. So the jury does not necessarily accept H 0 but fails to reject H 0 . 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 . What statisticians call an alternative hypothesis is simply a hypothesis that contradicts the null hypothesis. Working from a null hypothesis , two broad categories of error are recognized: Standard deviation refers to
10752-478: The expected value assumes on a given sample (also called prediction). 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. 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
10880-474: 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. An example of an observational study
11008-402: 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. 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
11136-450: The extent to which members of the distribution depart from its center and each other. Inferences made using mathematical statistics employ the framework of probability theory , which deals with the analysis of random phenomena. 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
11264-432: 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 . 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
11392-402: 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
11520-605: 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. 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,
11648-435: The home, the children on the streets, the common man in the market-place and note carefully how they talk, then translate accordingly. They will then understand what is said to them because it is German. When Christ says ' ex abundantia cordis os loquitur ,' I would translate, if I followed the papists, aus dem Überflusz des Herzens redet der Mund . But tell me is this talking German? What German understands such stuff? No,
11776-409: The index" in order to preserve and enlarge university, government, and private grant support—and indirectly promote conservative, safe, mainstream research and publications. In spite of these objections, today the product is used by numerous universities. Statistics Statistics (from German : Statistik , orig. "description of a state , a country" ) is the discipline that concerns
11904-474: The influence of Luther's Bible as an unofficial written standard, a widely accepted standard for written German did not appear until the middle of the eighteenth century. German was the language of commerce and government in the Habsburg Empire , which encompassed a large area of Central and Eastern Europe . Until the mid-nineteenth century, it was essentially the language of townspeople throughout most of
12032-424: The most celebrated argument in evolutionary biology ") and Fisherian runaway , a concept in sexual selection about a positive feedback runaway effect found in evolution . 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
12160-402: The mother in the home and the plain man would say, Wesz das Herz voll ist, des gehet der Mund über . Luther's translation of the Bible into High German was also decisive for the German language and its evolution from Early New High German to modern Standard German. The publication of Luther's Bible was a decisive moment in the spread of literacy in early modern Germany , and promoted
12288-630: The ninth century, chief among them being the Muspilli , Merseburg charms , and Hildebrandslied , and other religious texts (the Georgslied , Ludwigslied , Evangelienbuch , and translated hymns and prayers). The Muspilli is a Christian poem written in a Bavarian dialect offering an account of the soul after the Last Judgment , and the Merseburg charms are transcriptions of spells and charms from
12416-412: 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. Although in principle the acceptable level of statistical significance may be subject to debate, the significance level is the largest p-value that allows
12544-407: The particular discipline. Individual program scores can then be combined to demonstrate the quality of the scholarly work of the entire university. This information is gathered for over 230,000 faculty members representing 118 academic disciplines in roughly 7,300 Ph.D. programs throughout more than 350 universities in the United States. Unlike other annual college and university rankings , e.g. ,
12672-410: The planning of data collection in terms of the design of surveys and experiments . 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
12800-415: 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). 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
12928-544: The population. 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
13056-494: The problem of how to analyze big data . 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 . 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
13184-462: The pronunciation of the ending -ig as [ɪk] instead of [ɪç]. In Northern Germany, High German was a foreign language to most inhabitants, whose native dialects were subsets of Low German. It was usually encountered only in writing or formal speech; in fact, most of High German was a written language, not identical to any spoken dialect, throughout the German-speaking area until well into the 19th century. However, wider standardization of pronunciation
13312-466: 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
13440-490: The qualitative and subjective reputation assessments favored by the NRC and other ranking systems. The system for evaluating university programs that forms the basis of the FSPI was developed by Lawrence Martin and Anthony Olejniczak of Stony Brook University . Martin had been studying, speaking, and writing about faculty scholarly productivity since 1995. During that period, a series of discipline-specific, per-capita regression models
13568-467: The regression line were also apparent; that is to say, some schools were outperforming their reputation, while others were under-performing. The prototype materials based on this method, and the data from the 1995 NRC study, were subsequently presented at numerous academic conferences from 1996 to 2004, and have formed the basis on which the FSP Index was developed. Like many academic productivity algorithms,
13696-528: The reputation of a program (as measured by faculty scholarly reputation from a survey conducted by the National Research Council ) could be predicted well using a discipline-specific regression equation derived from quantitative, per capita data available for each program (the number of journal articles, citations, federally funded grants, and honorific awards). Reputation could be predicted with high statistical significance but important deviations from
13824-461: 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
13952-439: 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
14080-399: 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 are needed. It uses patterns in
14208-405: 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 that can lessen these issues at the outset of a study, strengthening its capability to discern truths about
14336-412: 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
14464-541: The states of North Dakota and South Dakota , German is the most common language spoken at home after English. As a legacy of significant German immigration to the country , German geographical names can be found throughout the Midwest region , such as New Ulm and Bismarck (North Dakota's state capital), plus many other regions. A number of German varieties have developed in the country and are still spoken today, such as Pennsylvania Dutch and Texas German . In Brazil,
14592-408: 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 . A random variable that is a function of the random sample and of the unknown parameter, but whose probability distribution does not depend on
14720-418: 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. Two main statistical methods are used in data analysis : descriptive statistics , which summarize data from a sample using indexes such as
14848-436: 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. German language German (German: Deutsch , pronounced [dɔʏtʃ] )
14976-496: The third most commonly learned second language in the United States in K-12 education. The language has been influential in the fields of philosophy, theology, science, and technology. It is the second most commonly used language in science and the third most widely used language on websites . The German-speaking countries are ranked fifth in terms of annual publication of new books, with one-tenth of all books (including e-books) in
15104-420: 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
15232-416: 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. 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
15360-485: 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 . 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
15488-521: The use of sample size in frequency analysis. Although the term statistic was introduced by the Italian scholar Girolamo Ghilini in 1589 with reference to a collection of facts and information about a state, it was the German Gottfried Achenwall in 1749 who started using the term as a collection of quantitative information, in the modern use for this science. The earliest writing containing statistics in Europe dates back to 1663, with
15616-543: The world being published in German. German is most closely related to other West Germanic languages, namely Afrikaans , Dutch , English , the Frisian languages , and Scots . It also contains close similarities in vocabulary to some languages in the North Germanic group , such as Danish , Norwegian , and Swedish . Modern German gradually developed from Old High German , which in turn developed from Proto-Germanic during
15744-462: 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
15872-579: The written form of German. One of the central events in the development of ENHG was the publication of Luther's translation of the Bible into High German (the New Testament was published in 1522; the Old Testament was published in parts and completed in 1534). Luther based his translation primarily on the Meißner Deutsch of Saxony , spending much time among the population of Saxony researching
16000-429: Was a "neutral" language as there were virtually no English native speakers in Namibia at that time. German, Afrikaans, and several indigenous languages thus became "national languages" by law, identifying them as elements of the cultural heritage of the nation and ensuring that the state acknowledged and supported their presence in the country. Today, Namibia is considered to be the only German-speaking country outside of
16128-530: Was an artificial standard that did not correspond to any traditional spoken dialect. Rather, it was based on the pronunciation of German in Northern Germany, although it was subsequently regarded often as a general prescriptive norm, despite differing pronunciation traditions especially in the Upper-German-speaking regions that still characterise the dialect of the area today – especially
16256-408: Was created and tested to evaluate their accuracy and the feasibility of predicting the academic reputation of the faculty of doctoral programs. These prototype materials employed data from the National Research Council 's 1995 publication Continuity and Change (and the subsequent CD-ROM publication of data), describing and evaluating American Ph.D. programs by field. Martin and Olejniczak found that
16384-485: Was established on the basis of public speaking in theatres and the media during the 20th century and documented in pronouncing dictionaries. Official revisions of some of the rules from 1901 were not issued until the controversial German orthography reform of 1996 was made the official standard by governments of all German-speaking countries. Media and written works are now almost all produced in Standard German which
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