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132-521: PFT may refer to: Medical and fitness [ edit ] Physical Fitness Test , a test of an individual's physical fitness such as ability to exercise, etc. Pulmonary Function Testing , testing of the respiratory system Pore-forming toxins , a class of proteins Other [ edit ] Patrimoine Ferroviaire et Tourisme , a Belgian railway preservation society Paul F. Tompkins , contemporary American comedian and podcaster Pearce-Ford Tower,
264-431: A cheat sheet . A test developer's choice of which style or format to use when developing a written test is usually arbitrary given that there is no single invariant standard for testing. Be that as it may, certain test styles and formats have become more widely used than others. Below is a list of those formats of test items that are widely used by educators and test developers to construct paper or computer-based tests. As
396-558: A computer , or in a predetermined area that requires a test taker to demonstrate or perform a set of skills. Tests vary in style, rigor and requirements. There is no general consensus or invariable standard for test formats and difficulty. Often, the format and difficulty of the test is dependent upon the educational philosophy of the instructor, subject matter, class size, policy of the educational institution, and requirements of accreditation or governing bodies. A test may be administered formally or informally. An example of an informal test
528-469: 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
660-405: A computer (as an eExam ). A test taker who takes a written test could respond to specific test items by writing or typing within a given space of the test or on a separate form or document. In some tests; where knowledge of many constants or technical terms is required to effectively answer questions, like Chemistry or Biology – the test developer may allow every test taker to bring with them
792-418: 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
924-458: 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
1056-484: 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
1188-471: 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
1320-476: A large number of participants. A test may be developed and administered by an instructor, a clinician, a governing body, or a test provider. In some instances, the developer of the test may not be directly responsible for its administration. For example, in the United States, Educational Testing Service (ETS), a nonprofit educational testing and assessment organization, develops standardized tests such as
1452-555: 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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#17327878302201584-1033: 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
1716-499: 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
1848-411: A period of times as a reading section or a given exercise in were the most important part of the class was summarize. However, a simple quiz usually does not count very much, and instructors usually provide this type of test as a formative assessment to help determine whether the student is learning the material. In addition, doing this at the time the instructor collected all can make a significant part of
1980-404: 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
2112-412: 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
2244-632: A result of the French Revolution but it collapsed after only ten years. Germany implemented the examination system around 1800. Englishmen in the 18th century such as Eustace Budgell recommended imitating the Chinese examination system but the first English person to recommend competitive examinations to qualify for employment was Adam Smith in 1776. In 1838, the Congregational church missionary Walter Henry Medhurst considered
2376-425: A result, these tests may consist of only one type of test item format (e.g., multiple-choice test, essay test) or may have a combination of different test item formats (e.g., a test that has multiple-choice and essay items). In a test that has items formatted as multiple-choice questions, a candidate would be given a number of set answers for each question, and the candidate must choose which answer or group of answers
2508-497: A sample using indexes such as the mean or standard deviation , and inferential statistics , which draw conclusions from data that are subject to random variation (e.g., observational errors, sampling variation). Descriptive statistics are most often concerned with two sets of properties of a distribution (sample or population): central tendency (or location ) seeks to characterize the distribution's central or typical value, while dispersion (or variability ) characterizes
2640-433: A specific set of skills. For example, a test taker who intends to become a lawyer is usually required by a governing body such as a governmental bar licensing agency to pass a bar exam . Standardized tests are also used in certain countries to regulate immigration. For example, intended immigrants to Australia are legally required to pass a citizenship test as part of that country's naturalization process. When analyzed in
2772-465: 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
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#17327878302202904-450: A student to write a freehand response. Marks are given more for the steps taken than for the correct answer. If the question has multiple parts, later parts may use answers from previous sections, and marks may be granted if an earlier incorrect answer was used but the correct method was followed, and an answer which is correct (given the incorrect input) is returned. Higher-level mathematical papers may include variations on true/false, where
3036-434: A student's proficiency in specific subjects such as mathematics, science, or literature. In contrast, high school students in other countries such as the United States may not be required to take a standardized test to graduate. Moreover, students in these countries usually take standardized tests only to apply for a position in a university program and are typically given the option of taking different standardized tests such as
3168-637: 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
3300-403: A test taker to write a response to fulfill the requirements of the item. In administrative terms, essay items take less time to construct. As an assessment tool, essay items can test complex learning objectives as well as processes used to answer the question. The items can also provide a more realistic and generalizable task for test. Finally, these items make it difficult for test takers to guess
3432-401: A tool to select for participants that have potential to succeed in a competition such as a sporting event. For example, skaters who wish to participate in figure skating competitions in the United States must pass official U.S. Figure Skating tests just to qualify. Tests are sometimes used by a group to select for certain types of individuals to join the group. For example, Mensa International
3564-399: 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
3696-419: 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
3828-401: A wide range of difficulty, and can easily diagnose a test taker's difficulty with certain concepts. As an educational tool, multiple-choice items test many levels of learning as well as a test taker's ability to integrate information, and it provides feedback to the test taker about why distractors were wrong and why correct answers were right. Nevertheless, there are difficulties associated with
3960-449: Is a high-IQ society that requires individuals to score at the 98th percentile or higher on a standardized, supervised IQ test. Assessment types include: Criterion-referenced tests are designed to measure student performance against a fixed set of criteria or learning standards. It is possible for all test takers to pass, just like it is possible for all test takers to fail. These tests can use individual's scores to focus on improving
4092-432: Is a reading test administered by a parent to a child. A formal test might be a final examination administered by a teacher in a classroom or an IQ test administered by a psychologist in a clinic. Formal testing often results in a grade or a test score . A test score may be interpreted with regards to a norm or criterion , or occasionally both. The norm may be established independently, or by statistical analysis of
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4224-429: Is an item that provides a defined term and requires a test taker to match identifying characteristics to the correct term. A fill-in-the-blank item provides a test taker with identifying characteristics and requires the test taker to recall the correct term. There are two types of fill-in-the-blank tests. The easier version provides a word bank of possible words that will fill in the blanks. For some exams all words in
4356-575: 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
4488-465: 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
4620-834: 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
4752-597: Is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments . 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
4884-636: Is correct. There are two families of multiple-choice questions. The first family is known as the True/False question and it requires a test taker to choose all answers that are appropriate. The second family is known as One-Best-Answer question and it requires a test taker to answer only one from a list of answers. There are several reasons to using multiple-choice questions in tests. In terms of administration, multiple-choice questions usually requires less time for test takers to answer, are easy to score and grade, provide greater coverage of material, allows for
5016-416: Is different from Wikidata All article disambiguation pages All disambiguation pages Physical Fitness Test An examination ( exam or evaluation ) or test is an educational assessment intended to measure a test-taker's knowledge , skill , aptitude , physical fitness , or classification in many other topics (e.g., beliefs ). A test may be administered verbally, on paper, on
5148-428: 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
5280-418: 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
5412-451: 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
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5544-408: 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
5676-402: 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
5808-449: 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
5940-480: The ACT or SAT , which are used primarily to measure a student's reasoning skill. High school students in the United States may also take Advanced Placement tests on specific subjects to fulfill university-level credit. Depending on the policies of the test maker or country, administration of standardized tests may be done in a large hall, classroom, or testing center. A proctor or invigilator may also be present during
6072-765: 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
6204-591: The GCE A-levels or Cambridge Pre-U . In contrast, universities in the United States use an applicant's test score on the SAT or ACT as just one of their many admission criteria to determine whether an applicant should be admitted into one of its undergraduate programs. The other criteria in this case may include the applicant's grades from high school, extracurricular activities, personal statement, and letters of recommendations. Once admitted, undergraduate students in
6336-615: The Joint Entrance Examination or to secondary schools . Types are civil service examinations , required for positions in the public sector ; the U.S. Foreign Service Exam , and the United Nations Competitive Examination. Competitive examinations are considered an egalitarian way to select worthy applicants without risking influence peddling , bias or other concerns. A single test can have multiple qualities. For example,
6468-476: The Organisation for Economic Co-operation and Development (OECD) uses Programme for International Student Assessment (PISA) to evaluate certain skills and knowledge of students from different participating countries. Standardized tests are sometimes used by certain governing bodies to determine whether a test taker is allowed to practice a profession, to use a specific job title, or to claim competency in
6600-596: The SAT but may not directly be involved in the administration or proctoring of these tests. Informal, unofficial, and non-standardized tests and testing systems have existed throughout history. For example, tests of skill such as archery contests have existed in China since the Zhou dynasty (or, more mythologically, Yao ). Oral exams were administered in various parts of the world including ancient China and Europe. A precursor to
6732-777: The United Kingdom itself, and in other Western nations. Like the British, the development of the French and American civil service was influenced by the Chinese system. When Thomas Jenckes made a Report from the Joint Select Committee on Retrenchment in 1868, it contained a chapter on the civil service in China. In 1870, William Spear wrote a book called The Oldest and the Newest Empire-China and
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#17327878302206864-487: 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
6996-466: The bar exam for aspiring lawyers may be a norm-referenced, standardized, summative assessment. This means that only the test takers with higher scores will pass, that all of them took the same test under the same circumstances and were graded with the same scoring standards, and that the test is meant to determine whether the law school graduates have learned enough to practice their profession. Written tests are tests that are administered on paper or on
7128-546: 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
7260-494: The imperial examinations ( keju ). The bureaucratic imperial examinations as a concept has its origins in the year 605 during the short lived Sui dynasty . Its successor, the Tang dynasty , implemented imperial examinations on a relatively small scale until the examination system was extensively expanded during the reign of Wu Zetian . Included in the expanded examination system was a military exam that tested physical ability, but
7392-432: 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
7524-719: 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
7656-420: The "evidence is not very clear." In Prussia , medication examinations began in 1725. The Mathematical Tripos , founded in 1747, is commonly believed to be the first honor examination, but James Bass Mullinger considered "the candidates not having really undergone any examination whatsoever" because the qualification for a degree was merely four years of residence. France adopted the examination system in 1791 as
7788-602: The Chinese exams to be "worthy of imitating." In 1806, the British established a Civil Service College near London for training of the East India Company's administrators in India. This was based on the recommendations of British East India Company officials serving in China and had seen the Imperial examinations. In 1829, the company introduced civil service examinations in India on a limited basis. This established
7920-413: The Chinese had "perfected moral science" and François Quesnay advocated an economic and political system modeled after that of the Chinese. According to Ferdinand Brunetière (1849-1906), followers of Physiocracy such as François Quesnay, whose theory of free trade was based on Chinese classical theory, were sinophiles bent on introducing "l'esprit chinois" to France. He also admits that French education
8052-545: The English "did not know that it was necessary for them to take lessons from the Celestial Empire." In 1875, Archibald Sayce voiced concern over the prevalence of competitive examinations, which he described as "the invasion of this new Chinese culture." After Great Britain's successful implementation of systematic, open, and competitive examinations in India in the 19th century, similar systems were instituted in
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#17327878302208184-625: The National Football League in the United States Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title PFT . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=PFT&oldid=958226351 " Category : Disambiguation pages Hidden categories: Short description
8316-667: The United Kingdom or United States may be required by their respective programs to take a comprehensive examination as a requirement for passing their courses or for graduating from their respective programs. Standardized tests are sometimes used by certain countries to manage the quality of their educational institutions. For example, the No Child Left Behind Act in the United States requires individual states to develop assessments for students in certain grades. In practice, these assessments typically appear in
8448-671: The United States , in which he urged the United States government to adopt the Chinese examination system. Like in Britain, many of the American elites scorned the plan to implement competitive examinations, which they considered foreign, Chinese, and "un-American." As a result, the civil services reform introduced into the House of Representatives in 1868 was not passed until 1883. The Civil Service Commission tried to combat such sentiments in its report: ...with no intention of commending either
8580-632: The advancement of men of talent and merit only." Both Thomas Babington Macaulay , who was instrumental in passing the Saint Helena Act 1833 , and Stafford Northcote, 1st Earl of Iddesleigh , who prepared the Northcote–Trevelyan Report that catalyzed the British civil service , were familiar with Chinese history and institutions. The Northcote–Trevelyan Report of 1854 made four principal recommendations: that recruitment should be on
8712-421: The annual average figures are a necessary artifact of quantitative analysis. The operations of the examination system were part of the imperial record keeping system, and the date of receiving the jinshi degree is often a key biographical datum: sometimes the date of achieving jinshi is the only firm date known for even some of the most historically prominent persons in Chinese history. A brief interruption to
8844-401: The basis of merit determined through standardized written examination, that candidates should have a solid general education to enable inter-departmental transfers, that recruits should be graded into a hierarchy, and that promotion should be through achievement, rather than 'preferment, patronage, or purchase'. When the report was brought up in parliament in 1853, Lord Monteagle argued against
8976-423: The candidate is given a statement and asked to verify its validity by direct proof or stating a counterexample . Statistics Statistics (from German : Statistik , orig. "description of a state , a country" ) is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data . In applying statistics to a scientific, industrial, or social problem, it
9108-439: 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
9240-572: The compass, gunpowder, and the multiplication table, during centuries when this continent was a wilderness, should deprive our people of those conveniences. Standardized testing began to influence the method of examination in British universities from the 1850s, where oral exams had common since the Middle Ages . In the US, the transition happened under the influence of the educational reformer Horace Mann . The shift helped standardize an expansion of
9372-540: 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
9504-542: 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
9636-709: The content of the examinations focused on the Confucian canon and ensured a loyal scholar bureaucrat class which upheld the throne. The Confucian examination system in Vietnam was established in 1075 under the Lý dynasty Emperor Lý Nhân Tông and lasted until the Nguyễn dynasty Emperor Khải Định (1919). There were only three levels of examinations in Vietnam: interprovincial, pre-court, and court. The imperial examination system
9768-418: The context of language texting in the naturalization processes, the ideology can be found from two distinct but nearly related points. One refers to the construction and deconstruction of the nation's constitutive elements that makes their own identity, while the second has a more restricted view of the notion of specific language and ideologies that may served in a specific purpose. Tests are sometimes used as
9900-539: The correct answers and require test takers to demonstrate their writing skills as well as correct spelling and grammar. The difficulties with essay items are primarily administrative: for example, test takers require adequate time to be able to compose their answers. When these questions are answered, the answers themselves are usually poorly written because test takers may not have time to organize and proofread their answers. In turn, it takes more time to score or grade these items. When these items are being scored or graded,
10032-403: The curricula into the sciences and humanities , creating a rationalized method for the evaluation of teachers and institutions and creating a basis for the streaming of students according to ability. Both World War I and World War II demonstrated the necessity of standardized testing and the benefits associated with these tests. Tests were used to determine the mental aptitude of recruits to
10164-425: 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
10296-406: 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
10428-495: 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
10560-614: The examinations occurred at the beginning of the Mongol Yuan dynasty in the 13th century, but was later brought back with regional quotas which favored the Mongols and disadvantaged Southern Chinese. During the Ming and Qing dynasties, the system contributed to the narrow and focused nature of intellectual life and enhanced the autocratic power of the emperor. The system continued with some modifications until its abolition in 1905 during
10692-566: The examinee to respond in a particular way, for example by describing or defining a concept, or comparing and contrasting two or more scenarios or events. Some command words require more insight or skill than others: for example, "analyse" and "synthesise" assess higher-level skills than "describe". More demanding command words usually attract greater mark weighting in the examination. In the UK, Ofqual maintains an official list of command words explaining their meaning. The Welsh government 's guidance on
10824-478: 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
10956-474: 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
11088-402: 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
11220-450: 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
11352-477: The final course grade. Most mathematics questions, or calculation questions from subjects such as chemistry , physics , or economics employ a style which does not fall into any of the above categories, although some papers, notably the Maths Challenge papers in the United Kingdom employ multiple choice. Instead, most mathematics questions state a mathematical problem or exercise that requires
11484-432: 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
11616-413: The form of standardized tests. Test scores of students in specific grades of an educational institution are then used to determine the status of that educational institution, i.e., whether it should be allowed to continue to operate in the same way or to receive funding. Finally, standardized tests are sometimes used to compare proficiencies of students from different institutions or countries. For example,
11748-402: 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
11880-605: 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,
12012-410: The grading process itself becomes subjective as non-test related information may influence the process. Thus, considerable effort is required to minimize the subjectivity of the grading process. Finally, as an assessment tool, essay questions may potentially be unreliable in assessing the entire content of a subject matter. Instructions to exam candidates rely on the use of command words , which direct
12144-623: The hereditary system during the Samurai era. The examination system was established in Korea in 958 under the reign of Gwangjong of Goryeo . Any free man (not Nobi ) was able to take the examinations. By the Joseon period, high offices were closed to aristocrats who had not passed the exams. The examination system continued until 1894 when it was abolished by the Gabo Reform . As in China,
12276-423: The imperial examinations were often discussed in conjunction with Confucianism, which attracted great attention from contemporary European thinkers such as Gottfried Wilhelm Leibniz , Voltaire , Montesquieu , Baron d'Holbach , Johann Wolfgang von Goethe , and Friedrich Schiller . In France and Britain , Confucian ideology was used in attacking the privilege of the elite. Figures such as Voltaire claimed that
12408-487: The implementation of open examinations because it was a Chinese system and China was not an "enlightened country." Lord Stanley called the examinations the "Chinese Principle." The Earl of Granville did not deny this but argued in favor of the examination system, considering that the minority Manchus had been able to rule China with it for over 200 years. In 1854, Edwin Chadwick reported that some noblemen did not agree with
12540-404: The largest residence hall in the state of Kentucky at Western Kentucky University Plant Functional Type , a classification of plants for use in climatology Polish Fighting Team , or "Skalski's Circus", a group of World War II Polish fighter pilots Print for time , a business arrangement between a photographer and a model Profootballtalk.com , a news and rumor website that focuses on
12672-531: The last years of the Qing dynasty. The modern examination system for selecting civil servants also indirectly evolved from the imperial one. Japan implemented the examination system for 200 years during the Heian period (794-1185). Like the Chinese examinations, the curriculum revolved around the Confucian canon. However, unlike in China, it was only ever applied to the minor nobility and so gradually faded away under
12804-568: The later Chinese imperial examinations was in place since the Han dynasty , during which the Confucian characteristic of the examinations was determined. However these examinations did not offer an official avenue to government appointment, the majority of which were filled through recommendations based on qualities such as social status, morals, and ability. Standardized written examinations were first implemented in China. They were commonly known as
12936-587: The measures introduced because they were Chinese. The examination system was finally implemented in the British Indian Civil Service in 1855, prior to which admission into the civil service was purely a matter of patronage, and in England in 1870. Even as late as ten years after the competitive examination plan was passed, people still attacked it as an "adopted Chinese culture." Alexander Baillie-Cochrane, 1st Baron Lamington insisted that
13068-468: The military exam never had a significant impact on the Chinese officer corps and military degrees were seen as inferior to their civil counterpart. The exact nature of Wu's influence on the examination system is still a matter of scholarly debate. During the Song dynasty the emperors expanded both examinations and the government school system, in part to counter the influence of hereditary nobility, increasing
13200-618: The military. The US Army used the Stanford–Binet Intelligence Scale to test the IQ of the soldiers. After the War, industry began using tests to evaluate applicants for various jobs based on performance. In 1952, the first Advanced Placement (AP) test was administered to begin closing the gap between high schools and colleges. Tests are used throughout most educational systems. Tests may range from brief, informal questions chosen by
13332-424: 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
13464-599: The number of degree holders to more than four to five times that of the Tang. From the Song dynasty onward, the examinations played the primary role in selecting scholar-officials, who formed the literati elite of society. However the examinations co-existed with other forms of recruitment such as direct appointments for the ruling family, nominations, quotas, clerical promotions, sale of official titles, and special procedures for eunuchs . The regular higher level degree examination cycle
13596-412: 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
13728-415: 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
13860-544: 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
13992-591: The principle of qualification process for civil servants in England. In 1847 and 1856, Thomas Taylor Meadows strongly recommended the adoption of the Chinese principle of competitive examinations in Great Britain in his Desultory Notes on the Government and People of China . According to Meadows, "the long duration of the Chinese empire is solely and altogether owing to the good government which consists in
14124-494: 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
14256-480: The process, perceive these items to be tricky or picky. Finally, multiple-choice items do not test a test taker's attitudes towards learning because correct responses can be easily faked. True/False questions present candidates with a binary choice – a statement is either true or false. This method presents problems, as depending on the number of questions, a significant number of candidates could get 100% just by guesswork, and should on average get 50%. A matching item
14388-470: 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
14520-466: The religion or the imperialism of China, we could not see why the fact that the most enlightened and enduring government of the Eastern world had acquired an examination as to the merits of candidates for office, should any more deprive the American people of that advantage, if it might be an advantage, than the facts that Confucius had taught political morality, and the people of China had read books, used
14652-461: 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
14784-439: 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
14916-399: 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
15048-405: 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
15180-482: The sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation. Two main statistical methods are used in data analysis : descriptive statistics , which summarize data from
15312-412: 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
15444-422: The skills that were lacking in comprehension. Competitive exams are norm-referenced, high-stakes tests in which candidates are ranked according to their grades and/or percentile, and then top rankers are selected. If the examination is open for n positions, then the first n candidates in ranks pass, the others are rejected. They are used as entrance examinations for university and college admissions such as
15576-408: 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
15708-540: The teacher to major tests that students and teachers spend months preparing for. Some countries such as the United Kingdom and France require all their secondary school students to take a standardized test on individual subjects such as the General Certificate of Secondary Education (GCSE) (in England) and Baccalauréat respectively as a requirement for graduation. These tests are used primarily to assess
15840-470: The testing period to provide instructions, to answer questions, or to prevent cheating. Grades or test scores from standardized test may also be used by universities to determine whether a student applicant should be admitted into one of its academic or professional programs. For example, universities in the United Kingdom admit applicants into their undergraduate programs based primarily or solely on an applicant's grades on pre-university qualifications such as
15972-420: 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
16104-416: 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
16236-485: 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
16368-640: 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
16500-458: The use of command words advises that they should be used "consistently and correctly", but notes that some subjects have their own traditions and expectations in regard to candidates' responses, and Cambridge Assessment notes that in some cases, subject-specific command words may be in used. A quiz is a brief assessment which may cover a small amount of material that was given in a class. Some of them cover two to three lectures that were given in
16632-739: The use of multiple-choice questions. In administrative terms, multiple-choice items that are effective usually take a great time to construct. As an educational tool, multiple-choice items do not allow test takers to demonstrate knowledge beyond the choices provided and may even encourage guessing or approximation due to the presence of at least one correct answer. For instance, a test taker might not work out explicitly that 6.14 ⋅ 7.95 = 48.813 {\displaystyle 6.14\cdot 7.95=48.813} , but knowing that 6 ⋅ 8 = 48 {\displaystyle 6\cdot 8=48} , they would choose an answer close to 48. Moreover, test takers may misinterpret these items and in
16764-550: The word bank are used exactly once. If a teacher wanted to create a test of medium difficulty, they would provide a test with a word bank, but some words may be used more than once and others not at all. The hardest variety of such a test is a fill-in-the-blank test in which no word bank is provided at all. This generally requires a higher level of understanding and memory than a multiple-choice test. Because of this, fill-in-the-blank tests with no word bank are often feared by students. Items such as short answer or essay typically require
16896-468: 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
17028-705: Was accused of atheism and forced to give up his position at the university. The earliest evidence of examinations in Europe date to 1215 or 1219 in Bologna . These were chiefly oral in the form of a question or answer, disputation, determination, defense, or public lecture. The candidate gave a public lecture of two prepared passages assigned to him from the civil or canon law, and then doctors asked him questions, or expressed objections to answers. Evidence of written examinations do not appear until 1702 at Trinity College, Cambridge . According to Sir Michael Sadler , Europe may have had written examinations since 1518 but he admits
17160-409: Was decreed in 1067 to be 3 years but this triennial cycle only existed in nominal terms. In practice both before and after this, the examinations were irregularly implemented for significant periods of time: thus, the calculated statistical averages for the number of degrees conferred annually should be understood in this context. The jinshi exams were not a yearly event and should not be considered so;
17292-583: Was known to Europeans as early as 1570. It received great attention from the Jesuit Matteo Ricci (1552–1610), who viewed it and its Confucian appeal to rationalism favorably in comparison to religious reliance on "apocalypse." Knowledge of Confucianism and the examination system was disseminated broadly in Europe following the Latin translation of Ricci's journal in 1614. During the 18th century,
17424-566: Was really based on Chinese literary examinations which were popularized in France by philosophers, especially Voltaire. Western perception of China in the 18th century admired the Chinese bureaucratic system as favourable over European governments for its seeming meritocracy. However those who admired China such as Christian Wolff were sometimes persecuted. In 1721 he gave a lecture at the University of Halle praising Confucianism, for which he
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