NationMaster - Encyclopedia: Statistical methods

Statistics is a mathematical science pertaining to collection, analysis, interpretation and presentation of data. It is applicable to a wide variety of academic disciplines from the physical and social sciences to the humanities, as well as to business, government, and industry. Image File history File links Download high resolution version (1200x687, 38 KB) Summary A chart comparing the various grading methods in a normal distribution. ... Image File history File links Download high resolution version (1200x687, 38 KB) Summary A chart comparing the various grading methods in a normal distribution. ... The graph of the probability density function of the normal distribution is sometimes called the bell curve or the bell-shaped curve; see normal distribution. ... A grade in education can mean either a teachers evaluation of a students work or a students level of educational progress, usually one grade per year (often denoted by an ordinal number, such as the 3rd Grade or the 12th Grade). This article is about evaluation of... Mathematics is often defined as the study of topics such as quantity, structure, space, and change. ... Data is the plural of datum. ... This is a list of academic disciplines (and academic fields). ... Wikimedia Commons has media related to: Science For the scientific journal named Science, see Science (journal). ... The examples and perspective in this article may not represent a worldwide view. ... This article or section does not cite its references or sources. ...

Given a collection of data, statistics may be employed to summarize or describe the data; this use is called descriptive statistics. In addition, patterns in the data may be modeled, in a way that accounts for randomness and uncertainty in the observations, in order to draw inferences about the larger population; this use is called inferential statistics. Both of these uses may be termed applied statistics. There is also a discipline of mathematical statistics concerned with the theoretical basis of the subject. Descriptive statistics is a branch of statistics that denotes any of the many techniques used to summarize a set of data. ... Model may refer to more than one thing : For models in society, art, fashion, and cosmetics, see; role model model (person) supermodel figure drawing modeling section In science and technology, a model (abstract) is understood as an abstract or theoretical representation of a phenomenon,see; geologic modeling model (economics) model... In ordinary language, the word random is used to express apparent lack of purpose or cause. ... It has been suggested that this article or section be merged with statistical inference. ... Applied statistics is the use of statistics and statistical theory in real-life situations. ... Mathematical statistics uses probability theory and other branches of mathematics to study statistics from a purely mathematical standpoint. ...

The word statistics is also the plural of statistic (singular), which refers to the result of applying a statistical algorithm to a set of data. A statistic (singular) is the result of applying a statistical algorithm to a set of data. ...

Historical overview

The word statistics ultimately derives from the modern Latin term statisticum collegium ("council of state") and the Italian word statista ("statesman" or "politician"). The German Statistik, first introduced by Gottfried Achenwall (1749), originally designated the analysis of data about the state, signifying the "science of state". It acquired the meaning of the collection and classification of data generally in the early 19th century. It was introduced into English by Sir John Sinclair. Modern Latin is the form of the Latin language that was developed in the Western world after the Middle Ages. ... The term statesman is a respectful term used to refer to diplomats, politicians, and other notable figures of state. ... A politician is an individual involved in politics to the extent of holding or running for public office. ... Gottfried Achenwall (born 20 October 1719 in ElblÄ…g, Poland - died 1 May 1772) was a German statistician. ... A state is an organized political community, occupying a territory, and possessing internal and external sovereignty, which successfully claims the monopoly of the use of force. ... Alternative meaning: Nineteenth Century (periodical) (18th century — 19th century — 20th century — more centuries) As a means of recording the passage of time, the 19th century was that century which lasted from 1801-1900 in the sense of the Gregorian calendar. ... Sir John Sinclair (May 10, 1754 - December 21, 1835) Scottish writer on finance and agriculture and statistician. ...

Thus, the original principal purpose of statistics was data to be used by governmental and (often centralized) administrative bodies. The collection of data about states and localities continues, largely through national and international statistical services; in particular, censuses provide regular information about the population. National statistical services Australia: Australian Bureau of Statistics Brazil: Brazilian Institute of Geography and Statistics (IBGE) Belgium: Statistics Belgium Canada: Statistics Canada Colombia: Departamento Administrativo Nacional de Estadistica (DANE) Denmark: Danmarks statistik - http://www. ... A census is the process of obtaining information about every member of a population (not necessarily a human population). ...

Statistics eventually merged with the more mathematically oriented field of inverse probability, referring to the estimation of a parameter from experimental data in the experimental sciences (most notably astronomy). Today the use of statistics has broadened far beyond the service of a state or government, to include such areas as business, natural and social sciences, and medicine, among others. Lunar astronomy: the large crater is Daedalus, photographed by the crew of Apollo 11 as they circled the Moon in 1969. ...

Because of its history and wide applicability, statistics is generally regarded not as a subfield of mathematics but as a distinct, albeit allied, field. Many large universities maintain separate mathematics and statistics departments. Statistics is also taught in departments as diverse as psychology, education, and public health. A university is an institution of higher education and of research, which grants academic degrees at all levels (bachelor, master, and doctor) in a variety of subjects. ... This is a list of academic disciplines (and academic fields). ... Auguste Rodins The Thinker, bronze cast by Alexis Rudier, Laeken Cemetery, Brussels, Belgium. ... Public health is concerned with threats to the overall health of a community based on population health analysis. ...

Important contributors to statistics

See also list of statisticians. Johann Carl Friedrich Gauss Johann Carl Friedrich Gauss (Gauß) (April 30, 1777 _ February 23, 1855) was a legendary German mathematician, astronomer and physicist with a very wide range of contributions; he is considered to be one of the greatest mathematicians of all time. ... Blaise Pascal (June 19, 1623â€“August 19, 1662) was a French mathematician, physicist, and religious philosopher. ... Francis Galton Sir Francis Galton F.R.S. (February 16, 1822 â€“ January 17, 1911), half-cousin of Charles Darwin, was a Victorian polymath, British anthropologist, eugenicist, tropical explorer, geographer, inventor, meteorologist, proto-geneticist, psychometrician, and statistician. ... William Sealy Gosset (June 13, 1876 – October 16, 1937) was a chemist and statistician, better known by his pen name Student. ... Karl Pearson (pencil sketch in notebook; there is some see-through of writing on next page) Karl Pearson (March 27, 1857 â€“ April 27, 1936) was a major contributor to the early development of statistics as a serious scientific discipline in its own right. ... Sir Ronald Fisher Sir Ronald Aylmer Fisher, FRS (17 February 1890 â€“ 29 July 1962) was a British eugenicist, evolutionary biologist, geneticist and statistician. ... Gertrude Mary Cox (1900-1978) was an influential American statistican and founder of the department of Experimental Statistics at North Carolina State University. ... Charles Edward Spearman (September 10, 1863 - September 7, 1945) was an English psychologist known for work in statistics, as a pioneer of factor analysis, and for Spearmans rank correlation coefficient. ... Pafnuty Lvovich Chebyshev Pafnuty Lvovich Chebyshev (ÐŸÐ°Ñ„Ð½ÑƒÌÑ‚Ð¸Ð¹ Ð›ÑŒÐ²Ð¾ÌÐ²Ð¸Ñ‡ Ð§ÐµÐ±Ñ‹ÑˆÑ‘Ð²) (May 16, 1821 - December 9, 1894) was a Russian mathematician. ... Aleksandr Mikhailovich Lyapunov (ÐÐ»ÐµÐºÑÐ°Ð½Ð´Ñ€ ÐœÐ¸Ñ…Ð°Ð¹Ð»Ð¾Ð²Ð¸Ñ‡ Ð›ÑÐ¿ÑƒÐ½Ð¾Ð²) (June 6, 1857 â€“ November 3, 1918, all new style) was a Russian mathematician, mechanician and physicist. ... Sir Isaac Newton, PRS, (4 January [O.S. 25 December 1642] 1643 â€“ 31 March [O.S. 20 March] 1727) was an English physicist, mathematician, astronomer, alchemist, inventor and natural philosopher who is generally regarded as one of the most influential scientists in history. ... Abraham de Moivre Abraham de Moivre (May 26, 1667 in Vitry-le-FranÃ§ois, Champagne, France â€“ November 27, 1754 in London, England) was a French mathematician famous for de Moivres formula, which links complex numbers and trigonometry, and for his work on the normal distribution and probability theory. ... This article needs to be wikified. ... Florence Nightingale, OM (12 May 1820 â€“ 13 August 1910), who came to be known as The Lady with the Lamp, was the pioneer of modern nursing. ... John Wilder Tukey (June 16, 1915 - July 26, 2000) was a statistician. ... George Bernard Dantzig (8 November 1914 â€“ 13 May 2005) was a mathematician who introduced the simplex algorithm and is considered the Father of linear programming. He was the recipient of many honors, including the National Medal of Science in 1975, the John von Neumann Theory Prize in 1974. ... Thomas Bayes Reverend Thomas Bayes (c. ... Statisticians or people who made notable contributions to the theories of statistics, or related aspects of probability, or machine learning: Peter Armitage M. S. Bartlett Laurence Baxter Thomas Bayes Allan Birnbaum David Blackwell Chester Bliss Ladislaus Bortkiewicz George Box Bento de Jesus CaraÃ§a Pafnuty Chebyshev Alexey Chervonenkis Len Cook...

Conceptual overview

In applying statistics to a scientific, industrial, or societal problem, one begins with a population to be studied. This might be a population of people in a country, of crystal grains in a rock, or of goods manufactured by a particular factory. The population may even consist of a single process observed at various times; data collected about this kind of "population" constitute what is called a time series. In statistics and signal processing, a time series is a sequence of data points, measured typically at successive times, spaced apart at uniform time intervals. ...

For practical reasons, rather than compiling data about the entire population one instead studies a chosen subset of the population, called a sample. Data are collected about the sample in some kind of experimental setting. The data are then subjected to statistical analysis, which serves two related purposes: description and inference. Sampling is that part of statistical practice concerned with the selection of individual observations intended to yield some knowledge about a population of concern, especially for the purposes of statistical inference. ... In the scientific method, an experiment is a set of actions and observations, performed to support or falsify a hypothesis or research concerning phenomena. ...

The concept of correlation is particularly noteworthy. Statistical analysis of a data set may reveal that two variables (that is, two properties of the population under consideration) tend to vary together, as if they are connected. For example, a study of annual income and age of death among people might find that poor people tend to have shorter lives, on average, than affluent people. The two variables are said to be correlated. However, one cannot immediately infer the existence of a causal relationship between the two variables; see correlation implies causation (logical fallacy). Descriptive statistics is a branch of statistics that denotes any of the many techniques used to summarize a set of data. ... In statistics, mean has two related meanings: the average in ordinary English, which is more correctly called the arithmetic mean, to distinguish it from geometric mean or harmonic mean. ... In probability and statistics, the standard deviation is the most commonly used measure of statistical dispersion. ... It has been suggested that this article or section be merged with statistical inference. ... One may be faced with the problem of making a definite decision with respect to an uncertain hypothesis which is known only through its observable consequences. ... Estimation is generally the calculation of an approximate or uncertain result, often based on approximate, uncertain, incomplete, or noisy data. ... A prediction or forecast is a statement or claim that a particular event will occur in the future. ... In probability theory and statistics, correlation, also called correlation coefficient, is a numeric measure of the strength of linear relationship between two random variables. ... Regression analysis is any statistical method where the mean of one or more random variables is predicted conditioned on other (measured) random variables. ... Model may refer to more than one thing : For models in society, art, fashion, and cosmetics, see; role model model (person) supermodel figure drawing modeling section In science and technology, a model (abstract) is understood as an abstract or theoretical representation of a phenomenon,see; geologic modeling model (economics) model... In statistics, analysis of variance (ANOVA) is a collection of statistical models and their associated procedures which compare means by splitting the overall observed variance into different parts. ... In statistics and signal processing, a time series is a sequence of data points, measured typically at successive times, spaced apart at uniform time intervals. ... Data mining, also known as knowledge-discovery in databases (KDD), is the practice of automatically searching large stores of data for patterns. ... Correlation implies causation, also known as cum hoc ergo propter hoc (Latin for with this, therefore because of this) and false cause, is a logical fallacy by which two events that occur together are claimed to be cause and effect. ...

If the sample is representative of the population, then inferences and conclusions made from the sample can be extended to the population as a whole. A major problem lies in determining the extent to which the chosen sample is representative. Statistics offers methods to estimate and correct for randomness (uncertainty) in the sample and in the data collection procedure, as well as methods for designing robust experiments in the first place; see experimental design. The first statistician to consider a methodology for the design of experiments was Sir Ronald A. Fisher. ...

The fundamental mathematical concept employed in understanding such randomness is probability. Mathematical statistics (also called statistical theory) is the branch of applied mathematics that uses probability theory and analysis to examine the theoretical basis of statistics. The word probability derives from the Latin probare (to prove, or to test). ... Mathematical statistics uses probability theory and other branches of mathematics to study statistics from a purely mathematical standpoint. ... The theory of statistics includes a number of topics: Statistical models of the sources of data and typical problem formulation: Sampling from a finite population Measuring observational error and refining procedures Studying statistical relations Planning statistical research to measure and control observational error: Design of experiments to determine treatment effects... Applied mathematics is a branch of mathematics that concerns itself with the application of mathematical knowledge to other domains. ... Probability theory is the mathematical study of probability. ... Analysis is the generic name given to any branch of mathematics which depends upon the concepts of limits and convergence, and studies closely related topics such as continuity, integration, differentiability and transcendental functions. ...

The use of any statistical method is valid only when the system or population under consideration satisfies the basic mathematical assumptions of the method. Misuse of statistics can produce subtle but serious errors in description and interpretation — subtle in that even experienced professionals sometimes make such errors, and serious in that they may affect social policy, medical practice and the reliability of structures such as bridges and nuclear power plants. A misuse of statistics occurs when a statistical argument asserts a falsehood. ...

Even when statistics is correctly applied, the results can be difficult to interpret for a non-expert. For example, the statistical significance of a trend in the data — which measures the extent to which the trend may be caused by random variation in the sample — may not agree with one's intuitive sense of its significance. The set of basic statistical skills (and skepticism) needed by people to deal with information in their everyday lives is referred to as statistical literacy. In statistics, a result is significant if it is unlikely to have occurred by chance, given that a presumed null hypothesis is true. ... Wikipedia does not have an article with this exact name. ...

Statistical methods

Experimental and observational studies

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 a response or dependent variable. There are two major types of causal statistical studies, experimental studies and observational studies. In both types of studies, 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 is in how the study is actually conducted. An independent variable is that variable presumed to affect or determine a dependent variable. ... In experimental design, a dependent variable is a variable dependent on another variable (called the independent variable). ...

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 may have 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 the response are investigated.

An example of an experimental study is the famous Hawthorne studies which attempted to test changes to the working environment at the Hawthorne plant of the Western Electric Company. The researchers were interested in whether increased illumination would increase the productivity of the assembly line workers. The researchers first measured productivity in the plant then modified the illumination in an area of the plant to see if changes in illumination would affect productivity. Due to errors in experimental procedures, specifically the lack of a control group and blindedness, the researchers were unable to do what they planned, in what is known as the Hawthorne effect. It has been suggested that this article or section be merged with Hawthorne effect. ... An assembly line is a manufacturing process in which interchangeable parts are added to a product in a sequential manner to create an end product. ... From Latin ex- + -periri (akin to periculum attempt). ... To meet Wikipedias quality standards, this article or section may require cleanup. ...

An example of an observational study is a study which explores the correlation between smoking and lung cancer. This type of study typically uses a survey to collect observations about the area of interest and then perform statistical analysis. In this case, the researchers would collect observations of both smokers and non-smokers and then look at the number of cases of lung cancer in each group.

Most scientific work starts with a question about the world we live in. ... Ethics (from Greek ethikos) is the branch of axiology â€“ one of the four major branches of philosophy, alongside metaphysics, epistemology, and logic â€“ which attempts to understand the nature of morality; to define that which is right from that which is wrong. ... The first statistician to consider a methodology for the design of experiments was Sir Ronald A. Fisher. ... In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate as much as possible as simply as possible. ... Descriptive statistics is a branch of statistics that denotes any of the many techniques used to summarize a set of data. ... The topics below are usually included in the area of interpreting statistical data. ... The topics below are usually included in the area of interpreting statistical data. ...

Levels of measurement

There are four types of measurements or measurement scales used in statistics. The four types or levels of measurement (ordinal, nominal, interval, and ratio) have different degrees of usefulness in statistical research. Ratio measurements, where both a zero value and distances between different measurements are defined, provide the greatest flexibility in statistical methods that can be used for analysing the data. Interval measurements, with meaningful distances between measurements but no meaningful zero value (such as IQ measurements or temperature measurements in degrees Celsius). Ordinal measurements have imprecise differences between consecutive values but a meaningful order to those values. Nominal measurements have no meaningful rank order among values. The level of measurement of a variable in mathematics and statistics is a classifcation that was proposed in order to describe how much information the numbers associated with the variable contain. ... Research is often described as an active, diligent, and systematic process of inquiry aimed at discovering, interpreting and revising facts. ... A degree Celsius (Â°C) is a unit of temperature named after the Swedish astronomer Anders Celsius (1701-1744), who first proposed a similar system in 1742. ...

Statistical techniques

Some well known statistical tests and procedures for research observations are: Look up test in Wiktionary, the free dictionary. ... A procedure is a series of activities, tasks, steps, decisions, calculations and other processes, that when undertaken in the sequence laid down produces the described result, product or outcome. ... Research is often described as an active, diligent, and systematic process of inquiry aimed at discovering, interpreting and revising facts. ... Observation is an activity of an intelligent living being, to sense and assimiliate the knowledge of a phenomenon in its framework of previous knowledge and ideas. ...

A t-test is any statistical hypothesis test in which the test statistic has a Students t-distribution if the null hypothesis is true. ... For any positive integer , the chi-square distribution with k degrees of freedom is the probability distribution of the random variable where Z1, ..., Zk are independent normal variables, each having expected value 0 and variance 1. ... In statistics, analysis of variance (ANOVA) is a collection of statistical models and their associated procedures which compare means by splitting the overall observed variance into different parts. ... The Mann-Whitney U test is one of the best-known non-parametric statistical significance tests. ... Regression analysis is any statistical method where the mean of one or more random variables is predicted conditioned on other (measured) random variables. ... In probability theory and statistics, correlation, also called correlation coefficient, is a numeric measure of the strength of linear relationship between two random variables. ... In mathematics, and in particular statistics, the Pearson product-moment correlation coefficient (r) is a measure of how well a linear equation describes the relation between two variables X and Y measured on the same object or organism. ... In statistics, Spearmans rank correlation coefficient, named for Charles Spearman and often denoted by the Greek letter Ï (rho), is a non-parametric measure of correlation â€“ that is, it assesses how well an arbitrary monotonic function could describe the relationship between two variables, without making any assumptions about the frequency...

Specialized disciplines

Some sciences use applied statistics so extensively that they have specialized terminology. These disciplines include: Applied statistics is the use of statistics and statistical theory in real-life situations. ... Jargon redirects here. ...

Statistics form a key basis tool in business and manufacturing as well. It is used to understand measurement systems variability, control processes (as in statistical process control or SPC), for summarizing data, and to make data-driven decisions. In these roles it is a key tool, and perhaps the only reliable tool. Actuarial science applies mathematical and statistical methods to finance and insurance, particularly to the assessment of risk. ... Biostatistics or biometry is the application of statistics to a wide range of topics in biology. ... Business statistics is the science of ‘good decision making in the face of uncertainty and is used in many disciplines such as financial analysis, econometrics, auditing, production and operations including services improvement, and marketing research. ... Data mining, also known as knowledge-discovery in databases (KDD), is the practice of automatically searching large stores of data for patterns. ... Pattern recognition is a field within the area of machine learning. ... Econometrics literally means economic measurement. It is the branch of economics that applies statistical methods to the empirical study of economic theories and relationships. ... Engineering statistics is a branch of statistics that has two subtopics which are particular to engineering: Quality control and process control use statistics as a tool to manage conformance to specifications of manufacturing processes and their products. ... Statistical physics, one of the fundamental theories of physics, uses methods of statistics in solving physical problems. ... Demography is the study of human population dynamics. ... Psychological statistics is the application of statistics to psychology. ... Social statistics is the use of statistical measurement systems to study human behavior in a social environment. ... Wikipedia does not have an article with this exact name. ... Chemometrics is the application of mathematical or statistical methods to chemical data. ... Analytical chemistry is the analysis of material samples to gain an understanding of their chemical composition and structure. ... Chemical engineering is the application of science, in particular chemistry, physics and mathematics, to the process of converting raw materials or chemicals into more useful or valuable forms. ... As with many sports, and perhaps even more so, statistics are very important to baseball. ... Cricket is a sport that generates a large number of statistics. ... Statistical process control (SPC) is a method for achieving quality control in manufacturing processes. ...

Software

Modern statistics is supported by computers to perform some of the very large and complex calculations required.

Whole branches of statistics have been made possible by computing, for example neural networks. A neural network is an interconnected group of neurons. ...

The computer revolution has implications for the future of statistics, with a new emphasis on 'experimental' and 'empirical' statistics.

Statistical packages in common use include: A statistical package is a kind of large computer program that is specialised for statistical analysis. ...

Open source refers to projects that are open to the public and which draw on other projects that are freely available to the general public. ... Freeware is computer software which is made available free of charge, as opposed to payware where the user is required to pay. ... Proprietary indicates that a party exercises private ownership, control or use over an item of property, usually to the exclusion of other parties. ... GNU PSPP is the name of a computer program used for performing statistical analysis on sampled data. ... OpenOffice. ... For other uses of the term calculus see calculus (disambiguation) Calculus is a branch of mathematics, developed from algebra and geometry, built on two major complementary ideas. ... Gnumeric is a free spreadsheet program that is part of the GNOME desktop. ... Primary and secondary roots in a cotton plant In vascular plants, the root is that organ of a plant body that typically lies below the surface of the soil (compare with stem). ... Microsoft Excel is a spreadsheet program written and distributed by Microsoft for computers using the Microsoft Windows operating system and for Apple Macintosh computers. ...

Contents

Historical overview

Important contributors to statistics

Conceptual overview

Statistical methods

Experimental and observational studies

Levels of measurement

Statistical techniques

Specialized disciplines

Software

See also

External links

General sites and organizations

Link collections

Online courses and textbooks

Statistical software

Other resources

Additional references

Contents

Historical overview GA_googleFillSlot("encyclopedia_square");

Important contributors to statistics

Conceptual overview

Statistical methods

Experimental and observational studies

Levels of measurement

Statistical techniques

Specialized disciplines

Software

See also

External links

General sites and organizations

Link collections

Online courses and textbooks

Statistical software

Other resources

Additional references

Historical overview