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Encyclopedia > Statistics
A graph of a normal bell curve showing statistics used in standardized testing assessment. The scales include standard deviations, cumulative percentages, percentile equivalents, Z-scores, T-scores, standard nines, and percentages in standard nines.
A graph of a normal bell curve showing statistics used in standardized testing assessment. The scales include standard deviations, cumulative percentages, percentile equivalents, Z-scores, T-scores, standard nines, and percentages in standard nines.

Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the natural and social sciences to the humanities, and to government and business. Wikipedia (IPA: , or ( ) is a multilingual, web-based, free content encyclopedia project, operated by the Wikimedia Foundation, a non-profit organization. ... Statistics is a mathematical science pertaining to the collection, analysis, interpretation, and presentation of data. ... Image File history File links The_Normal_Distribution. ... Image File history File links The_Normal_Distribution. ... The normal distribution, also called the Gaussian distribution, is an important family of continuous probability distributions, applicable in many fields. ... Standardized testing is: in theory: a tool to ensure that student knowledge and aptitude in a given subject are examined with the same criteria across different schools. ... In probability and statistics, the standard deviation is the most commonly used measure of statistical dispersion. ... For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... For other uses, see Data (disambiguation). ... This is a list of academic disciplines (and academic fields). ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... For other uses, see Humanities (disambiguation). ...


Statistical methods can be used to summarize or describe a collection of data; this 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, and then used to draw inferences about the process or population being studied; this is called inferential statistics. Both descriptive and inferential statistics comprise applied statistics. There is also a discipline called mathematical statistics, which is concerned with the theoretical basis of the subject. Descriptive statistics are used to describe the basic features of the data in a study. ... A mathematical model is an abstract model that uses mathematical language to describe a system. ... Random redirects here. ... It has been suggested that this article or section be merged with statistical inference. ... 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, as in economic statistics, crime statistics, etc. A statistic (singular) is the result of applying a statistical algorithm to a set of data. ... Econometrics literally means economic measurement. It is the branch of economics that applies statistical methods to the empirical study of economic theories and relationships. ... It has been suggested that Crime rate be merged into this article or section. ...

Contents

History

Main article: History of statistics

"Five men, Conring, Achenwall, Süssmilch, Graunt and Petty have been honored by different writers as the founder of statistics." claims one source (Willcox, Walter (1938) The Founder of Statistics. Review of the International Statistical Institute 5(4):321-328.) Hermann Conring (November 9, 1606 – December 12, 1681) was a North German intellectual. ... Gottfried Achenwall (born 20 October 1719 in ElblÄ…g, Poland - died 1 May 1772) was a German statistician. ... John Graunt (1620-1674) was one of the first demographers. ... Sir William Petty (May 27, 1623 – December 16, 1687) was an English economist, scientist and philosopher. ...


Some scholars pinpoint the origin of statistics to 1662, with the publication of "Observations on 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. 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 is widely employed in government, business, and the natural and social sciences. 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. ...


Because of its empirical roots and its applications, statistics is generally considered not to be a subfield of pure mathematics, but rather a distinct branch of applied mathematics. Its mathematical foundations were laid in the 17th century with the development of probability theory by Pascal and Fermat. Probability theory arose from the study of games of chance. The method of least squares was first described by Carl Friedrich Gauss around 1794. The use of modern computers has expedited large-scale statistical computation, and has also made possible new methods that are impractical to perform manually. Probability theory is the branch of mathematics concerned with analysis of random phenomena. ... The pascal (symbol: Pa) is the SI unit of pressure. ... Pierre de Fermat Pierre de Fermat (August 17, 1601 – January 12, 1665) was a French lawyer at the Parliament of Toulouse and a mathematician who is given credit for the development of modern calculus. ... Least squares is a mathematical optimization technique that attempts to find a best fit to a set of data by attempting to minimize the sum of the squares of the differences (called residuals) between the fitted function and the data. ... Johann Carl Friedrich Gauss (pronounced ,  ; in German usually Gauß, Latin: ) (30 April 1777 – 23 February 1855) was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, electrostatics, astronomy, and optics. ... This article is about the machine. ...


Overview

In applying statistics to a scientific, industrial, or societal problem, one begins with a process or 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 during a given period. It may instead be a process observed at various times; data collected about this kind of "population" constitute what is called a time series. In statistics, signal processing, and econometrics, a time series is a sequence of data points, measured typically at successive times, spaced at (often uniform) time intervals. ...


For practical reasons, rather than compiling data about an entire population, one usually studies a chosen subset of the population, called a sample. Data are collected about the sample in an observational or 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 (Latin: ex- periri, of (or from) trying) is a set of observations performed in the context of solving a particular problem or question, to retain or falsify a hypothesis or research concerning phenomena. ...

“… it is only the manipulation of uncertainty that interests us. We are not concerned with the matter that is uncertain. Thus we do not study the mechanism of rain; only whether it will rain.”
Dennis Lindley, "The Philosophy of Statistics", The Statistician (2000).

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 than affluent people. The two variables are said to be correlated (which is a positive correlation in this case). However, one cannot immediately infer the existence of a causal relationship between the two variables. (See Correlation does not imply causation.) The correlated phenomena could be caused by a third, previously unconsidered phenomenon, called a lurking variable or confounding variable. Descriptive statistics are used to describe the basic features of the data in a study. ... This article is about mathematical mean. ... In probability and statistics, the standard deviation of a probability distribution, random variable, or population or multiset of values is a measure of the spread of its values. ... 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 the calculated approximation of a result which is usable even if input data may be incomplete, uncertain, or noisy. ... Several sets of (x, y) points, with the correlation coefficient of x and y for each set. ... In statistics, regression analysis examines the relation of a dependent variable (response variable) to specified independent variables (explanatory variables). ... A mathematical model is an abstract model that uses mathematical language to describe a system. ... 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, signal processing, and econometrics, a time series is a sequence of data points, measured typically at successive times, spaced at (often uniform) time intervals. ... Data mining is the principle of sorting through large amounts of data and picking out relevant information. ... Dennis Victor Lindley born 25 July 1923 is a noted British statistician, decision theorist and leading advocate of Bayesian statistics. ... A data set (or dataset) is a collection of data, usually presented in tabular form. ... Correlation does not imply causation is a phrase used in the sciences and statistics to emphasize that correlation between two variables does not imply there is a cause-and-effect relationship between the two. ... This article contains information that has not been verified and thus might not be reliable. ... In statistics, a spurious relationship (or, sometimes, spurious correlation) is a mathematical relationship in which two occurrences have no logical connection, yet it may be implied that they do, due to a certain third, unseen factor (referred to as a confounding factor or lurking variable). The spurious relationship gives an...


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 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. Probability is the likelihood or chance that something is the case or will happen. ... 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 mathematical techniques typically used in the application of mathematical knowledge to other domains. ... Analysis has its beginnings in the rigorous formulation of calculus. ...


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 the sense that even experienced professionals sometimes make such errors, serious in the sense that they may affect, for instance, social policy, medical practice and the reliability of structures such as bridges. Even when statistics is correctly applied, the results can be difficult for the non-expert to interpret. For example, the statistical significance of a trend in the data, which measures the extent to which the trend could 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. A misuse of statistics occurs when a statistical argument asserts a falsehood. ... In statistics, a result is called statistically significant if it is unlikely to have occurred by chance. ... Statistical literacy is a term used to describe an individuals ability to understand statistics. ...


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 response or dependent variables. 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 lies in how the study is actually conducted. Each can be very effective. Causality or causation denotes the relationship between one event (called cause) and another event (called effect) which is the consequence (result) of the first. ... In an experimental design, the independent variable (argument of a function, also called a predictor variable) is the variable that is manipulated or selected by the experimenter to determine its relationship to an observed phenomenon (the dependent variable). ... In experimental design, a dependent variable (also known as response variable, responding variable or regressand) is a factor whose values in different treatment conditions are compared. ...


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. Instead, data are gathered and correlations between predictors and response are investigated.


An example of an experimental study is the famous Hawthorne studies, which attempted to test the changes to the working environment at the Hawthorne plant of 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 the productivity. It turned out that the productivity indeed improved (under the experimental conditions). (See Hawthorne effect.) However, the study is heavily criticized today for errors in experimental procedures, specifically for the lack of a control group and blindedness. It has been suggested that this article or section be merged with Hawthorne effect. ... Modern car assembly line. ... The Hawthorne effect refers to a phenomenon of observing workers behavior or their performance and changing it temporarily. ... From Latin ex- + -periri (akin to periculum attempt). ... The double blind is ray charles is ray charlesis ray charlesis ray charlesis ray charlesis ray charlesis ray charlesis ray charlesis ray charlesis ray charlesis ray charlesis ray charlesis ray charlesis ray charlesis ray charlesis ray charlesis ray charlesis ray charlesis ray charlesof the scientific method, used to prevent research...


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 performs statistical analysis. In this case, the researchers would collect observations of both smokers and non-smokers, perhaps through a case-control study, and then look for the number of cases of lung cancer in each group. Case-control studies are one type of epidemiological study design. ...


The basic steps of an experiment are;

  1. Planning the research, including determining information sources, research subject selection, and ethical considerations for the proposed research and method.
  2. Design of experiments, concentrating on the system model and the interaction of independent and dependent variables.
  3. Summarizing a collection of observations to feature their commonality by suppressing details. (Descriptive statistics)
  4. Reaching consensus about what the observations tell about the world being observed. (Statistical inference)
  5. Documenting / presenting the results of the study.

For other uses, see Ethics (disambiguation). ... 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 are used to describe the basic features of the data in a study. ... It has been suggested that this article or section be merged with inferential statistics. ... It has been suggested that this article or section be merged with inferential statistics. ...

Levels of measurement

See: Stanley Stevens' "Scales of measurement" (1946): nominal, ordinal, interval, ratio

There are four types of measurements or levels of measurement or measurement scales used in statistics: nominal, ordinal, interval, and ratio. They have different degrees of usefulness in statistical research. Ratio measurements have both a zero value defined and the distances between different measurements defined; they provide the greatest flexibility in statistical methods that can be used for analyzing the data. Interval measurements have meaningful distances between measurements defined, but have no meaningful zero value defined (as in the case with IQ measurements or with temperature measurements in Fahrenheit). Ordinal measurements have imprecise differences between consecutive values, but have 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 describes how much information the numbers associated with the variable contain. ... The level of measurement of a variable in mathematics and statistics is a classification that was proposed in order to describe the nature of information contained within numbers assigned to objects and, therefore, within the variable. ... This article is about the concept. ... For other uses, see Fahrenheit (disambiguation). ...


Since variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically, sometimes they are called together as categorical variables, whereas ratio and interval measurements are grouped together as quantitative or continuous variables due to their numerical nature.


Statistical techniques

Some well known statistical tests and procedures for research observations are: 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. ... Look up Procedure in Wiktionary, the free dictionary. ... This article is about the concept. ... For other uses, see Observation (disambiguation). ...

A t-test is any statistical hypothesis test in which the test statistic has a Students t distribution if the null hypothesis is true. ... A chi-square test is any statistical hypothesis test in which the test statistic has a chi-square distribution when the null hypothesis is true, or any in which the probability distribution of the test statistic (assuming the null hypothesis is true) can be made to approximate a chi-square... 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, the Mann-Whitney U test (also called the Mann-Whitney-Wilcoxon (MWW), Wilcoxon rank-sum test, or Wilcoxon-Mann-Whitney test) is a non-parametric test for assessing whether two samples of observations come from the same distribution. ... In statistics, regression analysis examines the relation of a dependent variable (response variable) to specified independent variables (explanatory variables). ... Factor analysis is a statistical method used to explain variability among observed random variables in terms of fewer unobserved random variables called factors. ... Several sets of (x, y) points, with the correlation coefficient of x and y for each set. ... In statistics, the Pearson product-moment correlation coefficient (sometimes known as the PMCC) (r) is a measure of the correlation of two variables X and Y measured on the same object or organism, that is, a measure of the tendency of the variables to increase or decrease together. ... In statistics, Spearmans rank correlation coefficient, named after Charles Spearman and often denoted by the Greek letter (rho) or as , is a non-parametric measure of correlation – that is, it assesses how well an arbitrary monotonic function could describe the relationship between two variables, without making any assumptions about... 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. ...

Specialized disciplines

Some fields of inquiry use applied statistics so extensively that they have specialized terminology. These disciplines include: 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. 2003 US mortality (life) table, Table 1, Page 1 Actuarial science applies mathematical and statistical methods to finance and insurance, particularly to the assessment of risk. ... The creator of or main contributor to this page may have a conflict of interest with the subject of this article. ... Biostatistics or biometry is the application of statistics to a wide range of topics in biology. ... It has been suggested that this article or section be merged with Bootstrap (statistics). ... In statistics, resampling is any of a variety of methods for doing one of the following: Estimating the precision of sample statistics (medians, variances, percentiles) by using subsets of available data (jackknife) or drawing randomly with replacement from a set of data points (bootstrapping) Exchanging labels on data points when... 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 is the principle of sorting through large amounts of data and picking out relevant information. ... Pattern recognition is a field within the area of machine learning. ... Map of countries by population Population growth showing projections for later this century Demography is the statistical study of all populations. ... Econometrics literally means economic measurement. It is the branch of economics that applies statistical methods to the empirical study of economic theories and relationships. ... Energy statistics refers to collecting, compiling, analyzing and disseminating data on commodities such as coal, crude oil, natural gas, electricity, or renewable energy sources (biomass, geothermal, wind or solar energy), when they are used for the energy they contain. ... Engineering statistics is a branch of statistics that has three subtopics which are particular to engineering: (DOE) or design of experiments uses statistical techniques to test and construct models of engineering components and systems. ... Epidemiology is the study of factors affecting the health and illness of populations, and serves as the foundation and logic of interventions made in the interest of public health and preventive medicine. ... A geographic information system (GIS) is a system for managing data that has a spatial specialized form of an information system. ... In statistics, spatial analysis or spatial statistics includes any of the formal techniques used in various fields of research which study entities using their topological, geometric, or geographic properties. ... UPIICSA IPN - Binary image Image processing is any form of information processing for which the input is an image, such as photographs or frames of video; the output is not necessarily an image, but can be for instance a set of features of the image. ... Multivariate statistics or multivariate statistical analysis in statistics describes a collection of procedures which involve observation and analysis of more than one statistical variable at a time. ... Psychological statistics is the application of statistics to psychology. ... For the Talib Kweli album Quality (album) Quality can refer to a. ... Social statistics is the use of statistical measurement systems to study human behavior in a social environment. ... Statistical literacy is a term used to describe an individuals ability to understand statistics. ... A statistical model is used in applied statistics. ... Statistical surveys are used to collect quantitative information about items in a population. ... Chemometrics is the application of mathematical or statistical methods to chemical data. ... This article does not cite any references or sources. ... Chemical engineers design, construct and operate plants Chemical engineering is the branch of engineering that deals with the application of physical science (e. ... Survival analysis is a branch of statistics which deals with death in biological organisms and failure in mechanical systems. ... Reliability engineering is an engineering field, that deals with the study of reliability: the ability of a system or component to perform its required functions under stated conditions for a specified period of time. ... Statistics are very important to baseball, perhaps as much as they are for cricket, and more than almost any other sport. ... 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. ...


Statistical computing

The rapid and sustained increases in computing power starting from the second half of the 20th century have had a substantial impact on the practice of statistical science. Early statistical models were almost always from the class of linear models, but powerful computers, coupled with suitable numerical algorithms, caused an increased interest in nonlinear models (especially neural networks and decision trees) as well as the creation of new types, such as generalised linear models and multilevel models. In statistics the linear model is given by where Y is an n×1 column vector of random variables, X is an n×p matrix of known (i. ... Flowcharts are often used to represent algorithms. ... dataset with approximating polynomials Nonlinear regression in statistics is the problem of fitting a model to multidimensional x,y data, where f is a nonlinear function of x with parameters θ. In general, there is no algebraic expression for the best-fitting parameters, as there is in linear regression. ... A neural network is an interconnected group of neurons. ... In operations research, specifically in decision analysis, a decision tree is a decision support tool that uses a graph or model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. ... In statistics, the generalized linear model (GLM) is a useful generalization of ordinary least squares regression. ... Multilevel models are known by several names: hierarchical models, nested models and split-plot designs. ...


Increased computing power has also led to the growing popularity of computationally-intensive methods based on resampling, such as permutation tests and the bootstrap, while techniques such as Gibbs sampling have made Bayesian methods more feasible. The computer revolution has implications for the future of statistics with new emphasis on "experimental" and "empirical" statistics. A large number of both general and special purpose statistical software are now available. In statistics, resampling is any of a variety of methods for doing one of the following: Estimating the precision of sample statistics (medians, variances, percentiles) by using subsets of available data (jackknife) or drawing randomly with replacement from a set of data points (bootstrapping) Exchanging labels on data points when... It has been suggested that this article or section be merged with Bootstrap (statistics). ... In mathematics and physics, Gibbs sampling is an algorithm to generate a sequence of samples from the joint probability distribution of two or more random variables. ... This is an incomplete list of software that is designed for the explicit purpose of performing statistical analyses. ...


Misuse

Main article: Misuse of statistics

There is a general perception that statistical knowledge is all-too-frequently intentionally misused by finding ways to interpret only the data that are favorable to the presenter. A famous saying attributed to Benjamin Disraeli is, "There are three kinds of lies: lies, damned lies, and statistics"; and Harvard President Lawrence Lowell wrote in 1909 that statistics, "like veal pies, are good if you know the person that made them, and are sure of the ingredients". A misuse of statistics occurs when a statistical argument asserts a falsehood. ... A misuse of statistics occurs when a statistical argument asserts a falsehood. ... Benjamin Disraeli, 1st Earl of Beaconsfield (December 21, 1804 - April 24, British Conservative Prime Minister of the United Kingdom and author. ... This well-known saying is part of a phrase attributed to Benjamin Disraeli and popularized in the U.S. by Mark Twain: There are three kinds of lies: lies, damned lies, and statistics. ... Abbott Lawrence Lowell (January 1, 1856–January 6, 1943), an educator, historian and Boston Brahmin, was the President of Harvard University from 1909 to 1933. ...


If various studies appear to contradict one another, then the public may come to distrust such studies. For example, one study may suggest that a given diet or activity raises blood pressure, while another may suggest that it lowers blood pressure. The discrepancy can arise from subtle variations in experimental design, such as differences in the patient groups or research protocols, that are not easily understood by the non-expert. (Media reports sometimes omit this vital contextual information entirely.) A sphygmomanometer, a device used for measuring arterial pressure. ...


By choosing (or rejecting, or modifying) a certain sample, results can be manipulated. Such manipulations need not be malicious or devious; they can arise from unintentional biases of the researcher. The graphs used to summarize data can also be misleading.


Deeper criticisms come from the fact that the hypothesis testing approach, widely used and in many cases required by law or regulation, forces one hypothesis (the null hypothesis) to be "favored", and can also seem to exaggerate the importance of minor differences in large studies. A difference that is highly statistically significant can still be of no practical significance. (See criticism of hypothesis testing and controversy over the null hypothesis.) In statistics, a null hypothesis is a hypothesis set up to be nullified or refuted in order to support an alternative hypothesis. ... 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. ... In statistics, a null hypothesis is a hypothesis set up to be nullified or refuted in order to support an alternative hypothesis. ...


One response is by giving a greater emphasis on the p-value than simply reporting whether a hypothesis is rejected at the given level of significance. The p-value, however, does not indicate the size of the effect. Another increasingly common approach is to report confidence intervals. Although these are produced from the same calculations as those of hypothesis tests or p-values, they describe both the size of the effect and the uncertainty surrounding it. In statistical hypothesis testing, the p-value of a random variable T used as a test statistic is the probability that T will assume a value at least as extreme as the observed value tobserved, given that a null hypothesis being considered is true. ... In statistics, a confidence interval (CI) is an interval estimate of a population parameter. ...


See also

Statistics is a mathematical science pertaining to the collection, analysis, interpretation, and presentation of data. ... Please add any Wikipedia articles related to statistics that are not already on this list. ... List of associations and societies American Statistical Association Belgian Statistical Society Danish Society For Theoretical Statistics Finnish Statistical Society French Statistical Society German Statistical Society Hong Kong Statistical Society Indian Statistical Institute Institute of Mathematical Statistics International Association for Statistical Education International Biometric Society International Chinese Statistical Association International Environmetrics... 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. ... // Probability The Doctrine of Chances Author: Abraham de Moivre Publication data: 1738 (2nd ed. ... Statisticians or people who made notable contributions to the theories of statistics, or related aspects of probability, or machine learning: // Odd Olai Aalen (1947–) Gottfried Achenwall (1719–1772) Abraham Manie Adelstein (1916–1992) John Aitchison (1926–) Alexander Aitken (1895–1967) Hirotsugu Akaike (1927–) Oskar Anderson (1887–1960) Peter Armitage (1924... Terms in statistics and probability theory : Concerned fields Probability theory Algebra of random variables (linear algebra) Statistics Measure theory Estimation theory Probability interpretations: Bayesian probability (or personal probability) Frequency probability Eclectic probability Glossary Atomic event : another name for elementary event. ... Look up forecast in Wiktionary, the free dictionary. ... Multivariate statistics or multivariate statistical analysis in statistics describes a collection of procedures which involve observation and analysis of more than one statistical variable at a time. ... In statistics, regression analysis examines the relation of a dependent variable (response variable) to specified independent variables (explanatory variables). ... This is not an attempt at a comprehensive list of statistical topics; see that article. ... Statisticians are mathematicians who work with theoretical and applied statistics in the both the private and public sectors. ... Structural equation modeling (SEM) is a statistical technique for building and testing statistical models, which are sometimes called causal models. ...

Bibliography

  • Best, Joel (2001). Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists. University of California Press. ISBN 0-520-21978-3. 
  • Desrosières, Alain (2004). The Politics of Large Numbers: A History of Statistical Reasoning, Trans. Camille Naish, Harvard University Press. ISBN 0-674-68932-1. 
  • Hacking, Ian (1990). The Taming of Chance. Cambridge University Press. ISBN 0-521-38884-8. 
  • Hand, David J. (1998). "Breaking Misconceptions—Statistics and Its Relationship to Mathematics". The Statistician 47: 245-250. 
  • Hogg, Robert (2006). Probability and Statistical Inference, 7th ed., Pearson. ISBN 0-13-146413-2. 
  • Lindley, D.V. (1985). Making Decisions, 2nd ed., John Wiley & Sons. ISBN 0-471-90808-8. 
  • Tijms, Henk (2004). Understanding Probability: Chance Rules in Everyday life. Cambridge University Press. ISBN 0-521-83329-9. 

Alain Desrosières is a statistician at the INSEE and a sociologist and historian at the EHESS (France), well-know for his work in the history of statistics. ... Ian Hacking, CC (born 1936 in Vancouver) is a philosopher, specializing in the philosophy of science. ... Dennis Victor Lindley born 25 July 1923 is a noted British statistician, decision theorist and leading advocate of Bayesian statistics. ...

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Descriptive statistics are used to describe the basic features of the data in a study. ... This article is about mathematical mean. ... In mathematics and statistics, the arithmetic mean (or simply the mean) of a list of numbers is the sum of all the members of the list divided by the number of items in the list. ... The geometric mean of a collection of positive data is defined as the nth root of the product of all the members of the data set, where n is the number of members. ... This article is about the statistical concept. ... In statistics, mode means the most frequent value assumed by a random variable, or occurring in a sampling of a random variable. ... Look up range in Wiktionary, the free dictionary. ... This article is about mathematics. ... In probability and statistics, the standard deviation of a probability distribution, random variable, or population or multiset of values is a measure of the spread of its values. ... It has been suggested that this article or section be merged with inferential statistics. ... 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. ... In statistics, a result is called statistically significant if it is unlikely to have occurred by chance. ... The power of a statistical test is the probability that the test will reject a false null hypothesis (that it will not make a Type II error). ... In statistics, a null hypothesis is a hypothesis set up to be nullified or refuted in order to support an alternative hypothesis. ... In statistics, the Alternative Hypothesis is the hypothesis proposed to explain a statistically significant difference between results, that is if the Null Hypothesis has been rejected. ... Type I errors (or α error, or false positive) and type II errors (β error, or a false negative) are two terms used to describe statistical errors. ... The Z-test is a statistical test used in inference. ... A t-test is any statistical hypothesis test in which the test statistic has a Students t distribution if the null hypothesis is true. ... Maximum likelihood estimation (MLE) is a popular statistical method used to make inferences about parameters of the underlying probability distribution from a given data set. ... Compares the various grading methods in a normal distribution. ... In statistical hypothesis testing, the p-value of a random variable T used as a test statistic is the probability that T will assume a value at least as extreme as the observed value tobserved, given that a null hypothesis being considered is true. ... 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. ... A meta-analysis is a statistical practice of combining the results of a number of studies. ... Survival analysis is a branch of statistics which deals with death in biological organisms and failure in mechanical systems. ... The survival function, also known as a survivor function or reliability function, is a property of any random variable that maps a set of events, usually associated with mortality or failure of some system, onto time. ... The Kaplan-Meier estimator (also known as the Product Limit Estimator) estimates the survival function from life-time data. ... The logrank test (sometimes called the Mantel-Haenszel test or the Mantel-Cox test) [1] is a hypothesis test to compare the survival distributions of two samples. ... Failure rate is the frequency with which an engineered system or component fails, expressed for example in failures per hour. ... // Proportional hazards models are a sub-class of survival models in statistics. ... Several sets of (x, y) points, with the correlation coefficient of x and y for each set. ... In statistics, a spurious relationship (or, sometimes, spurious correlation) is a mathematical relationship in which two occurrences have no logical connection, yet it may be implied that they do, due to a certain third, unseen factor (referred to as a confounding factor or lurking variable). The spurious relationship gives an... In statistics, the Pearson product-moment correlation coefficient (sometimes known as the PMCC) (r) is a measure of the correlation of two variables X and Y measured on the same object or organism, that is, a measure of the tendency of the variables to increase or decrease together. ... In statistics, rank correlation is the study of relationships between different rankings on the same set of items. ... In statistics, Spearmans rank correlation coefficient, named after Charles Spearman and often denoted by the Greek letter (rho) or as , is a non-parametric measure of correlation – that is, it assesses how well an arbitrary monotonic function could describe the relationship between two variables, without making any assumptions about... The Kendall tau rank correlation coefficient (or simply the Kendall tau coefficient, Kendalls Ï„ or Tau test(s)) is used to measure the degree of correspondence between two rankings and assessing the significance of this correspondence. ... In statistics, regression analysis examines the relation of a dependent variable (response variable) to specified independent variables (explanatory variables). ... In statistics, linear regression is a regression method that models the relationship between a dependent variable Y, independent variables Xi, i = 1, ..., p, and a random term ε. The model can be written as Example of linear regression with one dependent and one independent variable. ... dataset with approximating polynomials Nonlinear regression in statistics is the problem of fitting a model to multidimensional x,y data, where f is a nonlinear function of x with parameters θ. In general, there is no algebraic expression for the best-fitting parameters, as there is in linear regression. ... Logistic regression is a statistical regression model for Bernoulli-distributed dependent variables. ...

  Results from FactBites:
 
WIN - Statistics (2822 words)
To understand these statistics, it is necessary to know how overweight and obesity are defined and measured, something this publication addresses.
For age-adjusted rates, statistical procedures are used to remove the effect of age differences when comparing two or more populations at one point in time, or one population at two or more points in time.
Most of the statistics presented here represent the economic cost of overweight and obesity in the United States in 1995, updated to 2001 dollars.[10] Unless otherwise noted, these statistics are adapted from Wolf and Colditz,[11] who based their data on existing epidemiological studies that defined overweight and obesity as a BMI > 29.
Statistics - MSN Encarta (1432 words)
Simple forms of statistics have been used since the beginning of civilization, when pictorial representations or other symbols were used to record numbers of people, animals, and inanimate objects on skins, slabs, or sticks of wood and the walls of caves.
Registration of deaths and births was begun in England in the early 16th century, and in 1662 the first noteworthy statistical study of population, Observations on the London Bills of Mortality, was written.
At present, statistics is a reliable means of describing accurately the values of economic, political, social, psychological, biological, and physical data and serves as a tool to correlate and analyze such data.
  More results at FactBites »

 
 

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