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Statistical Regions Of Slovenia
Statistics
Statistics
is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.[1][2] In applying statistics to, for example, a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model process to be studied. Populations can be diverse topics such as "all people living in a country" or "every atom composing a crystal". Statistics
Statistics
deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments.[1] See glossary of probability and statistics. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole
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Statistics (other)
Statistics
Statistics
is a mathematical science pertaining to the collection, analysis, interpretation, and presentation of data. Statistic may also refer to:Statistic, the result of applying a statistical algorithm to a set of data Statistic
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Linear Algebra
Linear
Linear
algebra is the branch of mathematics concerning linear equations such as a 1 x 1 + ⋯ + a n x n = b , displaystyle a_ 1 x_ 1 +cdots +a_ n x_ n =b, linear functions such as ( x 1 , … , x n ) ↦ a 1 x 1 + … + a n x n , displaystyle (x_ 1 ,ldots ,x_ n )mapsto a_ 1 x_ 1 +ldots +a_ n x_ n , and their representations through matrices and vector spaces.[1][2][3] Linear
Linear
algebra is central to almost all areas of mathematics
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Null Hypothesis
In inferential statistics, the term "null hypothesis" is a general statement or default position that there is no relationship between two measured phenomena, or no association among groups.[1] Rejecting or disproving the null hypothesis—and thus concluding that there are grounds for believing that there is a relationship between two phenomena (e.g. that a potential treatment has a measurable effect)—is a central task in the modern practice of science; the field of statistics gives precise criteria for rejecting a null hypothesis[citation needed]. The null hypothesis is generally assumed to be true until evidence indicates otherwise. In statistics, it is often denoted H0 (read “H-nought”, "H-null", "H-oh", or "H-zero"). The concept of a null hypothesis is used differently in two approaches to statistical inference
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Type I Error
In statistical hypothesis testing, a type I error is the incorrect rejection of a true null hypothesis (also known as a "false positive" finding), while a type II error is incorrectly retaining a false null hypothesis (also known as a "false negative" finding).[1] More simply stated, a type I error is to falsely infer the existence of something that is not there, while a type II error is to falsely infer the absence of something that is.Contents1 Definition 2 Statistical test theory2.1 Type I error 2.2 Type II error 2.3 Table of error types3 Examples3.1 Example 1 3.2 Example 2 3.3 Example 3 3.4 Example 44 Etymology 5 Related terms5.1 Null hypothesis 5.2 Statistical significance6 Application domains6.1 Inventory control 6.2 Computers6.
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Type II Error
In statistical hypothesis testing, a type I error is the incorrect rejection of a true null hypothesis (also known as a "false positive" finding), while a type II error is incorrectly retaining a false null hypothesis (also known as a "false negative" finding).[1] More simply stated, a type I error is to falsely infer the existence of something that is not there, while a type II error is to falsely infer the absence of something that is.Contents1 Definition 2 Statistical test theory2.1 Type I error 2.2 Type II error 2.3 Table of error types3 Examples3.1 Example 1 3.2 Example 2 3.3 Example 3 3.4 Example 44 Etymology 5 Related terms5.1 Null hypothesis 5.2 Statistical significance6 Application domains6.1 Inventory control 6.2 Computers6.
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Bias (statistics)
Statistical bias is a feature of a statistical technique or of its results whereby the expected value of the results differs from the true underlying quantitative parameter being estimated. Types[edit] A statistic is biased if it is calculated in such a way that it is systematically different from the population parameter being estimated. The following lists some types of biases, which can overlap. Selection bias involves individuals being more likely to be selected for study than others, biasing the sample
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Missing Data
In statistics, missing data, or missing values, occur when no data value is stored for the variable in an observation. Missing data
Missing data
are a common occurrence and can have a significant effect on the conclusions that can be drawn from the data. Missing data
Missing data
can occur because of nonresponse: no information is provided for one or more items or for a whole unit ("subject"). Some items are more likely to generate a nonresponse than others: for example items about private subjects such as income. Attrition ("Dropout") is a type of missingness that can occur in longitudinal studies - for instance studying development where a measurement is repeated after a certain period of time
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Censoring (statistics)
In statistics, engineering, economics, and medical research, censoring is a condition in which the value of a measurement or observation is only partially known. For example, suppose a study is conducted to measure the impact of a drug on mortality rate. In such a study, it may be known that an individual's age at death is at least 75 years (but may be more). Such a situation could occur if the individual withdrew from the study at age 75, or if the individual is currently alive at the age of 75. Censoring also occurs when a value occurs outside the range of a measuring instrument. For example, a bathroom scale might only measure up to 300 pounds (140 kg)
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Calculus
Calculus
Calculus
(from Latin
Latin
calculus, literally 'small pebble', used for counting and calculations, as on an abacus)[1] is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. It has two major branches, differential calculus (concerning rates of change and slopes of curves),[2] and integral calculus (concerning accumulation of quantities and the areas under and between curves).[3] These two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. Generally, modern calculus is considered to have been developed in the 17th century by Isaac Newton and Gottfried Wilhelm Leibniz
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Arthur Lyon Bowley
Sir Arthur Lyon Bowley (Bristol, 6 November 1869 – Surrey, 21 January 1957) was an English statistician and economist[1] who worked on economic statistics and pioneered the use of sampling techniques in social surveys.Contents1 Early life 2 Academic career 3 Books 4 Honours 5 Personal life 6 Bowley's law 7 Main publications of A. L. Bowley 8 Discussions 9 See also 10 References 11 External linksEarly life[edit] Bowley's father, James William Lyon Bowley, was a minister in the Church of England. He died in 1870 when Arthur was under two, leaving Arthur's mother as mother or stepmother to seven children. Arthur was educated at a Christ's Hospital, and won a scholarship to Trinity College, Cambridge to study mathematics
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Mathematical Statistics
Mathematical statistics
Mathematical statistics
is the application of mathematics to statistics, which was originally conceived as the science of the state[citation needed] — the collection and analysis of facts about a country: its economy, land, military, population, and so on. Mathematical techniques which are used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure-theoretic probability theory.[1][2]Contents1 Introduction 2 Topics2.1
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Mathematical Analysis
Mathematical analysis
Mathematical analysis
is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.[1][2] These theories are usually studied in the context of real and complex numbers and functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis
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Stochastic Analysis
Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to stochastic processes
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Statistical Hypothesis Testing
A statistical hypothesis, sometimes called confirmatory data analysis, is a hypothesis that is testable on the basis of observing a process that is modeled via a set of random variables.[1] A statistical hypothesis test is a method of statistical inference. Commonly, two statistical data sets are compared, or a data set obtained by sampling is compared against a synthetic data set from an idealized model. A hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis that proposes no relationship between two data sets. The comparison is deemed statistically significant if the relationship between the data sets would be an unlikely realization of the null hypothesis according to a threshold probability—the significance level
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Differential Equations
A differential equation is a mathematical equation that relates some function with its derivatives. In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between the two. Because such relations are extremely common, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. In pure mathematics, differential equations are studied from several different perspectives, mostly concerned with their solutions—the set of functions that satisfy the equation. Only the simplest differential equations are solvable by explicit formulas; however, some properties of solutions of a given differential equation may be determined without finding their exact form. If a self-contained formula for the solution is not available, the solution may be numerically approximated using computers
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