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Item response theory

Index Item response theory

In psychometrics, item response theory (IRT) (also known as latent trait theory, strong true score theory, or modern mental test theory) is a paradigm for the design, analysis, and scoring of tests, questionnaires, and similar instruments measuring abilities, attitudes, or other variables. [1]

63 relations: Accuracy and precision, Additive map, Asymptote, Benjamin Drake Wright, Certification, Classical test theory, Computerized adaptive testing, Concept inventory, Confirmation bias, Correlation and dependence, Cronbach's alpha, Cumulative distribution function, Data, David Andrich, Differential item functioning, Educational Testing Service, Equating, Factor analysis, Fisher information, Frederic M. Lord, Function (mathematics), Georg Rasch, Google Books, Graduate Management Admission Test, Graduate Record Examinations, High-stakes testing, Intelligence, Karl Gustav Jöreskog, Likert scale, Local independence, Logistic function, Logit, Mathematical model, Mean, Measurement, Monotonic function, Multiple choice, Newton's method, Normal distribution, Observational error, Odds, Ogive, Ogive (statistics), Orthogonality, Parameter, Paul Lazarsfeld, Pearson's chi-squared test, Person-fit analysis, Personal computer, Point-biserial correlation coefficient, ..., Probability, Psychometrics, Questionnaire, Rasch model, Rating scale, Reliability (statistics), Scale (social sciences), Standard deviation, Standard error, Standardized test, Stata, Test (assessment), University of Illinois at Chicago. Expand index (13 more) »

Accuracy and precision

Precision is a description of random errors, a measure of statistical variability.

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Additive map

In algebra an additive map, Z-linear map or additive function is a function that preserves the addition operation: for every pair of elements and in the domain.

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Asymptote

In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity.

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Benjamin Drake Wright

Benjamin Drake Wright (March 30, 1926 – October 25, 2015) was an American psychometrician.

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Certification

Certification refers to the confirmation of certain characteristics of an object, person, or organization.

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Classical test theory

Classical test theory (CTT) is a body of related psychometric theory that predicts outcomes of psychological testing such as the difficulty of items or the ability of test-takers.

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Computerized adaptive testing

Computerized adaptive testing (CAT) is a form of computer-based test that adapts to the examinee's ability level.

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Concept inventory

A concept inventory is a criterion-referenced test designed to help determine whether a student has an accurate working knowledge of a specific set of concepts.

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Confirmation bias

Confirmation bias, also called confirmatory bias or myside bias,David Perkins, a professor and researcher at the Harvard Graduate School of Education, coined the term "myside bias" referring to a preference for "my" side of an issue.

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Correlation and dependence

In statistics, dependence or association is any statistical relationship, whether causal or not, between two random variables or bivariate data.

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Cronbach's alpha

In statistics (classical test theory), Cronbach's \alpha (alpha) is the trivial name used for tau-equivalent reliability (\rho_T)Cho (2016), https://dx.doi.org/10.1177/1094428116656239 as a (lowerbound) estimate of the reliability of a psychometric test.

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Cumulative distribution function

In probability theory and statistics, the cumulative distribution function (CDF, also cumulative density function) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. In the case of a continuous distribution, it gives the area under the probability density function from minus infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables.

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Data

Data is a set of values of qualitative or quantitative variables.

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David Andrich

David Andrich has made substantial contributions to quantitative social science including seminal work on the Polytomous Rasch model for measurement, which is used in the social sciences, in health and other areas.

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Differential item functioning

Differential item functioning (DIF) is a statistical characteristic of an item that shows the extent to which the item might be measuring different abilities for members of separate subgroups.

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Educational Testing Service

Educational Testing Service (ETS), founded in 1947, is the world's largest private nonprofit educational testing and assessment organization.

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Equating

Test equating traditionally refers to the statistical process of determining comparable scores on different forms of an exam.

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Factor analysis

Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors.

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Fisher information

In mathematical statistics, the Fisher information (sometimes simply called information) is a way of measuring the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X. Formally, it is the variance of the score, or the expected value of the observed information.

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Frederic M. Lord

Frederic Mather Lord (November 12, 1912 in Hanover, NH – February 5, 2000) was a psychometrician for Educational Testing Service.

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Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

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Georg Rasch

Georg Rasch (21 September 1901 – 19 October 1980) was a Danish mathematician, statistician, and psychometrician, most famous for the development of a class of measurement models known as Rasch models.

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Google Books

Google Books (previously known as Google Book Search and Google Print and by its codename Project Ocean) is a service from Google Inc. that searches the full text of books and magazines that Google has scanned, converted to text using optical character recognition (OCR), and stored in its digital database.

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Graduate Management Admission Test

The Graduate Management Admission Test (GMAT ()) is a computer adaptive test (CAT) intended to assess certain analytical, writing, quantitative, verbal, and reading skills in written English for use in admission to a graduate management program, such as an MBA.

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Graduate Record Examinations

The Graduate Record Examinations (GRE) is a standardized test that is an admissions requirement for most graduate schools in the United States.

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High-stakes testing

A high-stakes test is a test with important consequences for the test taker.

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Intelligence

Intelligence has been defined in many different ways to include the capacity for logic, understanding, self-awareness, learning, emotional knowledge, reasoning, planning, creativity, and problem solving.

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Karl Gustav Jöreskog

Karl Gustav Jöreskog (born 25 April 1935) is a Swedish statistician.

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Likert scale

A Likert scale (but more commonly pronounced) is a psychometric scale commonly involved in research that employs questionnaires.

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Local independence

Local independence is the underlying assumption of latent variable models.

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Logistic function

A logistic function or logistic curve is a common "S" shape (sigmoid curve), with equation: where.

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Logit

The logit function is the inverse of the sigmoidal "logistic" function or logistic transform used in mathematics, especially in statistics.

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Mathematical model

A mathematical model is a description of a system using mathematical concepts and language.

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Mean

In mathematics, mean has several different definitions depending on the context.

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Measurement

Measurement is the assignment of a number to a characteristic of an object or event, which can be compared with other objects or events.

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Monotonic function

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.

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Multiple choice

Multiple choice is a form of an objective assessment in which respondents are asked to select only correct answers out of the choices from a list.

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Newton's method

In numerical analysis, Newton's method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function.

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Normal distribution

In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution.

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Observational error

Observational error (or measurement error) is the difference between a measured value of a quantity and its true value.

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Odds

Odds are a numerical expression, usually expressed as a pair of numbers, used in both gambling and statistics.

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Ogive

An ogive is the roundly tapered end of a two-dimensional or three-dimensional object.

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Ogive (statistics)

In statistics, an ogive is a free-hand graph showing the curve of a cumulative distribution function.

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Orthogonality

In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms.

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Parameter

A parameter (from the Ancient Greek παρά, para: "beside", "subsidiary"; and μέτρον, metron: "measure"), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc.

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Paul Lazarsfeld

Paul Felix Lazarsfeld (February 13, 1901 – August 30, 1976) was an Austrian-American sociologist.

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Pearson's chi-squared test

Pearson's chi-squared test (χ) is a statistical test applied to sets of categorical data to evaluate how likely it is that any observed difference between the sets arose by chance.

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Person-fit analysis

Person-fit analysis is a technique for determining if the person's results on a given test are valid.

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Personal computer

A personal computer (PC) is a multi-purpose computer whose size, capabilities, and price make it feasible for individual use.

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Point-biserial correlation coefficient

The point biserial correlation coefficient (rpb) is a correlation coefficient used when one variable (e.g. Y) is dichotomous; Y can either be "naturally" dichotomous, like whether a coin lands heads or tails, or an artificially dichotomized variable.

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Probability

Probability is the measure of the likelihood that an event will occur.

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Psychometrics

Psychometrics is a field of study concerned with the theory and technique of psychological measurement.

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Questionnaire

A questionnaire is a research instrument consisting of a series of questions (or other types of prompts) for the purpose of gathering information from respondents.

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Rasch model

The Rasch model, named after Georg Rasch, is a psychometric model for analyzing categorical data, such as answers to questions on a reading assessment or questionnaire responses, as a function of the trade-off between (a) the respondent's abilities, attitudes, or personality traits and (b) the item difficulty.

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Rating scale

A rating scale is a set of categories designed to elicit information about a quantitative or a qualitative attribute.

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Reliability (statistics)

Reliability in statistics and psychometrics is the overall consistency of a measure.

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Scale (social sciences)

In the social sciences, scaling is the process of measuring or ordering entities with respect to quantitative attributes or traits.

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Standard deviation

In statistics, the standard deviation (SD, also represented by the Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values.

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Standard error

The standard error (SE) of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution or an estimate of that standard deviation.

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Standardized test

A standardized test is a test that is administered and scored in a consistent, or "standard", manner.

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Stata

Stata is a general-purpose statistical software package created in 1985 by StataCorp.

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Test (assessment)

A test or examination (informally, exam or evaluation) is an assessment intended to measure a test-taker's knowledge, skill, aptitude, physical fitness, or classification in many other topics (e.g., beliefs).

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University of Illinois at Chicago

The University of Illinois at Chicago (UIC) is a public research university located in Chicago, Illinois, United States.

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Item Response Theory, Item response, Item-response theory, Latent trait analysis, Latent trait theory.

References

[1] https://en.wikipedia.org/wiki/Item_response_theory

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