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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. It is a theory of testing based on the relationship between individuals’ performances on a test item and the test takers’ levels of performance on an overall measure of the ability that item was designed to measure. Several different statistical models are used to represent both item and test taker characteristics.[1] Unlike simpler alternatives for creating scales and evaluating questionnaire responses, it does not assume that each item is equally difficult
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Certification
Certification
Certification
refers to the confirmation of certain characteristics of an object, person, or organization. This confirmation is often, but not always, provided by some form of external review, education, assessment, or audit. Accreditation is a specific organization's process of certification. According to the National Council on Measurement in Education, a certification test is a credentialing test used to determine whether individuals are knowledgeable enough in a given occupational area to be labeled "competent to practice" in that area.[1]Contents1 Types 2 Third-party certification 3 In software testing 4 References 5 External linksTypes[edit] One of the most common types of certification in modern society is professional certification, where a person is certified as being able to competently complete a job or task, usually by the passing of an examination and/or the completion of a program of study
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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
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Test (student 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).[1] A test may be administered verbally, on paper, on a computer, or in a confined area that requires a test taker to physically perform a set of skills. Tests vary in style, rigor and requirements. For example, in a closed book test, a test taker is often required to rely upon memory to respond to specific items whereas in an open book test, a test taker may use one or more supplementary tools such as a reference book or calculator when responding to an item. A test may be administered formally or informally. An example of an informal test would be a reading test administered by a parent to a child. An example of a formal test would be a final examination administered by a teacher in a classroom or an I.Q. test administered by a psychologist in a clinic
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Local Independence
Local independence is the underlying assumption of latent variable models. The observed items are conditionally independent of each other given an individual score on the latent variable(s). This means that the latent variable explains why the observed items are related to another. This can be explained by the following example.Contents1 Example 2 See also 3 References 4 Further reading 5 External linksExample[edit] Local independence can be explained by an example of Lazarsfeld and Henry (1968). Suppose that a sample of 1000 people was asked whether they read journals A and B. Their responses were as follows:Read A Did not read A TotalRead B 260 140 400Did not read B 240 360 600Total 500 500 1000One can easily see that the two variables (reading A and reading B) are strongly related, and thus dependent on each other. Readers of A tend to read B more often (52%) than non-readers of A (28%)
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Mean
In mathematics, mean has several different definitions depending on the context. In probability and statistics, population mean and expected value are used synonymously to refer to one measure of the central tendency either of a probability distribution or of the random variable characterized by that distribution.[1] In the case of a discrete probability distribution of a random variable X, the mean is equal to the sum over every possible value weighted by the probability of that value; that is, it is computed by taking the product of each possible value x of X and its probability P(x), and then adding all these products together, giving μ = ∑ x P ( x ) displaystyle mu =sum xP(x) .[2] An analogous formula applies to the case of a continuous probability distribution
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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.[1] A low standard deviation indicates that the data points tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values. The standard deviation of a random variable, statistical population, data set, or probability distribution is the square root of its variance. It is algebraically simpler, though in practice less robust, than the average absolute deviation.[2][3] A useful property of the standard deviation is that, unlike the variance, it is expressed in the same units as the data
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Logit
The logit (/ˈloʊdʒɪt/ LOH-jit) function is the inverse of the sigmoidal "logistic" function or logistic transform used in mathematics, especially in statistics
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Odds
Odds are a numerical expression, usually expressed as a pair of numbers, used in both gambling and statistics. In statistics, the odds for or odds of some event reflect the likelihood that the event will take place, while odds against reflect the likelihood that it will not. In gambling, the odds are the ratio of payoff to stake, and do not necessarily reflect exactly the probabilities. Odds are expressed in several ways (see below), and sometimes the term is used incorrectly to mean simply the probability of an event.[1][2] Conventionally, gambling odds are expressed in the form "X to Y", where X and Y are numbers, and it is implied that the odds are odds against the event on which the gambler is considering wagering
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Orthogonal
In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms. Two elements u and v of a vector space with bilinear form B are orthogonal when B(u, v) = 0. Depending on the bilinear form, the vector space may contain nonzero self-orthogonal vectors. In the case of function spaces, families of orthogonal functions are used to form a basis. By extension, orthogonality is also used to refer to the separation of specific features of a system
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Ogive (statistics)
In statistics, an ogive is a free-hand graph showing the curve of a cumulative distribution function.[1] The points plotted are the upper class limit and the corresponding cumulative frequency.[2] (which, for the normal distribution, resembles one side of an Arabesque or ogival arch). The term can also be used to refer to the empirical cumulative distribution function. References[edit]^ Black, Ken (2009). Business Statistics: Contemporary Decision Making. John Wiley & Sons. p. 24.  ^ Everitt, B.S. (2002). The Cambridge Dictionary of Statistics
Statistics
(2nd ed.)
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Cumulative Normal
In probability theory, the normal (or Gaussian or Gauss or Laplace-Gauss) distribution is a very common continuous probability distribution. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known.[1][2] A random variable with a Gaussian distribution
Gaussian distribution
is said to be normally distributed and is called a normal deviate. The normal distribution is useful because of the central limit theorem. In its most general form, under some conditions (which include finite variance), it states that averages of samples of observations of random variables independently drawn from independent distributions converge in distribution to the normal, that is, become normally distributed when the number of observations is sufficiently large
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Benjamin Drake Wright
Benjamin Drake Wright
Benjamin Drake Wright
(March 30, 1926 – October 25, 2015) was an American psychometrician. He is largely responsible for the widespread adoption of Georg Rasch's measurement principles and models.[1] In the wake of what Rasch referred to as Wright's “almost unbelievable activity in this field”[1] in the period from 1960 to 1972, Rasch's ideas entered the mainstream in high-stakes testing, professional certification and licensure examinations, and in research employing tests, and surveys and assessments across a range of fields
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Ogive
An ogive (/ˈoʊdʒaɪv/ OH-jyve) is the roundly tapered end of a two-dimensional or three-dimensional object
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Confirmation Bias
Confirmation bias, also called confirmatory bias or myside bias,[Note 1] is the tendency to search for, interpret, favor, and recall information in a way that confirms one's preexisting beliefs or hypotheses.[1] It is a type of cognitive bias and a systematic error of inductive reasoning. People display this bias when they gather or remember information selectively, or when they interpret it in a biased way. The effect is stronger for emotionally charged issues and for deeply entrenched beliefs. Confirmation bias
Confirmation bias
is a variation of the more general tendency of apophenia. People also tend to interpret ambiguous evidence as supporting their existing position
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Chi-square Statistic
Pearson's chi-squared test
Pearson's chi-squared test
(χ2) 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. It is suitable for unpaired data from large samples.[1] It is the most widely used of many chi-squared tests (e.g., Yates, likelihood ratio, portmanteau test in time series, etc.) – statistical procedures whose results are evaluated by reference to the chi-squared distribution. Its properties were first investigated by Karl Pearson
Karl Pearson
in 1900.[2] In contexts where it is important to improve a distinction between the test statistic and its distribution, names similar to Pearson χ-squared test or statistic are used. It tests a null hypothesis stating that the frequency distribution of certain events observed in a sample is consistent with a particular theoretical distribution
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