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Bennett, Alpert, And Goldstein’s S
Bennett, Alpert & Goldstein’s ''S'' is a statistical measure of inter-rater agreement. It was created by Bennett ''et al.'' in 1954. Rationale for use Bennett ''et al.'' suggested adjusting inter-rater reliability to accommodate the percentage of rater agreement that might be expected by chance was a better measure than simple agreement between raters. They proposed an index which adjusted the proportion of rater agreement based on the number of categories employed. Mathematical formulation The formula for ''S'' is : S = \frac where ''Q'' is the number of categories and ''P''a is the proportion of agreement between raters. The variance In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance. Variance is a measure of dispersion ... of ''S'' is : \operatorname(S) = \left( \frac \right)^2 \frac Notes This stat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inter-rater Agreement
In statistics, inter-rater reliability (also called by various similar names, such as inter-rater agreement, inter-rater concordance, inter-observer reliability, inter-coder reliability, and so on) is the degree of agreement among independent observers who rate, code, or assess the same phenomenon. Assessment tools that rely on ratings must exhibit good inter-rater reliability, otherwise they are not valid tests. There are a number of statistics that can be used to determine inter-rater reliability. Different statistics are appropriate for different types of measurement. Some options are joint-probability of agreement, such as Cohen's kappa, Scott's pi and Fleiss' kappa; or inter-rater correlation, concordance correlation coefficient, intra-class correlation, and Krippendorff's alpha. Concept There are several operational definitions of "inter-rater reliability," reflecting different viewpoints about what is a reliable agreement between raters. There are three operational defin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Percentage
In mathematics, a percentage () is a number or ratio expressed as a fraction (mathematics), fraction of 100. It is often Denotation, denoted using the ''percent sign'' (%), although the abbreviations ''pct.'', ''pct'', and sometimes ''pc'' are also used. A percentage is a dimensionless quantity, dimensionless number (pure number), primarily used for expressing proportions, but percent is nonetheless a unit of measurement in its orthography and usage. Examples For example, 45% (read as "forty-five percent") is equal to the fraction , or 0.45. Percentages are often used to express a proportionate part of a total. (Similarly, one can also express a number as a fraction of 1,000, using the term "per mille" or the symbol "".) Example 1 If 50% of the total number of students in the class are male, that means that 50 out of every 100 students are male. If there are 500 students, then 250 of them are male. Example 2 An increase of $0.15 on a price of $2.50 is an increase by a fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proportionality (mathematics)
In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio. The ratio is called ''coefficient of proportionality'' (or ''proportionality constant'') and its reciprocal is known as ''constant of normalization'' (or ''normalizing constant''). Two sequences are inversely proportional if corresponding elements have a constant product. Two functions f(x) and g(x) are ''proportional'' if their ratio \frac is a constant function. If several pairs of variables share the same direct proportionality constant, the equation expressing the equality of these ratios is called a proportion, e.g., (for details see Ratio). Proportionality is closely related to ''linearity''. Direct proportionality Given an independent variable ''x'' and a dependent variable ''y'', ''y'' is directly proportional to ''x'' if there is a positive constant ''k'' such that: : y = kx The relation is oft ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Formula
In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a ''chemical formula''. The informal use of the term ''formula'' in science refers to the general construct of a relationship between given quantities. The plural of ''formula'' can be either ''formulas'' (from the most common English plural noun form) or, under the influence of scientific Latin, ''formulae'' (from the original Latin). In mathematics In mathematics, a formula generally refers to an equation or inequality relating one mathematical expression to another, with the most important ones being mathematical theorems. For example, determining the volume of a sphere requires a significant amount of integral calculus or its geometrical analogue, the method of exhaustion. However, having done this once in terms of some parameter (the radius for example), mathematicians have produced a formula to describe the volume of a sphere in terms of its radius: : V ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variance
In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. It is the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by \sigma^2, s^2, \operatorname(X), V(X), or \mathbb(X). An advantage of variance as a measure of dispersion is that it is more amenable to algebraic manipulation than other measures of dispersion such as the expected absolute deviation; for example, the variance of a sum of uncorrelated random variables is equal to the sum of their variances. A disadvantage of the variance for practical applications is that, unlike the standard deviation, its units differ from the random variable, which is why the standard devi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Categorical Variable Interactions
Categorical may refer to: * Categorical imperative, a concept in philosophy developed by Immanuel Kant * Categorical theory, in mathematical logic * Morley's categoricity theorem, a mathematical theorem in model theory * Categorical data analysis * Categorical distribution, a probability distribution * Categorical logic, a branch of category theory within mathematics with notable connections to theoretical computer science * Categorical syllogism, a kind of logical argument * Categorical proposition, a part of deductive reasoning * Categorization * Categorical perception * Category theory in mathematics ** Categorical set theory Categorical set theory is any one of several versions of set theory developed from or treated in the context of mathematical category theory. See also * Categorical logic __NOTOC__ Categorical logic is the branch of mathematics in which tools ... ** Categorical probability * Recursive categorical syntax in linguistics See also * Category (disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
