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Reduced Chi-squared Statistic
In statistics, the reduced chi-square statistic is used extensively in goodness of fit testing. It is also known as mean squared weighted deviation (MSWD) in isotopic dating and variance of unit weight in the context of weighted least squares. Its square root is called regression standard error, standard error of the regression, or standard error of the equation (see ) Definition It is defined as chi-square per degree of freedom: \chi^2_\nu = \frac \nu, where the chi-squared is a weighted sum of squared deviations: \chi^2 = \sum_ with inputs: variance \sigma_i^2, observations ''O'', and calculated data ''C''. The degree of freedom, \nu = n - m, equals the number of observations ''n'' minus the number of fitted parameters ''m''. In weighted least squares, the definition is often written in matrix notation as \chi^2_\nu = \frac, where ''r'' is the vector of residuals, and ''W'' is the weight matrix, the inverse of the input (diagonal) covariance matrix of observations. If ''W' ... [...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] |
Weighted Arithmetic Mean
The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of mathematics. If all the weights are equal, then the weighted mean is the same as the arithmetic mean. While weighted means generally behave in a similar fashion to arithmetic means, they do have a few counterintuitive properties, as captured for instance in Simpson's paradox. Examples Basic example Given two school with 20 students, one with 30 test grades in each class as follows: :Morning class = :Afternoon class = The mean for the morning class is 80 and the mean of the afternoon class is 90. The unweighted mean of the two means is 85. However, this does not account for the difference in numbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 the respondent's abilities, attitudes, or personality traits, and the item difficulty. For example, they may be used to estimate a student's reading ability or the extremity of a person's attitude to capital punishment from responses on a questionnaire. In addition to psychometrics and educational research, the Rasch model and its extensions are used in other areas, including the health profession, agriculture, and market research. The mathematical theory underlying Rasch models is a special case of item response theory. However, there are important differences in the interpretation of the model parameters and its philosophical implications that separate proponents of the Rasch model from the item response modeling tradition. A central aspect of this divide relates ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Deviation
In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its Expected value, mean. A low standard Deviation (statistics), deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. The standard deviation is commonly used in the determination of what constitutes an outlier and what does not. Standard deviation may be abbreviated SD or std dev, and is most commonly represented in mathematical texts and equations by the lowercase Greek alphabet, Greek letter Sigma, σ (sigma), for the population standard deviation, or the Latin script, Latin letter ''s'', for the sample standard deviation. The standard deviation of a random variable, Sample (statistics), sample, statistical population, data set, or probability distribution is the square root of its variance. (For a finite population, v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thorium
Thorium is a chemical element; it has symbol Th and atomic number 90. Thorium is a weakly radioactive light silver metal which tarnishes olive grey when it is exposed to air, forming thorium dioxide; it is moderately soft, malleable, and has a high melting point. Thorium is an electropositive actinide whose chemistry is dominated by the +4 oxidation state; it is quite reactive and can ignite in air when finely divided. All known thorium isotopes are unstable. The most stable isotope, 232Th, has a half-life of 14.05 billion years, or about the age of the universe; it decays very slowly via alpha decay, starting a decay chain named the thorium series that ends at stable 208 Pb. On Earth, thorium and uranium are the only elements with no stable or nearly-stable isotopes that still occur naturally in large quantities as primordial elements. Thorium is estimated to be over three times as abundant as uranium in the Earth's crust, and is chiefly refined from monazite sa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Helium
Helium (from ) is a chemical element; it has chemical symbol, symbol He and atomic number 2. It is a colorless, odorless, non-toxic, inert gas, inert, monatomic gas and the first in the noble gas group in the periodic table. Its boiling point is the lowest among all the Chemical element, elements, and it does not have a melting point at standard pressures. It is the second-lightest and second-most Abundance of the chemical elements, abundant element in the observable universe, after hydrogen. It is present at about 24% of the total elemental mass, which is more than 12 times the mass of all the heavier elements combined. Its abundance is similar to this in both the Sun and Jupiter, because of the very high nuclear binding energy (per nucleon) of helium-4 with respect to the next three elements after helium. This helium-4 binding energy also accounts for why it is a product of both nuclear fusion and radioactive decay. The most common isotope of helium in the universe is helium-4, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uranium
Uranium is a chemical element; it has chemical symbol, symbol U and atomic number 92. It is a silvery-grey metal in the actinide series of the periodic table. A uranium atom has 92 protons and 92 electrons, of which 6 are valence electrons. Uranium radioactive decay, radioactively decays, usually by emitting an alpha particle. The half-life of this decay varies between 159,200 and 4.5 billion years for different isotopes of uranium, isotopes, making them useful for dating the age of the Earth. The most common isotopes in natural uranium are uranium-238 (which has 146 neutrons and accounts for over 99% of uranium on Earth) and uranium-235 (which has 143 neutrons). Uranium has the highest atomic weight of the primordial nuclide, primordially occurring elements. Its density is about 70% higher than that of lead and slightly lower than that of gold or tungsten. It occurs naturally in low concentrations of a few Parts-per notation#Parts-per expressions, parts per million in soil, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Mean
In mathematics, the geometric mean is a mean or average which indicates a central tendency of a finite collection of positive real numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean of numbers is the Nth root, th root of their product (mathematics), product, i.e., for a collection of numbers , the geometric mean is defined as : \sqrt[n]. When the collection of numbers and their geometric mean are plotted in logarithmic scale, the geometric mean is transformed into an arithmetic mean, so the geometric mean can equivalently be calculated by taking the natural logarithm of each number, finding the arithmetic mean of the logarithms, and then returning the result to linear scale using the exponential function , :\sqrt[n] = \exp \left( \frac \right). The geometric mean of two numbers is the square root of their product, for example with numbers and the geometric mean is \textstyle \sqrt = The geometric mean o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic Mean
In mathematics and statistics, the arithmetic mean ( ), arithmetic average, or just the ''mean'' or ''average'' is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results from an experiment, an observational study, or a Survey (statistics), survey. The term "arithmetic mean" is preferred in some contexts in mathematics and statistics because it helps to distinguish it from other types of means, such as geometric mean, geometric and harmonic mean, harmonic. Arithmetic means are also frequently used in economics, anthropology, history, and almost every other academic field to some extent. For example, per capita income is the arithmetic average of the income of a nation's Human population, population. While the arithmetic mean is often used to report central tendency, central tendencies, it is not a robust statistic: it is greatly influenced by outliers (Value (mathematics), values much larger or smaller than ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Distribution
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f(x) = \frac e^\,. The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter \sigma^2 is the variance. The standard deviation of the distribution is (sigma). A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate. 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. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable—whose distribution c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Janet Hergt
Janet Margaret Hergt is an Australians, Australian Geochemistry, geochemist. She is a Redmond Barry Distinguished Professor in the School of Geography, Earth and Atmospheric Sciences at the University of Melbourne, Victoria (Australia), Victoria, Australia. The main focus of her research has been in the chemical analysis of Rock (geology), rocks and minerals to explore the exquisite record of Earth processes preserved within them. Hergt is best known for her Geochemistry, geochemical investigations of Igneous rock, magmatic rocks although she has employed similar techniques in Interdisciplinarity, interdisciplinary projects including areas of Archaeology, archaeological and Biological Science, biological science. Early life and education Hergt's earliest years were spent living on dairy farms in rural Victoria before moving to Frankston, Victoria, Frankston where she attended Karingal Primary School, and later Karingal High School. Hergt completed her undergraduate degree (BSc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geochronology
Geochronology is the science of Chronological dating, determining the age of rock (geology), rocks, fossils, and sediments using signatures inherent in the rocks themselves. Absolute geochronology can be accomplished through radioactive isotopes, whereas relative geochronology is provided by tools such as paleomagnetism and stable isotope ratios. By combining multiple geochronological (and biostratigraphic) indicators the precision of the recovered age can be improved. Geochronology is different in application from biostratigraphy, which is the science of assigning sedimentary rocks to a known geological period via describing, cataloging and comparing fossil floral and faunal assemblages. Biostratigraphy does not ''directly'' provide an absolute age determination of a rock, but merely places it within an ''interval'' of time at which that fossil assemblage is known to have coexisted. Both disciplines work together hand in hand, however, to the point where they share the same syste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
