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Shapiro–Francia Test
The Shapiro–Francia test is a Normality test, statistical test for the normality of a population, based on sample data. It was introduced by Samuel Sanford Shapiro, S. S. Shapiro and R. S. Francia in 1972 as a simplification of the Shapiro–Wilk test. Theory Let x_ be the i-th ordered value from our size-n sample. For example, if the sample consists of the values \left\, x_ = 3.4, because that is the second-lowest value. Let m_ be the mean of the ith order statistic when making n independent draws from a normal distribution. For example, m_ \approx -0.297, meaning that the second-lowest value in a sample of four draws from a normal distribution is typically about 0.297 standard deviations below the mean. Form the Pearson correlation coefficient between the x and the m: :W' = \frac = \frac Under the null hypothesis that the data is drawn from a normal distribution, this correlation will be strong, so W' values will cluster just under 1, with the peak becoming narrower and cl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normality Test
In statistics, normality tests are used to determine if a data set is well-modeled by a normal distribution and to compute how likely it is for a random variable underlying the data set to be normally distributed. More precisely, the tests are a form of model selection, and can be interpreted several ways, depending on one's interpretations of probability: * In descriptive statistics terms, one measures a goodness of fit of a normal model to the data – if the fit is poor then the data are not well modeled in that respect by a normal distribution, without making a judgment on any underlying variable. * In frequentist statistics statistical hypothesis testing, data are tested against the null hypothesis that it is normally distributed. * In Bayesian statistics, one does not "test normality" per se, but rather computes the likelihood that the data come from a normal distribution with given parameters ''μ'',''σ'' (for all ''μ'',''σ''), and compares that with the likelihood that t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Q–Q Plot
In statistics, a Q–Q plot (quantile-quantile plot) is a probability plot, a graphical method for comparing two probability distributions by plotting their '' quantiles'' against each other. A point on the plot corresponds to one of the quantiles of the second distribution (-coordinate) plotted against the same quantile of the first distribution (-coordinate). This defines a parametric curve where the parameter is the index of the quantile interval. If the two distributions being compared are similar, the points in the Q–Q plot will approximately lie on the identity line . If the distributions are linearly related, the points in the Q–Q plot will approximately lie on a line, but not necessarily on the line . Q–Q plots can also be used as a graphical means of estimating parameters in a location-scale family of distributions. A Q–Q plot is used to compare the shapes of distributions, providing a graphical view of how properties such as location, scale, and skewn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of The Punjab
The University of the Punjab (Urdu, pnb, ), also referred to as Punjab University, is a public, research, coeducational higher education institution located in Lahore, Pakistan. Punjab University is the oldest public university in Pakistan. With multiple campuses in Gujranwala, Jhelum, and Khanspur, the university was formally established by the British Government after convening the first meeting for establishing higher education institutions in October 1882 at Simla. Punjab University was the fourth university to be established by the British colonial authorities in the subcontinent; the first three universities were established in other parts of British-ruled Subcontinent. There are 45,678 students (27,907 morning students, 16,552 evening students and 1,219 diploma students). The university has 13 faculties of which there are 83 academic departments, research centres, and institutes. Punjab University has ranked first among large-sized multiple faculty universities ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
College Of Statistical And Actuarial Sciences
College of Statistical and Actuarial Sciences is a constituent college of the University of the Punjab in Lahore Lahore ( ; pnb, ; ur, ) is the second most populous city in Pakistan after Karachi and 26th most populous city in the world, with a population of over 13 million. It is the capital of the province of Punjab where it is the largest .... History The subject of Statistics was introduced in 1941 in the University. The college was established as the Department of Statistics in 1950 by Dr. M. Zia ud Din. The department was raised to the status of an Institute in 1952 and renamed to its current name in 2007. References {{authority control University of the Punjab 1950 establishments in Pakistan Universities and colleges in Lahore ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Power
In statistics, the power of a binary hypothesis test is the probability that the test correctly rejects the null hypothesis (H_0) when a specific alternative hypothesis (H_1) is true. It is commonly denoted by 1-\beta, and represents the chances of a true positive detection conditional on the actual existence of an effect to detect. Statistical power ranges from 0 to 1, and as the power of a test increases, the probability \beta of making a type II error by wrongly failing to reject the null hypothesis decreases. Notation This article uses the following notation: * ''β'' = probability of a Type II error, known as a "false negative" * 1 − ''β'' = probability of a "true positive", i.e., correctly rejecting the null hypothesis. "1 − ''β''" is also known as the power of the test. * ''α'' = probability of a Type I error, known as a "false positive" * 1 − ''α'' = probability of a "true negative", i.e., correctly not rejecting the null hypothesis Description For a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Royal Statistical Society
The Royal Statistical Society (RSS) is an established statistical society. It has three main roles: a British learned society for statistics, a professional body for statisticians and a charity which promotes statistics for the public good. History The society was founded in 1834 as the Statistical Society of London, though a perhaps unrelated London Statistical Society was in existence at least as early as 1824. At that time there were many provincial statistics societies throughout Britain, but most have not survived. The Manchester Statistical Society (which is older than the LSS) is a notable exception. The associations were formed with the object of gathering information about society. The idea of statistics referred more to political knowledge rather than a series of methods. The members called themselves "statists" and the original aim was "...procuring, arranging and publishing facts to illustrate the condition and prospects of society" and the idea of interpre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monte Carlo Method
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution. In physics-related problems, Monte Carlo methods are useful for simulating systems with many coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model, interacting particle systems, McKean–Vlasov processes, kinetic models of gases). Other examples include modeling phenomena with significant uncertainty in inputs such as the calculation of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closed-form Expression
In mathematics, a closed-form expression is a mathematical expression that uses a finite number of standard operations. It may contain constants, variables, certain well-known operations (e.g., + − × ÷), and functions (e.g., ''n''th root, exponent, logarithm, trigonometric functions, and inverse hyperbolic functions), but usually no limit, differentiation, or integration. The set of operations and functions may vary with author and context. Example: roots of polynomials The solutions of any quadratic equation with complex coefficients can be expressed in closed form in terms of addition, subtraction, multiplication, division, and square root extraction, each of which is an elementary function. For example, the quadratic equation :ax^2+bx+c=0, is tractable since its solutions can be expressed as a closed-form expression, i.e. in terms of elementary functions: :x=\frac. Similarly, solutions of cubic and quartic (third and fourth degree) equations can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Null Hypothesis
In scientific research, the null hypothesis (often denoted ''H''0) is the claim that no difference or relationship exists between two sets of data or variables being analyzed. The null hypothesis is that any experimentally observed difference is due to chance alone, and an underlying causative relationship does not exist, hence the term "null". In addition to the null hypothesis, an alternative hypothesis is also developed, which claims that a relationship does exist between two variables. Basic definitions The ''null hypothesis'' and the ''alternative hypothesis'' are types of conjectures used in statistical tests, which are formal methods of reaching conclusions or making decisions on the basis of data. The hypotheses are conjectures about a statistical model of the population, which are based on a sample of the population. The tests are core elements of statistical inference, heavily used in the interpretation of scientific experimental data, to separate scientific claims ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Samuel Sanford Shapiro
Samuel Sanford Shapiro (born July 13, 1930) is an American statistician and engineer. He is a professor emeritus of statistics at Florida International University. He is known for his co-authorship of the Shapiro–Wilk test and the Shapiro–Francia test. A native of New York City, Shapiro graduated from City College of New York with a degree in statistics in 1952, and took an MS in industrial engineering at Columbia University in 1954. He briefly served as a statistician in the US Army Chemical Corps The Chemical Corps is the branch of the United States Army tasked with defending against chemical, biological, radiological, and nuclear ( CBRN) weapons. The Chemical Warfare Service was established on 28 June 1918, combining activities that unt ..., before earning a MS (1960) and PhD (1963) in statistics at Rutgers University. In 1972 he joined the faculty at Florida International University. In 1987 he was elected a Fellow of the American Statistical Association. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pearson Correlation Coefficient
In statistics, the Pearson correlation coefficient (PCC, pronounced ) ― also known as Pearson's ''r'', the Pearson product-moment correlation coefficient (PPMCC), the bivariate correlation, or colloquially simply as the correlation coefficient ― is a measure of linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations. As a simple example, one would expect the age and height of a sample of teenagers from a high school to have a Pearson correlation coefficient significantly greater than 0, but less than 1 (as 1 would represent an unrealistically perfect correlation). Naming and history It was developed by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Society For Industrial And Applied Mathematics
Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community. SIAM is the world's largest scientific society devoted to applied mathematics, and roughly two-thirds of its membership resides within the United States. Founded in 1951, the organization began holding annual national meetings in 1954, and now hosts conferences, publishes books and scholarly journals, and engages in advocacy in issues of interest to its membership. Members include engineers, scientists, and mathematicians, both those employed in academia and those working in industry. The society supports educational institutions promoting applied mathematics. SIAM is one of the four member organizations of the Joint Policy Board for Mathematics. Membership Membership is open to both individuals and organizations. By the end of its first full year of operation, SIAM had 130 me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
