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Rayleigh test : Circular distribution Directional statistics Kuiper's test Rayleigh distribution Watson test Rayleigh plot |
Rayleigh test : A test for the significance of the mean direction and the concentration parameter of a circular distribution. Rao's spacing test - contrasted with Rayleigh test |
Regression control chart : In statistical quality control, the regression control chart allows for monitoring a change in a process where two or more variables are correlated. The change in a dependent variable can be detected and compensatory change in the independent variable can be recommended. Examples from the Pos... |
Regression control chart : Regression control chart differs from a traditional control chart in four main aspects: It is designed to control a varying (rather than a constant) average. The control limit lines are parallel to the regression line rather than the horizontal line. The computations here are much more comple... |
Regression diagnostic : In statistics, a regression diagnostic is one of a set of procedures available for regression analysis that seek to assess the validity of a model in any of a number of different ways. This assessment may be an exploration of the model's underlying statistical assumptions, an examination of the ... |
Regression diagnostic : Regression diagnostics have often been developed or were initially proposed in the context of linear regression or, more particularly, ordinary least squares. This means that many formally defined diagnostics are only available for these contexts. |
Regression diagnostic : Distribution of model errors Normal probability plot Homoscedasticity Goldfeld–Quandt test Breusch–Pagan test Park test White test Correlation of model errors Breusch–Godfrey test |
Regression diagnostic : Adequacy of existing explanatory variables Partial residual plot Ramsey RESET test F test for use when there are replicated observations, so that a comparison can be made between the lack-of-fit sum of squares and the pure error sum of squares, under the assumption that model errors are homosced... |
Regression diagnostic : Outliers Influential observations Leverage (statistics), partial leverage DFFITS Cook's distance == References == |
Reification (statistics) : In statistics, reification is the use of an idealized model of a statistical process. The model is then used to make inferences connecting model results, which imperfectly represent the actual process, with experimental observations. Also, a process whereby model-derived quantities such as pr... |
Reification (statistics) : Everitt, B.S. (2002) Cambridge Dictionary of Statistics (2nd Edition), CUP. ISBN 0-521-81099-X |
Repeated median regression : In robust statistics, repeated median regression, also known as the repeated median estimator, is a robust linear regression algorithm. The estimator has a breakdown point of 50%. Although it is equivariant under scaling, or under linear transformations of either its explanatory variable or... |
Repeated median regression : The repeated median method estimates the slope of the regression line y = A + B x for a set of points ( X i , Y i ) ,Y_) as B ^ = median i median j ≠ i slope ( i , j ) = \ \ \operatorname (i,j) where slope ( i , j ) (i,j) is defined as ( Y j − Y i ) / ( X j − X i ) -Y_)/(X_-X_) . Th... |
Repeated median regression : Theil–Sen estimator == References == |
Researcher degrees of freedom : Researcher degrees of freedom is a concept referring to the inherent flexibility involved in the process of designing and conducting a scientific experiment, and in analyzing its results. The term reflects the fact that researchers can choose between multiple ways of collecting and analy... |
Researcher degrees of freedom : Steegen et al. (2016) showed how, starting from a single raw data set, applying different reasonable data processing decisions can give rise to a multitude of processed data sets (called the data multiverse), often leading to different statistical results. Wicherts et al. (2016) provided... |
Researcher degrees of freedom : Overfitting Multiverse analysis == References == |
Respondent error : In survey sampling, respondent error refers to any error introduced into the survey results due to respondents providing untrue or incorrect information. It is a type of systemic bias. Language and educational issues can lead to a misunderstanding of the question by the respondent, or similarly, a mi... |
Restricted maximum likelihood : In statistics, the restricted (or residual, or reduced) maximum likelihood (REML) approach is a particular form of maximum likelihood estimation that does not base estimates on a maximum likelihood fit of all the information, but instead uses a likelihood function calculated from a trans... |
Sammon mapping : Sammon mapping or Sammon projection is an algorithm that maps a high-dimensional space to a space of lower dimensionality (see multidimensional scaling) by trying to preserve the structure of inter-point distances in high-dimensional space in the lower-dimension projection. It is particularly suited fo... |
Sammon mapping : Prefrontal cortex basal ganglia working memory State–action–reward–state–action Constructing skill trees |
Sammon mapping : HiSee – an open-source visualizer for high dimensional data A C# based program with code on CodeProject. Matlab code and method introduction |
Sample ratio mismatch : In the design of experiments, a sample ratio mismatch (SRM) is a statistically significant difference between the expected and actual ratios of the sizes of treatment and control groups in an experiment. Sample ratio mismatches also known as unbalanced sampling often occur in online controlled e... |
Sample ratio mismatch : Suppose we run an A/B test in which we randomly assign 1000 users to equally sized treatment and control groups (a 50–50 split). The expected size of each group is 500. However, the actual sizes of the treatment and control groups are 600 and 400. Using Pearson's chi-squared goodness of fit test... |
Sampling fraction : In sampling theory, the sampling fraction is the ratio of sample size to population size or, in the context of stratified sampling, the ratio of the sample size to the size of the stratum. The formula for the sampling fraction is f = n N , , where n is the sample size and N is the population size. A... |
Sampling in order : In statistics, some Monte Carlo methods require independent observations in a sample to be drawn from a one-dimensional distribution in sorted order. In other words, all n order statistics are needed from the n observations in a sample. The naive method performs a sort and takes O(n log n) time. The... |
Sampling in order : Bentley, Jon Louis; Saxe, James B. (1979), "Generating sorted lists of random numbers", Computer Science Department, Paper 2450, retrieved January 4, 2014 Gerontidis, I.; Smith, R. L. (1982), "Monte Carlo Generation of Order Statistics from General Distributions", Journal of the Royal Statistical So... |
Saturated array : In experiments in which additional factors are not likely to interact with any of the other factors, a saturated array can be used. In a saturated array, a controllable factor is substituted for the interaction of two or more by-products. Using a saturated array, a two-factor test matrix could be used... |
Scagnostics : Scagnostics (scatterplot diagnostics) is a series of measures that characterize certain properties of a point cloud in a scatter plot. The term and idea was coined by John Tukey and Paul Tukey, though they didn't publish it; later it was elaborated by Wilkinson, Anand, and Grossman. The following nine dim... |
Scagnostics : Python library pyscagnostics R package scagnostics |
Scale analysis (statistics) : In statistics, scale analysis is a set of methods to analyze survey data, in which responses to questions are combined to measure a latent variable. These items can be dichotomous (e.g. yes/no, agree/disagree, correct/incorrect) or polytomous (e.g. disagree strongly/disagree/neutral/agree/... |
Scale analysis (statistics) : The item-total correlation approach is a way of identifying a group of questions whose responses can be combined into a single measure or scale. This is a simple approach that works by ensuring that, when considered across a whole population, responses to the questions in the group tend to... |
Scale analysis (statistics) : Measurement is the assignment of numbers to subjects in such a way that the relations between the objects are represented by the relations between the numbers (Michell, 1990). |
Scale analysis (statistics) : Michell, J (1990). An Introduction to the logic of Psychological Measurement. Hillsdales, NJ: Lawrences Erlbaum Associates Publ. |
Scan statistic : In statistics, a scan statistic or window statistic is a problem relating to the clustering of randomly positioned points. An example of a typical problem is the maximum size of a cluster of points on a line or the longest series of successes recorded by a moving window of fixed length. Joseph Naus fir... |
Scan statistic : SaTScan free software for the spatial, temporal and space-time scan statistics |
Scatter matrix : For the notion in quantum mechanics, see scattering matrix. In multivariate statistics and probability theory, the scatter matrix is a statistic that is used to make estimates of the covariance matrix, for instance of the multivariate normal distribution. |
Scatter matrix : Given n samples of m-dimensional data, represented as the m-by-n matrix, X = [ x 1 , x 2 , … , x n ] _,\mathbf _,\ldots ,\mathbf _] , the sample mean is x ¯ = 1 n ∑ j = 1 n x j =\sum _^\mathbf _ where x j _ is the j-th column of X . The scatter matrix is the m-by-m positive semi-definite matrix ... |
Scatter matrix : The maximum likelihood estimate, given n samples, for the covariance matrix of a multivariate normal distribution can be expressed as the normalized scatter matrix C M L = 1 n S . =S. When the columns of X are independently sampled from a multivariate normal distribution, then S has a Wishart distrib... |
Scatter matrix : Estimation of covariance matrices Sample covariance matrix Wishart distribution Outer product— X X ⊤ or X⊗X is the outer product of X with itself. Gram matrix == References == |
SCORUS : An acronym for "Standing Committee of Regional and Urban Statistics", SCORUS is a sub-committee of the International Association for Official Statistics (IAOS) which is a section of the International Statistical Institute. The sub-committee has specific responsibility for regional and urban statistics and rese... |
SCORUS : http://www.scorus.org == References == |
Sealedenvelope.com : Sealedenvelope.com is British collaboration that provides support services for clinical trials. They provide services such as randomization, allocation concealment, code-break services, and case report management through a web-based design. They also perform certain calculations such as power calcu... |
Sensitivity index : The sensitivity index or discriminability index or detectability index is a dimensionless statistic used in signal detection theory. A higher index indicates that the signal can be more readily detected. |
Sensitivity index : The discriminability index is the separation between the means of two distributions (typically the signal and the noise distributions), in units of the standard deviation. |
Sensitivity index : It has been shown that for two univariate normal distributions, d a ′ ≤ d e ′ ≤ d b ′ \leq d'_\leq d'_ , and for multivariate normal distributions, d a ′ ≤ d e ′ \leq d'_ still. Thus, d a ′ and d e ′ underestimate the maximum discriminability d b ′ of univariate normal distributions. d a ′ can u... |
Sensitivity index : In general, the contribution to the total discriminability by each dimension or feature may be measured using the amount by which the discriminability drops when that dimension is removed. If the total Bayes discriminability is d ′ and the Bayes discriminability with dimension i removed is d − i ′... |
Sensitivity index : We may sometimes want to scale the discriminability of two data distributions by moving them closer or farther apart. One such case is when we are modeling a detection or classification task, and the model performance exceeds that of the subject or observed data. In that case, we can move the model ... |
Sensitivity index : Receiver operating characteristic (ROC) Summary statistics Effect size |
Sensitivity index : Wickens, Thomas D. (2001). Elementary Signal Detection Theory. OUP USA. ch. 2, p. 20. ISBN 0-19-509250-3. |
Sensitivity index : Interactive signal detection theory tutorial including calculation of d′. |
Separation test : A separation test is a statistical procedure for early-phase research, to decide whether to pursue further research. It is designed to avoid the prevalent situation in early-phase research, when a statistically underpowered test gives a negative result. |
Separation test : Aickin M. (2004) "Separation Tests for Early-Phase Complementary and Alternative Medicine Comparative Trials". Evidence-Based Integrative Medicine, 1(4), 225–231 |
Seriation (statistics) : In combinatorial data analysis, seriation is the process of finding an arrangement of all objects in a set, in a linear order, given a loss function. The main goal is exploratory, to reveal structural information. == References == |
Sheppard's correction : In statistics, Sheppard's corrections are approximate corrections to estimates of moments computed from binned data. The concept is named after William Fleetwood Sheppard. Let m k be the measured kth moment, μ ^ k _ the corresponding corrected moment, and c the breadth of the class interval (i... |
Sheppard's correction : Sheppard, W.F. (1897). "On the Calculation of the most Probable Values of Frequency-Constants, for Data arranged according to Equidistant Division of a Scale". Proc. Lond. Math. Soc. s1-29: 353–380. doi:10.1112/plms/s1-29.1.353. Weisstein, Eric W. "Sheppard's Correction". MathWorld—A Wolfram Web... |
Shrinkage (statistics) : In statistics, shrinkage is the reduction in the effects of sampling variation. In regression analysis, a fitted relationship appears to perform less well on a new data set than on the data set used for fitting. In particular the value of the coefficient of determination 'shrinks'. This idea is... |
Shrinkage (statistics) : Many standard estimators can be improved, in terms of mean squared error (MSE), by shrinking them towards zero (or any other finite constant value). In other words, the improvement in the estimate from the corresponding reduction in the width of the confidence interval can outweigh the worsenin... |
Shrinkage (statistics) : An example arises in the estimation of the population variance by sample variance. For a sample size of n, the use of a divisor n−1 in the usual formula (Bessel's correction) gives an unbiased estimator, while other divisors have lower MSE, at the expense of bias. The optimal choice of divisor ... |
Shrinkage (statistics) : Types of regression that involve shrinkage estimates include ridge regression, where coefficients derived from a regular least squares regression are brought closer to zero by multiplying by a constant (the shrinkage factor), and lasso regression, where coefficients are brought closer to zero b... |
Shrinkage (statistics) : Additive smoothing Boosting (machine learning) Decision stump Chapman estimator Principal component regression Regularization (mathematics) Shrinkage estimation in the estimation of covariance matrices Stein's example Tikhonov regularization == References == |
Sieve estimator : In statistics, sieve estimators are a class of non-parametric estimators which use progressively more complex models to estimate an unknown high-dimensional function as more data becomes available, with the aim of asymptotically reducing error towards zero as the amount of data increases. This method ... |
Sieve estimator : Sieve estimators have been used extensively for estimating density functions in high-dimensional spaces such as in Positron emission tomography (PET). The first exploitation of Sieves in PET for solving the maximum-likelihood image reconstruction problem was by Donald Snyder and Michael Miller, where ... |
Sieve estimator : Nonparametric regression |
Sieve estimator : Stuart Geman, Chii-Ruey Hwang. "Nonparametric Maximum Likelihood Estimation by the Method of Sieves" (PDF). The Annals of Statistics, Vol. 10, No. 2 (Jun., 1982), pp. 401-414. "Sieve Estimation" (PDF). Archived from the original (PDF) on September 2, 2006. |
Signal-to-noise statistic : In mathematics the signal-to-noise statistic distance between two vectors a and b with mean values μ a and μ b and standard deviation σ a and σ b respectively is: D s n = ( μ a − μ b ) ( σ a + σ b ) =-\mu _) \over (\sigma _+\sigma _) In the case of Gaussian-distributed data and unbiased ... |
Signal-to-noise statistic : Distance Uniform norm Manhattan distance Signal-to-noise ratio Signal to noise ratio (imaging) == Notes == |
SimFiT : Simfit is a free open-source Windows package for simulation, curve fitting, statistics, and plotting, using a library of models or user-defined mathematical equations. Simfit has been developed by Bill Bardsley of the University of Manchester. Although it is written for Windows, it can easily be installed and ... |
SimFiT : Main Website Website of the Silverfrost version Website of the Spanish version |
Size (statistics) : In statistics, the size of a test is the probability of falsely rejecting the null hypothesis. That is, it is the probability of making a type I error. It is denoted by the Greek letter α (alpha). For a simple hypothesis, α = P ( test rejects H 0 ∣ H 0 ) . H_\mid H_). In the case of a composite null... |
Smearing retransformation : The Smearing retransformation is used in regression analysis, after estimating the logarithm of a variable. Estimating the logarithm of a variable instead of the variable itself is a common technique to more closely approximate normality. In order to retransform the variable back to level fr... |
Southern Region, Ireland : The Southern Region has been a region in Ireland since 1 January 2015. It is a NUTS Level II statistical region of Ireland (coded IE05). NUTS 2 Regions may be classified as less developed regions, transition regions, or more developed regions to determine eligibility for funding under the Eur... |
Southern Region, Ireland : Southern Regional Assembly |
Sparse binary polynomial hashing : Sparse binary polynomial hashing (SBPH) is a generalization of Bayesian spam filtering that can match mutating phrases as well as single words. SBPH is a way of generating a large number of features from an incoming text automatically, and then using statistics to determine the weight... |
Sparse binary polynomial hashing : A paper on the subject as it relates to spam (some article text comes from this document, which is under the GFDL) Ending Spam: Bayesian Content Filtering and the Art of Statistical Language Classification. No Starch Press. 2005. p. 108. ISBN 978-1-59327-052-0. |
Spatial statistics : Spatial statistics is a field of applied statistics dealing with spatial data. It involves stochastic processes (random fields, point processes), sampling, smoothing and interpolation, regional (areal unit) and lattice (gridded) data, point patterns, as well as image analysis and stereology. |
Spatial statistics : Geostatistics Modifiable areal unit problem Spatial analysis Spatial econometrics Statistical geography Spatial epidemiology Spatial network Statistical shape analysis == References == |
Speed prior : The speed prior is a complexity measure similar to Kolmogorov complexity, except that it is based on computation speed as well as program length. The speed prior complexity of a program is its size in bits plus the logarithm of the maximum time we are willing to run it to get a prediction. When compared t... |
Speed prior : Computational complexity theory Inductive inference Minimum message length Minimum description length |
Speed prior : Speed Prior web site |
Squared ranks test : In statistics, the Conover squared ranks test is a non-parametric version of the parametric Levene's test for equality of variance. Conover's squared ranks test is the only equality of variance test that appears to be non-parametric. Other tests of significance of difference of data dispersion are ... |
Stability postulate : In probability theory, to obtain a nondegenerate limiting distribution for extremes of samples, it is necessary to "reduce" the actual greatest value by applying a linear transformation with coefficients that depend on the sample size. If X 1 , X 2 , … , X n ,\ X_,\ \dots ,\ X_\ are independent r... |
Stability postulate : To distinguish the limiting cumulative distribution function from the "reduced" greatest value from F ( x ) , we will denote it by G ( y ) . It follows that G ( y ) must satisfy the functional equation [ G ( y ) ] n = G ( a n y + b n ) . =G\!\left(\ a_\ y+b_\ \right)~. Boris Vladimirovich Gnede... |
Standard normal deviate : A standard normal deviate is a normally distributed deviate. It is a realization of a standard normal random variable, defined as a random variable with expected value 0 and variance 1. Where collections of such random variables are used, there is often an associated (possibly unstated) assump... |
Standard normal deviate : Standard normal table == References == |
Standardized rate : Standardized rates are a statistical measure of any rates in a population. These are adjusted rates that take into account the vital differences between populations that may affect their birthrates or death rates. |
Standardized rate : The most common are birth, death and unemployment rates. For example, in a community made up of primarily young couples, the birthrate might appear to be high when compared to that of other populations. However, by calculating the standardized birthrates that is by comparing the same age group in ot... |
Standardized rate : The formula for standardized rates is as follows: Σ(crude rate for age group × standard population for age group) / Σstandard population |
Standardized rate : Medical Biostatistics, Third Edition (MedicalBiostatistics.synthasite.com), A. Indrayan (indrayan.weebly.com), Chapman & Hall/ CRC Press, 2012 Introduction to Sociology, Bruce J. Cohen and Terri L. Orbuch |
State Statistics Service of Ukraine : State Statistics Committee of Ukraine (Ukrainian: Державний Комітет Статистики України, Derzhavnyi Komitet Statystyky Ukrainy) is the government agency responsible for collection and dissemination of statistics in Ukraine. For brevity, it was also referred to as Derzhkomstat. In 20... |
State Statistics Service of Ukraine : Science and Research Institute of Statistics, keeps track of the Classification of objects of the administrative-territorial system of Ukraine |
State Statistics Service of Ukraine : Ukrainian Census (2001), Censuses in Ukraine |
State Statistics Service of Ukraine : Official website (Ukrainian, Russian, English) 2001 Ukraine Census Presidential decree #1085/2010 "For optimization the system of central bodies of executive power (Ukrainian) |
Statistical assembly : In statistics, for example in statistical quality control, a statistical assembly is a collection of parts or components which makes up a statistical unit. Thus a statistical unit, which would be the prime item of concern, is made of discrete components like organs or machine parts. The reliabili... |
Statistical assembly : "1 2D Overview7/92". adcats.et.byu.edu. Retrieved 2018-08-20. |
Statisticians in the Pharmaceutical Industry : Statisticians in the Pharmaceutical Industry, abbreviated to PSI[1], is an organisation for the promotion of statistical thinking in order to improve the quality of research and development in the pharmaceutical industry. |
Statisticians in the Pharmaceutical Industry : PSI is a non-profit organisation formed in 1977 which was later converted to a company limited by guarantee, a process which was completed in January 2003. PSI achieves its vision by providing a forum for regular discussion of statistics and matters relating to the practic... |
Statisticians in the Pharmaceutical Industry : PSI has held an annual conference every year since 1978. In its early years the conference was typically held at an English university, but later moved to hotel conference facilities. The first conference to be held outside the United Kingdom was in 2008, but since then th... |
Statisticians in the Pharmaceutical Industry : ^ The abbreviation PSI is chosen in preference to the more literal SPI to avoid connotations with the word "spy", and to tie in with the Greek letter Ψ - Greek letters playing a substantial part in statistics. Ψ was the original logo of PSI. ^ The 2020 conference had been ... |
Statisticians in the Pharmaceutical Industry : PSI Website PharmaClik Website Pharmaceutical Statistics (PSI Journal) |
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