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Noncentral T-distribution
The noncentral ''t''-distribution generalizes Student's t-distribution, Student's ''t''-distribution using a noncentrality parameter. Whereas the central probability distribution describes how a test statistic ''t'' is distributed when the difference tested is null, the noncentral distribution describes how ''t'' is distributed when the null is false. This leads to its use in statistics, especially calculating statistical power. The noncentral ''t''-distribution is also known as the singly noncentral ''t''-distribution, and in addition to its primary use in statistical inference, is also used in Robust statistics, robust modeling for data. Definitions If ''Z'' is a standard normal distribution, normal random variable, and ''V'' is a Chi-squared distribution, chi-squared distributed random variable with ν Degrees of freedom (statistics), degrees of freedom that is independent of ''Z'', then :T=\frac is a noncentral ''t''-distributed random variable with ν degrees of freedom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nc Student T Pdf
NC may refer to: People * Naga Chaitanya, an Indian Telugu film actor; sometimes nicknamed by the initials of his first and middle name, NC * Nathan Connolly, lead guitarist for Snow Patrol * Nostalgia Critic, the alter ego of Internet comedian Doug Walker from ''That Guy with the Glasses'' Places * New Caledonia, special collectivity of France (ISO 3166-1 country code NC) * New Canaan, a town in Connecticut, U.S. * North Carolina, a U.S. state by postal abbreviation * Northern Cyprus, a self-declared state on the island of Cyprus Science, technology, and mathematics Biology and medicine * Nasal cannula, a device used to deliver supplemental oxygen * Nasal chondrocytes, the cell type within the hyaline cartilage of the nasal septum * Neural crest, a transient component of the ectoderm * Effective number of codons, a measure to study the state of codon usage biases in genes Chemistry * Isocyanide, (-NC) Isocyanide, an organic functional group. Computing and internet *NC (compl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
R (programming Language)
R is a programming language for statistical computing and Data and information visualization, data visualization. It has been widely adopted in the fields of data mining, bioinformatics, data analysis, and data science. The core R language is extended by a large number of R package, software packages, which contain Reusability, reusable code, documentation, and sample data. Some of the most popular R packages are in the tidyverse collection, which enhances functionality for visualizing, transforming, and modelling data, as well as improves the ease of programming (according to the authors and users). R is free and open-source software distributed under the GNU General Public License. The language is implemented primarily in C (programming language), C, Fortran, and Self-hosting (compilers), R itself. Preprocessor, Precompiled executables are available for the major operating systems (including Linux, MacOS, and Microsoft Windows). Its core is an interpreted language with a na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Linear Model
The general linear model or general multivariate regression model is a compact way of simultaneously writing several multiple linear regression models. In that sense it is not a separate statistical linear model. The various multiple linear regression models may be compactly written as : \mathbf = \mathbf\mathbf + \mathbf, where Y is a Matrix (mathematics), matrix with series of multivariate measurements (each column being a set of measurements on one of the dependent variables), X is a matrix of observations on independent variables that might be a design matrix (each column being a set of observations on one of the independent variables), B is a matrix containing parameters that are usually to be estimated and U is a matrix containing Errors and residuals in statistics, errors (noise). The errors are usually assumed to be uncorrelated across measurements, and follow a multivariate normal distribution. If the errors do not follow a multivariate normal distribution, generalized li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Power
In frequentist statistics, power is the probability of detecting a given effect (if that effect actually exists) using a given test in a given context. In typical use, it is a function of the specific test that is used (including the choice of test statistic and significance level), the sample size (more data tends to provide more power), and the effect size (effects or correlations that are large relative to the variability of the data tend to provide more power). More formally, in the case of a simple hypothesis test with two hypotheses, the power of the test is the probability that the test correctly rejects the null hypothesis (H_0) when the alternative hypothesis (H_1) is true. It is commonly denoted by 1-\beta, where \beta is the probability of making a type II error (a false negative) conditional on there being a true effect or association. Background Statistical testing uses data from samples to assess, or make inferences about, a statistical population. Fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sample 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 devia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Test Statistic
Test statistic is a quantity derived from the sample for statistical hypothesis testing.Berger, R. L.; Casella, G. (2001). ''Statistical Inference'', Duxbury Press, Second Edition (p.374) A hypothesis test is typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test. In general, a test statistic is selected or defined in such a way as to quantify, within observed data, behaviours that would distinguish the null from the alternative hypothesis, where such an alternative is prescribed, or that would characterize the null hypothesis if there is no explicitly stated alternative hypothesis. An important property of a test statistic is that its sampling distribution under the null hypothesis must be calculable, either exactly or approximately, which allows ''p''-values to be calculated. A ''test statistic'' shares some of the same qualities of a descriptive stat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Student's T-test
Student's ''t''-test is a statistical test used to test whether the difference between the response of two groups is statistically significant or not. It is any statistical hypothesis test in which the test statistic follows a Student's ''t''-distribution under the null hypothesis. It is most commonly applied when the test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known (typically, the scaling term is unknown and is therefore a nuisance parameter). When the scaling term is estimated based on the data, the test statistic—under certain conditions—follows a Student's ''t'' distribution. The ''t''-test's most common application is to test whether the means of two populations are significantly different. In many cases, a ''Z''-test will yield very similar results to a ''t''-test because the latter converges to the former as the size of the dataset increases. History The term "''t''-statistic" is abbreviated from " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alternative Hypothesis
In statistical hypothesis testing, the alternative hypothesis is one of the proposed propositions in the hypothesis test. In general the goal of hypothesis test is to demonstrate that in the given condition, there is sufficient evidence supporting the credibility of alternative hypothesis instead of the exclusive proposition in the test (null hypothesis). It is usually consistent with the research hypothesis because it is constructed from literature review, previous studies, etc. However, the research hypothesis is sometimes consistent with the null hypothesis. In statistics, alternative hypothesis is often denoted as Ha or H1. Hypotheses are formulated to compare in a statistical hypothesis test. In the domain of inferential statistics, two rival hypotheses can be compared by explanatory power and predictive power. Basic definition The ''alternative hypothesis'' and ''null hypothesis'' are types of conjectures used in statistical tests, which are formal methods of reaching ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Null Hypothesis
The null hypothesis (often denoted ''H''0) is the claim in scientific research that the effect being studied does not exist. The null hypothesis can also be described as the hypothesis in which no relationship exists between two sets of data or variables being analyzed. If the null hypothesis is true, any experimentally observed effect is due to chance alone, hence the term "null". In contrast with the null hypothesis, an alternative hypothesis (often denoted ''H''A or ''H''1) is 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 to make statistical inferences, which are formal methods of reaching conclusions and separating scientific claims from statistical noise. The statement being tested in a test of statistical significance is called the null hypothesis. The test of significance is designed to assess the strength of the e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noncentral F-distribution
In probability theory and statistics, the noncentral ''F''-distribution is a continuous probability distribution that is a noncentral generalization of the (ordinary) ''F''-distribution. It describes the distribution of the quotient (''X''/''n''1)/(''Y''/''n''2), where the numerator ''X'' has a noncentral chi-squared distribution with ''n''1 degrees of freedom and the denominator ''Y'' has a central chi-squared distribution with ''n''2 degrees of freedom. It is also required that ''X'' and ''Y'' are statistically independent of each other. It is the distribution of the test statistic in analysis of variance problems when the null hypothesis is false. The noncentral ''F''-distribution is used to find the power function of such a test. Occurrence and specification If X is a noncentral chi-squared random variable with noncentrality parameter \lambda and \nu_1 degrees of freedom, and Y is a chi-squared random variable with \nu_2 degrees of freedom that is statistically indepe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scale Parameter
In probability theory and statistics, a scale parameter is a special kind of numerical parameter of a parametric family of probability distributions. The larger the scale parameter, the more spread out the distribution. Definition If a family of probability distributions is such that there is a parameter ''s'' (and other parameters ''θ'') for which the cumulative distribution function satisfies :F(x;s,\theta) = F(x/s;1,\theta), \! then ''s'' is called a scale parameter, since its value determines the " scale" or statistical dispersion of the probability distribution. If ''s'' is large, then the distribution will be more spread out; if ''s'' is small then it will be more concentrated. If the probability density exists for all values of the complete parameter set, then the density (as a function of the scale parameter only) satisfies :f_s(x) = f(x/s)/s, \! where ''f'' is the density of a standardized version of the density, i.e. f(x) \equiv f_(x). An estimator of a scale ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
