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Standardized Testing (statistics)
A ''Z''-test is any statistical test for which the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution. Z-tests test the mean of a distribution. For each significance level in the confidence interval, the ''Z''-test has a single critical value (for example, 1.96 for 5% two tailed) which makes it more convenient than the Student's ''t''-test whose critical values are defined by the sample size (through the corresponding degrees of freedom). Both the Z test and Student's t-test have similarities in that they both help determine the significance of a set of data. However, the z-test is rarely used in practice because the population deviation is difficult to determine. Applicability Because of the central limit theorem, many test statistics are approximately normally distributed for large samples. Therefore, many statistical tests can be conveniently performed as approximate ''Z''-tests if the sample size is large or the pop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Graphics Pipeline
In computer graphics, a computer graphics pipeline, rendering pipeline or simply graphics pipeline, is a conceptual model that describes what steps a graphics system needs to perform to render a 3D scene to a 2D screen. Once a 3D model has been created, for instance in a video game or any other 3D computer animation, the graphics pipeline is the process of turning that 3D model into what the computer displays. Because the steps required for this operation depend on the software and hardware used and the desired display characteristics, there is no universal graphics pipeline suitable for all cases. However, graphics application programming interfaces (APIs) such as Direct3D and OpenGL were created to unify similar steps and to control the graphics pipeline of a given hardware accelerator. These APIs abstract the underlying hardware and keep the programmer away from writing code to manipulate the graphics hardware accelerators (AMD/Intel/NVIDIA etc.). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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P-values
In null-hypothesis significance testing, the ''p''-value is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. A very small ''p''-value means that such an extreme observed outcome would be very unlikely under the null hypothesis. Reporting ''p''-values of statistical tests is common practice in academic publications of many quantitative fields. Since the precise meaning of ''p''-value is hard to grasp, misuse is widespread and has been a major topic in metascience. Basic concepts In statistics, every conjecture concerning the unknown probability distribution of a collection of random variables representing the observed data X in some study is called a ''statistical hypothesis''. If we state one hypothesis only and the aim of the statistical test is to see whether this hypothesis is tenable, but not to investigate other specific hypotheses, then such a test is called a null ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Effect Size
In statistics, an effect size is a value measuring the strength of the relationship between two variables in a population, or a sample-based estimate of that quantity. It can refer to the value of a statistic calculated from a sample of data, the value of a parameter for a hypothetical population, or to the equation that operationalizes how statistics or parameters lead to the effect size value. Examples of effect sizes include the correlation between two variables, the regression coefficient in a regression, the mean difference, or the risk of a particular event (such as a heart attack) happening. Effect sizes complement statistical hypothesis testing, and play an important role in power analyses, sample size planning, and in meta-analyses. The cluster of data-analysis methods concerning effect sizes is referred to as estimation statistics. Effect size is an essential component when evaluating the strength of a statistical claim, and it is the first item (magnitude) in the MA ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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P-value
In null-hypothesis significance testing, the ''p''-value is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. A very small ''p''-value means that such an extreme observed outcome would be very unlikely under the null hypothesis. Reporting ''p''-values of statistical tests is common practice in academic publications of many quantitative fields. Since the precise meaning of ''p''-value is hard to grasp, misuse is widespread and has been a major topic in metascience. Basic concepts In statistics, every conjecture concerning the unknown probability distribution of a collection of random variables representing the observed data X in some study is called a ''statistical hypothesis''. If we state one hypothesis only and the aim of the statistical test is to see whether this hypothesis is tenable, but not to investigate other specific hypotheses, then such a test is called a null ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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One-tailed
In statistical significance testing, a one-tailed test and a two-tailed test are alternative ways of computing the statistical significance of a parameter inferred from a data set, in terms of a test statistic. A two-tailed test is appropriate if the estimated value is greater or less than a certain range of values, for example, whether a test taker may score above or below a specific range of scores. This method is used for null hypothesis testing and if the estimated value exists in the critical areas, the alternative hypothesis is accepted over the null hypothesis. A one-tailed test is appropriate if the estimated value may depart from the reference value in only one direction, left or right, but not both. An example can be whether a machine produces more than one-percent defective products. In this situation, if the estimated value exists in one of the one-sided critical areas, depending on the direction of interest (greater than or less than), the alternative hypothesis is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Standard Error (statistics)
The standard error (SE) of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution or an estimate of that standard deviation. If the statistic is the sample mean, it is called the standard error of the mean (SEM). The sampling distribution of a mean is generated by repeated sampling from the same population and recording of the sample means obtained. This forms a distribution of different means, and this distribution has its own mean and variance. Mathematically, the variance of the sampling mean distribution obtained is equal to the variance of the population divided by the sample size. This is because as the sample size increases, sample means cluster more closely around the population mean. Therefore, the relationship between the standard error of the mean and the standard deviation is such that, for a given sample size, the standard error of the mean equals the standard deviation divided by the square root of the sample siz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Sampling (statistics)
In statistics, quality assurance, and survey methodology, sampling is the selection of a subset (a statistical sample) of individuals from within a statistical population to estimate characteristics of the whole population. Statisticians attempt to collect samples that are representative of the population in question. Sampling has lower costs and faster data collection than measuring the entire population and can provide insights in cases where it is infeasible to measure an entire population. Each observation measures one or more properties (such as weight, location, colour or mass) of independent objects or individuals. In survey sampling, weights can be applied to the data to adjust for the sample design, particularly in stratified sampling. Results from probability theory and statistical theory are employed to guide the practice. In business and medical research, sampling is widely used for gathering information about a population. Acceptance sampling is used to determi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Consistent Estimator
In statistics, a consistent estimator or asymptotically consistent estimator is an estimator—a rule for computing estimates of a parameter ''θ''0—having the property that as the number of data points used increases indefinitely, the resulting sequence of estimates converges in probability to ''θ''0. This means that the distributions of the estimates become more and more concentrated near the true value of the parameter being estimated, so that the probability of the estimator being arbitrarily close to ''θ''0 converges to one. In practice one constructs an estimator as a function of an available sample of size ''n'', and then imagines being able to keep collecting data and expanding the sample ''ad infinitum''. In this way one would obtain a sequence of estimates indexed by ''n'', and consistency is a property of what occurs as the sample size “grows to infinity”. If the sequence of estimates can be mathematically shown to converge in probability to the true value ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Slutsky's Theorem
In probability theory, Slutsky’s theorem extends some properties of algebraic operations on convergent sequences of real numbers to sequences of random variables. The theorem was named after Eugen Slutsky. Slutsky's theorem is also attributed to Harald Cramér. Statement Let X_n, Y_n be sequences of scalar/vector/matrix random elements. If X_n converges in distribution to a random element X and Y_n converges in probability to a constant c, then * X_n + Y_n \ \xrightarrow\ X + c ; * X_nY_n \ \xrightarrow\ Xc ; * X_n/Y_n \ \xrightarrow\ X/c, provided that ''c'' is invertible, where \xrightarrow denotes convergence in distribution. Notes: # The requirement that ''Yn'' converges to a constant is important — if it were to converge to a non-degenerate random variable, the theorem would be no longer valid. For example, let X_n \sim (0,1) and Y_n = -X_n. The sum X_n + Y_n = 0 for all values of ''n''. Moreover, Y_n \, \xrightarrow \, (-1,0), but X_n + Y_n does not conv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Nuisance Parameter
Nuisance (from archaic ''nocence'', through Fr. ''noisance'', ''nuisance'', from Lat. ''nocere'', "to hurt") is a common law tort. It means that which causes offence, annoyance, trouble or injury. A nuisance can be either public (also "common") or private. A public nuisance was defined by English scholar Sir James Fitzjames Stephen as, "an act not warranted by law, or an omission to discharge a legal duty, which act or omission obstructs or causes inconvenience or damage to the public in the exercise of rights common to all Her Majesty's subjects". ''Private nuisance'' is the interference with the right of specific people. Nuisance is one of the oldest causes of action known to the common law, with cases framed in nuisance going back almost to the beginning of recorded case law. Nuisance signifies that the "right of quiet enjoyment" is being disrupted to such a degree that a tort is being committed. Definition Under the common law, persons in possession of real property (lan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Paired Difference Test
In statistics, a paired difference test is a type of location test that is used when comparing two sets of measurements to assess whether their population means differ. A paired difference test uses additional information about the sample that is not present in an ordinary unpaired testing situation, either to increase the statistical power, or to reduce the effects of confounders. Specific methods for carrying out paired difference tests are, for normally distributed difference t-test (where the population standard deviation of difference is not known) and the paired Z-test (where the population standard deviation of the difference is known), and for differences that may not be normally distributed the Wilcoxon signed-rank test. The most familiar example of a paired difference test occurs when subjects are measured before and after a treatment. Such a "repeated measures" test compares these measurements within subjects, rather than across subjects, and will generally have great ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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T-test
A ''t''-test 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 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 different. History The term "''t''-statistic" is abbreviated from "hypothesis test statistic". In statistics, the t-distribution was first derived as a posterior distribution in 1876 by Helmert and Lüroth. The t-distribution also appeared in a more general form as Pearson Type IV distribution in Karl Pearson's 1895 paper. However, the T-Distribution, also known as Student's t-distr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |