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Durbin Test
In the analysis of designed experiments, the Friedman test is the most common non-parametric test for complete block designs. The Durbin test is a nonparametric test for balanced incomplete designs that reduces to the Friedman test in the case of a complete block design. Background In a randomized block design, ''k'' treatments are applied to ''b'' blocks. In a complete block design, every treatment is run for every block and the data are arranged as follows: For some experiments, it may not be realistic to run all treatments in all blocks, so one may need to run an incomplete block design. In this case, it is strongly recommended to run a balanced incomplete design. A balanced incomplete block design has the following properties: #Every block contains ''k'' experimental units. #Every treatment appears in ''r'' blocks. #Every treatment appears with every other treatment an equal number of times. Test assumptions The Durbin test is based on the following assumptions: #The ''b' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Designed Experiment
The design of experiments (DOE, DOX, or experimental design) is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associated with experiments in which the design introduces conditions that directly affect the variation, but may also refer to the design of quasi-experiments, in which natural conditions that influence the variation are selected for observation. In its simplest form, an experiment aims at predicting the outcome by introducing a change of the preconditions, which is represented by one or more independent variables, also referred to as "input variables" or "predictor variables." The change in one or more independent variables is generally hypothesized to result in a change in one or more dependent variables, also referred to as "output variables" or "response variables." The experimental design may also identify control variables that must be h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiple Comparisons
In statistics, the multiple comparisons, multiplicity or multiple testing problem occurs when one considers a set of statistical inferences simultaneously or infers a subset of parameters selected based on the observed values. The more inferences are made, the more likely erroneous inferences become. Several statistical techniques have been developed to address that problem, typically by requiring a stricter significance threshold for individual comparisons, so as to compensate for the number of inferences being made. History The problem of multiple comparisons received increased attention in the 1950s with the work of statisticians such as Tukey and Scheffé. Over the ensuing decades, many procedures were developed to address the problem. In 1996, the first international conference on multiple comparison procedures took place in Israel. Definition Multiple comparisons arise when a statistical analysis involves multiple simultaneous statistical tests, each of which has a potent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Van Der Waerden Test
Named after the Dutch mathematician Bartel Leendert van der Waerden, the Van der Waerden test is a statistical test that ''k'' population distribution functions are equal. The Van der Waerden test converts the ranks from a standard Kruskal-Wallis one-way analysis of variance to quantiles of the standard normal distribution (details given below). These are called normal scores and the test is computed from these normal scores. The ''k'' population version of the test is an extension of the test for two populations published by Van der Waerden (1952,1953). Background Analysis of Variance (ANOVA) is a data analysis technique for examining the significance of the factors (independent variables) in a multi-factor model. The one factor model can be thought of as a generalization of the two sample t-test. That is, the two sample t-test is a test of the hypothesis that two population means are equal. The one factor ANOVA tests the hypothesis that ''k'' population means are equal. The stan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analysis Of Variance
Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among means. ANOVA was developed by the statistician Ronald Fisher. ANOVA is based on the law of total variance, where the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether two or more population means are equal, and therefore generalizes the ''t''-test beyond two means. In other words, the ANOVA is used to test the difference between two or more means. History While the analysis of variance reached fruition in the 20th century, antecedents extend centuries into the past according to Stigler. These include hypothesis testing, the partitioning of sums of squares, experimental techniques and the additive model. Laplace was performing hypothesis testing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cochran's Q Test
In statistics, in the analysis of two-way randomized block designs where the response variable can take only two possible outcomes (coded as 0 and 1), Cochran's Q test is a non-parametric statistical test to verify whether ''k'' treatments have identical effects. It is named after William Gemmell Cochran. Cochran's Q test should not be confused with Cochran's C test, which is a variance outlier test. Put in simple technical terms, Cochran's Q test requires that there only be a binary response (e.g. success/failure or 1/0) and that there be more than 2 groups of the same size. The test assesses whether the proportion of successes is the same between groups. Often it is used to assess if different observers of the same phenomenon have consistent results (interobserver variability). Background Cochran's Q test assumes that there are ''k'' > 2 experimental treatments and that the observations are arranged in ''b'' blocks; that is, Description Cochran's Q test is :Null hypo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chi-squared Distribution
In probability theory and statistics, the chi-squared distribution (also chi-square or \chi^2-distribution) with k degrees of freedom is the distribution of a sum of the squares of k independent standard normal random variables. The chi-squared distribution is a special case of the gamma distribution and is one of the most widely used probability distributions in inferential statistics, notably in hypothesis testing and in construction of confidence intervals. This distribution is sometimes called the central chi-squared distribution, a special case of the more general noncentral chi-squared distribution. The chi-squared distribution is used in the common chi-squared tests for goodness of fit of an observed distribution to a theoretical one, the independence of two criteria of classification of qualitative data, and in confidence interval estimation for a population standard deviation of a normal distribution from a sample standard deviation. Many other statistical tests a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Durbin
__NOTOC__ James Durbin FBA (30 June 1923 – 23 June 2012) was a British statistician and econometrician, known particularly for his work on time series analysis and serial correlation. Education The son of a greengrocer, Durbin was born in Widnes, where he attended the Wade Deacon Grammar School. He studied mathematics at St John's College, Cambridge, where his contemporaries included David Cox and Denis Sargan. After wartime service in the Army Operational Research Group, he worked as a statistician for two years with the British Boot, Shoe and Allied Trades Research Association and took a postgraduate diploma in mathematical statistics at Cambridge, supervised by Henry Daniels. Career After two years at the department of applied economics in Cambridge, Durbin joined the London School of Economics in 1950 and was appointed professor of statistics in 1961, a post he held until his retirement in 1988. Awards and honours He served as president of the International Statist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Student's T-distribution
In probability and statistics, Student's ''t''-distribution (or simply the ''t''-distribution) is any member of a family of continuous probability distributions that arise when estimating the mean of a normally distributed population in situations where the sample size is small and the population's standard deviation is unknown. It was developed by English statistician William Sealy Gosset under the pseudonym "Student". The ''t''-distribution plays a role in a number of widely used statistical analyses, including Student's ''t''-test for assessing the statistical significance of the difference between two sample means, the construction of confidence intervals for the difference between two population means, and in linear regression analysis. Student's ''t''-distribution also arises in the Bayesian analysis of data from a normal family. If we take a sample of n observations from a normal distribution, then the ''t''-distribution with \nu=n-1 degrees of freedom can be de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
F Distribution
In probability theory and statistics, the ''F''-distribution or F-ratio, also known as Snedecor's ''F'' distribution or the Fisher–Snedecor distribution (after Ronald Fisher and George W. Snedecor) is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the analysis of variance (ANOVA) and other ''F''-tests. Definition The F-distribution with ''d''1 and ''d''2 degrees of freedom is the distribution of : X = \frac where S_1 and S_2 are independent random variables with chi-square distributions with respective degrees of freedom d_1 and d_2. It can be shown to follow that the probability density function (pdf) for ''X'' is given by : \begin f(x; d_1,d_2) &= \frac \\ pt&=\frac \left(\frac\right)^ x^ \left(1+\frac \, x \right)^ \end for real ''x'' > 0. Here \mathrm is the beta function. In many applications, the parameters ''d''1 and ''d''2 are positive integers, but the distribution is well-def ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Friedman Test
The Friedman test is a non-parametric statistical test developed by Milton Friedman. Similar to the parametric repeated measures ANOVA, it is used to detect differences in treatments across multiple test attempts. The procedure involves ranking each row (or ''block'') together, then considering the values of ranks by columns. Applicable to complete block designs, it is thus a special case of the Durbin test. Classic examples of use are: * ''n'' wine judges each rate ''k'' different wines. Are any of the ''k'' wines ranked consistently higher or lower than the others? * ''n'' welders each use ''k'' welding torches, and the ensuing welds were rated on quality. Do any of the ''k'' torches produce consistently better or worse welds? The Friedman test is used for one-way repeated measures analysis of variance by ranks. In its use of ranks it is similar to the Kruskal–Wallis one-way analysis of variance by ranks. The Friedman test is widely supported by many statistical software ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantile Function
In probability and statistics, the quantile function, associated with a probability distribution of a random variable, specifies the value of the random variable such that the probability of the variable being less than or equal to that value equals the given probability. Intuitively, the quantile function associates with a range at and below a probability input the likelihood that a random variable is realized in that range for some probability distribution. It is also called the percentile function, percent-point function or inverse cumulative distribution function. Definition Strictly monotonic distribution function With reference to a continuous and strictly monotonic cumulative distribution function F_X\colon \mathbb \to ,1/math> of a random variable ''X'', the quantile function Q\colon , 1\to \mathbb returns a threshold value ''x'' below which random draws from the given c.d.f. would fall ''100*p'' percent of the time. In terms of the distribution function ''F'', the qua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
