Otheruses2 Statistics A statistic singular is a single measure of some attribute of a sample e.g. its arithmetic mean value . It is calculated by applying a function mathematics function statistical algorithm to the values of the items comprising the sample which are known together as a Data set set of data . More formally, statistical theory defines a statistic as a function of a sample statistics ... can be stated before realisation of the data. The term statistic is used both for the function and for the value of the function on a given sample. A statistic is distinct from a statistical parameter ... its items. However a statistic, when used to estimate a population parameter, is called an estimator . For instance, the sample mean is a statistic which estimates the population mean , which is a parameter .... This single measure, the mean of the sample, is called a statistic and its value is frequently used .... The population mean is also a single measure however it is not called a statistic instead it is called ... the median , e.g., quartile s and percentile s t statistic s, chi square statistic s, f test f statistics Order statistic s, including sample maximum and minimum Sample moment mathematics moments ... distribution function Properties Observability A statistic is an observable random variable ... of 100 such men are measured the average of those 100 numbers is a statistic . The average of the heights of all members of the population is not a statistic unless that has somehow also been ascertained ... of genetically possible 25 year old North American men is a parameter and not a statistic . Statistical ... convenience. Information of a statistic Information of a statistic on model parameters can be defined in several ways. The most common one is the Fisher information which is defined on the statistic model induced by the statistic. Kullback information measure can also be used. See also Wiktionary statistic ... statistic Footnotes references Unreferenced date March 2010 Category Statistical theory de Statistik ... more details
DISPLAYTITLE t statistic Unreferenced date February 2011 In statistics , the t statistic is a ratio of the departure of an estimated parameter from its notional value and its Standard error statistics standard error . It is used in statistical hypothesis testing hypothesis testing , for example in the Student ... in some statistical model . Then a t statistic for this parameter is any quantity of the form ... math . By default, statistical packages report t statistic with nowrap sub 0 sub 0 these t statistics are used to test the significance of corresponding regressor . However, when t statistic is needed ... to sub 0 sub , then the sampling distribution of the t statistic is the Student s t distribution ... of this estimator, then the t statistic will have asymptotically the standard normal distribution. In some models the distribution of t statistic is different from normal, even asymptotically. For example ... t statistic will asymptotically have one of the Dickey Fuller distributions depending on the test setting ... testing , and in the computation of certain confidence interval s. The key property of the t statistic ..., the t statistic of a future observation math X n 1 , math after one has made n observations, is an ancillary statistic a pivotal quantity does not depend on the values of and sup 2 sup that is a statistic ... X n 1 math will fall in that interval. History details Student s t test The term t statistic is abbreviated from test statistic , Citation needed date February 2011 while Student was the pen name of William Sealy Gosset , who introduced the t statistic and t test in 1908, while working for the Guinness ..., then rather than computing the t statistic, one can compute the z score analogously, rather than using ... also Portal Statistics F statistic Student s t distribution Student s t test References Reflist External links http www.childrens mercy.org stats definitions tstat.htm What is a t statistic? at The Children s Mercy Hospital Use dmy dates date November 2010 DEFAULTSORT T statistic Category Statistical ... more details
The Q statistic is a test statistic output by either the Box Pierce test or, in a modified version which provides better small sample properties, by the Ljung Box test . It follows the chi squared distribution . See also Portmanteau test . The q statistic or studentized range statistic is a statistic used for multiple significance testing across a number of means see Tukey Kramer method . Unreferenced date July 2010 Category Statistical tests statistics stub de Q Statistik ... more details
In statistical hypothesis testing , a hypothesis test is typically specified in terms of a test statistic , which is a function of the sample ref name CasellaBerger R. L. Berger and G. Casella 2001 . Statistical Inference , Duxbury Press, Second Edition, 2001, p.374. ref it is considered as a numerical summary of a set of data that reduces the data to one or a small number of values that can be used to perform a hypothesis test. Given a null hypothesis and a test statistic T , we can specify a null value T sub 0 sub such that values of T close to T sub 0 sub present the strongest evidence in favor of the null hypothesis, whereas values of T far from T sub 0 sub present the strongest evidence against the null hypothesis. An important property of a test statistic is that we must be able to determine its sampling distribution under the null hypothesis, which allows us to calculate p values . For example, suppose we wish to test whether a coin is fair i.e. has equal probabilities of producing a head or a tail . If we flip the coin 100 times and record the results, the raw data can be represented as a sequence of 100 Heads and Tails. If our interest is in the marginal distribution marginal probability of obtaining a head, we only need to record the number T out of the 100 flips that produced a head, and use T sub 0 sub 50 as our null value. In this case, the exact sampling ... is fair. Note that the test statistic in this case reduces a set of 100 numbers to a single numerical summary that can be used for testing. A test statistic shares some of the same qualities of a descriptive statistics descriptive statistic , and many statistics can be used as both test statistics and descriptive statistics. However a test statistic is specifically intended for use in statistical testing, whereas the main quality of a descriptive statistic is that it is easily interpretable. Some ... See also Sufficiency statistics Neyman Pearson lemma DEFAULTSORT Test Statistic Category Statistical ... more details
In statistics , an ancillary statistic is a statistic whose sampling distribution does not depend on which of the probability distributions among those being considered is the distribution of the statistical population from which the data were taken. An ancillary statistic is a pivotal quantity function of observations whose distribution does not depend on parameters that is also a statistic computed in terms of observations, not depending on any unobserved quantities . They can be used to construct prediction interval s. This concept was introduced by the statistical geneticist Sir Ronald Fisher . Example Suppose X sub 1 sub , ..., X sub n sub are Independent identically distributed random variables independent and identically distributed , and are normal distribution normally distributed with unknown expected value and known variance 1. Let math overline X n frac X 1 , cdots , X n n math be the Arithmetic mean sample mean . The following statistical measures of dispersion of the sample Range statistics Range max X sub 1 sub , ..., X sub n sub &minus min X sub 1 sub , ..., X sub n ... variance sup 2 sup , the sample mean math overline X math is not an ancillary statistic of the variance ... on dispersion. Ancillary complement Given a statistic T that is not Sufficiency statistics sufficient , an ancillary complement is a statistic U that is ancillary to T and such that T , U is sufficient ... without duplicating any . The statistic is particularly useful if one takes T to be a maximum likelihood ... data are the number N of at bats and the number X of hits the data X , N are a sufficient statistic ... . The number N of at bats is an ancillary statistic because It is a part of the observable data it is a statistic ... by a random process independent of the batter s ability. This ancillary statistic is an ancillary ... statistics sufficient statistic , in that it conveys less than all of the relevant information ... Ancillary Statistic Category Statistical theory pl statystyka pomocnicza ... more details
ref V statistics are closely related to U statistic s ref harvtxt Lee 1990 ref ref harvtxt Koroljuk ... harvtxt Hoeffding 1948 ref A V statistic is a statistical function of a sample defined by a particular ... test chi square goodness of fit statistic is a statistical function T F sub n sub , corresponding ... von Mises goodness of fit statistic if math w x F 0 F 0 x 1 F 0 x 1 math then T F sub n sub is the Anderson Darling statistic. li ol Representation as a V statistic Suppose x sub 1 sub , ..., x sub n sub is a sample. In typical applications the statistical function has a representation as the V statistic ... how to find the kernel in practice. V sub mn sub is called a V statistic of degree m . A symmetric ... of h. For samples x sub 1 sub , ..., x sub n sub , the corresponding V statistic is defined math V 2,n frac 1 n 2 sum i 1 n sum j 1 n h x i, x j . math Example of a V statistic ol start 4 li An example of a degree 2 V statistic is the second central moment m sub 2 sub . If h x , y x &minus y sup 2 sup 2, the corresponding V statistic is math V 2,n frac 1 n 2 sum i 1 n sum j 1 n frac 1 ... Population variance and sample variance variance . With the same kernel, the corresponding U statistic ... of the statistic is different in 1 it is Normal distribution normal , in 2 it is Chi square distribution ... of cases parallel to asymptotic theory of U statistic s. ref Serfling 1980, Ch. 5 6 Lee 1990 ... series for T . li ol Case m 1 Non degenerate kernel If A 1 is true, the statistic is a sample ... form of centered Gaussian random variables . The statistic V sub 2, n sub is called a degenerate kernel V statistic . The V statistic associated with the Cramer von Mises functional ref name VM Example 3 is an example of a degenerate kernel V statistic. ref See Lee 1990, p. 160 for the kernel function. ref See also U statistic Asymptotic distribution Asymptotic theory statistics Notes Reflist ... Mises statistic journal Annals of Mathematical Statistics volume 23 issue 4 pages 617 623 id jstor ... more details
In statistics , a sufficient statistic is a statistic which has the property of sufficiency bold for likely ... that no other statistic which can be calculated from the same sample statistics sample provides ... 91208 . JFM 48.1280.02 doi 10.1098 rsta.1922.0009 ref A statistic is sufficient for a Parametric ... information than does the statistic, as to which of those probability distributions is that of the population ... statistic is a function math T mathbf X math whose value contains all the information needed ... theorem see below , for a sufficient statistic math T mathbf X math , the joint distribution ... mathbf X math only through math T mathbf X math . Typically, the sufficient statistic is a simple ... that is unknown or not fully specified. In such a case, the sufficient statistic may be a set of functions, called a jointly sufficient statistic . Typically, there are as many functions as there are parameters ... sufficient statistic, from which maximum likelihood estimates of both parameters can be estimated ... of a sufficient statistic for a parameter, the joint probability distribution of the data does not depend on that parameter. Both the statistic and the underlying parameter can be vectors. A related ... cases where there is no sufficient statistic, although it is restricted to linear estimators. ref ... definition The concept is most general when defined as follows a statistic T X is sufficient for underlying ... the statistic T X , is not a function of the parameter , ref name CasellaBerger cite book last Casella ... statistic. If the probability density function is sub sub x , then T is sufficient for ... yielding the same value for the sufficient statistic T X will always yield the same inferences about ... sub 2 sub , ..., X sub n sub be a statistic whose pdf is g y . Then Y u X sub 1 sub , X sub 2 sub , ..., X sub n sub is a sufficient statistic for if and only if, for some function H , math prod i ... math and thus math T math is a sufficient statistic. ref cite web url http cnx.org content m11480 ... more details
In statistical theory , a U statistic is a class of statistics that is especially important in estimation theory . In elementary statistics, U statistics arise naturally in producing minimum variance unbiased estimator s. A bias of an estimator mean unbiased estimator that is conditioned on the order statistics of an sequence of independent and identically distributed random variables becomes the minimum variance unbiased estimator , by the Rao Blackwell theorem . ref Cox & Hinkley 1974 ,p. 200, p. 258 ref ref Hoeffding 1948 , between Eq s 4.3 , 4.4 ref Of even more importance ref Sen 1992 ref is that the theory related to U statistics allows a single theoretical framework to be used in non parametric statistics to prove results for a wide range of test statistics and estimators relating ... can be used to derive an unbiased estimate of the variance. The U statistic based on this estimator ... random variables. Formal definition The term U statistic, due to Hoeffding 1948 , is defined ... variables. For each math n ge r math the associated U statistic math f n colon R n to R math is equal ... math r math taken from math 1, ldots, n math . Each U statistic math f n x 1, ldots, x n math is necessarily ... sample &phi of size n taken from a population of size N , the U statistic has the property ... value &fnof sub N sub x . Examples Some examples If math f x x math the U statistic math f n x bar x n x 1 cdots x n n math is the sample mean. If math f x 1, x 2 x 1 x 2 math , the U statistic ... n ge 2 math . If math f x 1, x 2 x 1 x 2 2 2 math , the U statistic is the sample variance math ... math k math statistic math k 3,n x sum x i bar x n 3 n n 1 n 2 math , the sample skewness defined for math n ge 3 math , is a U statistic. The following case highlights an important point. If math ... distributions are being estimated by probability weighted moments or L moments . See also V statistic ...&ndash 519. DEFAULTSORT U Statistic Category Estimation theory Category Non parametric statistics ... more details
i enclosed in parentheses indicates the i th order statistic of the sample. The first order statistic or smallest order statistic is always the minimum of the sample, that is, math X 1 min ..., for a sample of size n , the n th order statistic or largest order statistic is the maximum , that is, math ...,X n , X n X 1 . math A similar important statistic in exploratory data analysis that is simply ... statistic, since there is a single middle value only when the number math n math of observations ... is math X m 1 math and so is an order statistic. On the other hand, when math n math is even , math ... is some function of the two usually the average and hence not an order statistic. Similar remarks ... statistic math U k math falling in the interval math u, u du math is equal to Citation needed date April 2009 math n over k 1 n k u k 1 1 u n k du O du 2 , math that is, the k th order statistic ... and p 3 P X x 1 F x . math . We can compute the cdf of the math k text th math order statistic by noting ... urlname OrderStatistic title Order Statistic Retrieved Feb 02,2005 Dr. Susan Holmes http www stat.stanford.edu ... Statistic Category Summary statistics Category Permutations de Ordnungsstatistik fr Statistique ... more details
, while a common alternative summary statistic is Spearman s rank correlation coefficient . Distance correlation equals zero implies independence. See also Descriptive statistics Sufficient statistic ... more details
The N50 statistic is a measure of the average length of a set of sequences, with greater weight given to longer sequences. It is used widely in genome assembly , especially in reference to contig lengths within a draft assembly. N50 is defined as the contig length such that using equal or longer contigs produces half the bases of the genome. The N50 size is computed by sorting all contigs from largest to smallest and by determining the minimum set of contigs whose sizes total 50 of the entire genome. Alternative definition Given a set of sequences of varying lengths, the N50 length is defined as the length N for which 50 of all bases in the sequences are in a sequence of length L N. This can be found mathematically as follows Take a list L of positive integers. Create another list L , which is identical to L, except that every element n in L has been replaced with n copies of itself. Then the median of L is the N50 of L. For example If L 2, 2, 2, 3, 3, 4, 8, 8 , then L consists of six 2 s, six 3 s, four 4 s, and sixteen 8 s e.g. We replaced every 2 in L with 2, 2, so in L there are six 2s in L the N50 of L is the median of L , which is the average of the 16th element 4 and 17th element 8, so it is 4 8 2 6. References Broad institute wiki http www.broad.harvard.edu crd wiki index.php N50 Assembly algorithms for next generation sequencing data , Miller JR, Koren S, Sutton G http www.ncbi.nlm.nih.gov pubmed 20211242 Category Bioinformatics Category Genomics ... more details
Youden s J statistic also called Youden s index is a single statistic that captures the performance of a diagnostic test. The use of such a single index is not generally to be recommended . ref Everitt B.S. 2002 The Cambridge Dictionary of Statistics. CUP ISBN 0 521 81099 x ref It is equal to the risk difference for a dichotomous test ref H C Kraemer 2004 Reconsidering the odds ratio as a measure of 2x2 association in a population. Statistics in Medicine 23 257 270. ref . Definition Y Sensitivity Specificity &minus 1 See also sensitivity tests specificity tests References references Youden W. J., Index for rating diagnostic tests. , Cancer 1950 3 32 35 Category Statistical theory Category Biostatistics statistics stub ... more details
In statistics , the Durbin Watson statistic is a test statistic used to detect the presence of autocorrelation a relationship between values separated from each other by a given time lag in the errors and residuals in statistics residuals prediction errors from a regression analysis . It is named after ... 1950, 1951 applied this statistic to the residuals from Ordinary least squares least squares regressions ... and Bhargava, 1983 . Computing and interpreting the Durbin Watson statistic If e sub t sub is the errors ... statistic is math d sum t 2 T e t e t 1 2 over sum t 1 T e t 2 , math where T is the number of observations ... of d always lies between 0 and 4. If the Durbin Watson statistic is substantially less than 2, there is evidence ... at significance , the test statistic d is compared to lower and upper critical values d .... To test for negative autocorrelation at significance , the test statistic 4 d is compared ... the appendices of statistical texts. An important note is that the Durbin Watson statistic, while ... Godfrey Serial Correlation LM Test. Durbin h statistic This section is linked from Autocorrelation The Durbin Watson statistic is bias of an estimator biased for autoregressive moving average model s, so ... Normal distribution normally distributed h statistic math h left 1 frac 1 2 d right sqrt frac T 1 T cdot widehat operatorname Var widehat beta 1 , , math using the Durbin Watson statistic d and the estimated ... Durbin Watson test for panel data For panel data this statistic was generalized as follows by Alok ... t , then the test statistic is math d pd frac sum i 1 N sum t 2 T e i,t e i,t 1 2 sum i 1 N sum t 1 T e i,t 2 . math This statistic can be compared with tabulated rejection values see Alok Bhargava ... . This test statistic can also be used for testing the null hypothesis of a unit root against ... d statistic is included as an option in the LinearModelFit function. SAS Is a standard output when ... function, the d statistic may be calculated using SUMXMY2 x array,y array SUMSQ array people will add ... more details
One source date August 2010 In mathematics the signal to noise statistic distance between two vector geometric vectors a and b with Arithmetic Mean mean values math mu a math and math mu b math and standard deviation math sigma a math and math sigma b math respectively is math D sn mu a mu b over sigma a sigma b math This distance is frequently used to identify vectors that have significant difference. One usage is in bioinformatics to locate genes that are differential Gene expression expressed on microarray experiments ref Pomeroy, S.L. et al. http www.broad.mit.edu mpr CNS Gene Expression Based Classification and Outcome Prediction of Central Nervous System Embryonal Tumors . Nature 415, 436 442. ref . See also Distance Uniform norm Manhattan distance Signal to noise ratio Signal to noise ratio imaging Notes Reflist DEFAULTSORT Signal To Noise Statistic Category Statistical distance measures Category Statistical ratios Statistics stub ... more details
tRA is a baseball statistic used to measure the performance of a pitcher. Similar to defense independent pitching statistics FIP , tRA uses a mathematical formula to isolate the pitcher from his defense. Thus, tRA is a defense independent pitching statistics defense independent pitching statistic . Unlike FIP and Defense Independent ERA dERA , however, tRA takes into account batted ball type that is, line drives, fly balls, pop ups, and ground balls as well as strikeouts, walks, and home runs. Theory and method tRA was developed by Graham MacAree. According to StatCorner, The batter may strike out looking, strike out swinging, walk, be walked intentionally or be hit by a pitch. The hitter may also hit a line drive, a ground ball, an outfield fly, a popup, a bunt or a home run. These possibilities can be regarded as being governed by the pitcher, provided that there is a large enough sample size. tRA is built around knowing how many runs and outs each of these events are worth. ref http www.statcorner.com tRAabout.html ref tRA uses play by play data gathered from each Major League Baseball MLB season in order to give each possible outcome between a pitcher and a batter a linear weight. For example, in 2008, a line drive went for an out 30.5 of the time, while it had a run value of 0.384. ref http www.statcorner.com tRAabout.html ref These statistics are used to calculate expected outs xOuts and expected runs xRuns . Once these values are obtained, tRA can be converted to runs per nine innings by taking xRuns xOuts 27. ref http www.fangraphs.com blogs index.php what is tra ref Like other sabermetrics, tRA has alternate versions. tRA is compared to league average. For example, a tRA of 120 would mean that pitcher was 20 better than league average. References See Wikipedia Footnotes on how to create references using ref ref tags which will then appear here automatically references ... Interlanguage links DEFAULTSORT Tra Baseball Statistic Category Baseball statistics ... more details
math , of the statistic s , as a function ? of math x 1, ldots,x m math with specifications in math ... law of the parameter T , compatible with math boldsymbol x math , the statistic must obey some technical properties. Namely, a statistic s is said to be well behaved if it satisfies the following ... s the statistic is well defined for every value of ?, i.e. any sample specification math x 1, ldots ... sufficiency of the statistic S . Example For instance, for both the Bernoulli distribution with parameter p and the exponential distribution with parameter ? the statistic math sum i 1 m x i math is well ... of the X range. The statistic math s A max x 1, ldots,x m math is well behaved in this case. Analogously ... Well behaved statistic Uniform discrete math f x n 1 n I 1,2, ldots,n x math math s n max i x i math ... Statistics volume 26 year 1955 pages 139&ndash 142 DEFAULTSORT Well Behaved Statistic Categories ... more details
RPG A statistic or stat in role playing game s is a piece of data which represents a particular property philosophy aspect of a fictional character . That piece of data is usually a Units of measurement unit less integer or, in some cases, a dice pool set of dice . For some types of statistics, this value may be accompanied with a descriptive adjective, sometimes called a specialisation or aspect , that either describes how the character developed that particular score or an affinity for a particular use of that statistic like Specialisations in Ars Magica or Attribute Aspects in Aria Canticle of the Monomyth Aria . Most games divide their statistics into several categories. The set of categories actually used in a game system, as well as the precise statistics within each category, vary greatly. The most often used types of statistic include Attributes Attribute s describe to what extent a character possesses natural, in born characteristics common to all characters. Advantages and disadvantages Advantages and disadvantages are useful or problematic characteristics that are not common to all characters. Powers Power s represent unique or special qualities of the character. In game ... type of statistic, although they may use some other term for them, such as abilities . Derived ... of different categories, as well as within categories. The most common are Prerequisite Only if statistic A has a value of at least x , statistic B may exceed value y . Where y is often 0 number 0 ... . Limitation If statistic A has a value of at least x , then statistic B cannot exceed value y . This is the opposite of prerequisite . Only if statistic A has a value of at most x , statistic B may ... in the example to a certain maximum value no more than average . Bonus or base value If statistic A has a value of x , then the value of statistic B is increased by or starts at y . The term base ..., then the value of statistic C is a function mathematics function of x, y . Derived statistics ... more details
Expert subject Statistics date November 2008 Sinkov statistics , also known as log weight statistics , is a specialized field of statistics that was developed by Abraham Sinkov , while working for the small Signal Intelligence Service organization, the primary mission of which was to compile code s and cipher s for use by the United States Army U.S. Army . The mathematics involved include modular arithmetic , a bit of number theory , some linear algebra of two dimensions with Matrix mathematics matrices , some combinatorics , and a little statistics . ref http www.amazon.co.uk Elementary Cryptanalysis Mathematical Approach Library dp 0883856220 Amazon.com Elementary Cryptanalysis A Mathematical Approach ref Sinkov did not explain the theoretical underpinnings of his statistics, or characterized its Distribution mathematics distribution , nor did he give a decision procedure for accepting or rejecting candidate plaintext s on the basis of their S sub 1 sub scores. The situation becomes more difficult when comparing String computer science strings of different lengths because Sinkov does not explain how the distribution of his statistics changes with length, especially when applied to higher order grams. As for how to accept or reject a candidate plaintext, Sinkov simply said to try all possibilities and to pick the one with the highest S sub 1 sub value. Although the procedure works for some applications, it is inadequate for applications that require on line decisions. Furthermore, it is desirable to have a meaningful interpretation of the S sub 1 sub values. ref http 72.14.235.104 search?q cache 0xzLluovNNAJ www.csee.umbc.edu pub REPORTS cs 93 02.ps.Z sinkov statistic&hl en&gl my&ct clnk&cd 7 Statistical Techniques for Language Recognition An Introduction and Guide for Cryptanalysts ref References references Category Cryptographic attacks Category Computational linguistics Category Statistical natural language processing statistics stub ... more details
Wiktionary Ancillary administration Ancillary jurisdiction Ancillary statistic Ancillary data Ancillary relief Ancillary doctrine Diacritic , an ancillary glyph added to a letter disambig ... more details
Summary Two Tailed test, The shaded area is the probability. The points on the x axis are the value we get from the test statistic. Licensing cc by sa 2.5 ... more details
RISP may stand for Rhode Island State Police Runner In Scoring Position , a baseball statistic indicating batting average with runners in scoring position disambig ... more details
Wiktionary statistics Statistics is a mathematical science pertaining to the collection, analysis, interpretation, and presentation of data. Statistic may also refer to Statistic , the result of applying a statistical algorithm to a set of data Statistic role playing games , a piece of data which represents a particular aspect of a fictional character Statistics band , an American rock band Statism , a political system disambig de Statistik Begriffskl rung ka ... more details
unreferenced date September 2007 Obava lang uk , lang hu Dunk falva is a village located in the Mukachivskyi Raion Raion district in the Zakarpattia Oblast Oblast province in western Ukraine . It has a population of 990. This statistic is from http de.wikipedia.org wiki Rajon Mukatschewe Please update it with a statistic that tells what year the statistic is from. Thanks references Zakarpattia Oblast coord 48 31 N 22 48 E region UA type city display title Category Villages in Ukraine Category Zakarpattia Oblast Zakarpattia geo stub eo Obava hu Dunk falva ru uk ... more details
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