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Z-score
In statistics, the standard score or ''z''-score is the number of standard deviations by which the value of a raw score (i.e., an observed value or data point) is above or below the mean value of what is being observed or measured. Raw scores above the mean have positive standard scores, while those below the mean have negative standard scores. It is calculated by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation. This process of converting a raw score into a standard score is called standardizing or normalizing (however, "normalizing" can refer to many types of ratios; see ''Normalization'' for more). Standard scores are most commonly called ''z''-scores; the two terms may be used interchangeably, as they are in this article. Other equivalent terms in use include z-value, z-statistic, normal score, standardized variable and pull in high energy physics. Computing a z-score requires knowledge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
T-statistic
In statistics, the ''t''-statistic is the ratio of the difference in a number’s estimated value from its assumed value to its standard error. It is used in hypothesis testing via Student's ''t''-test. The ''t''-statistic is used in a ''t''-test to determine whether to support or reject the null hypothesis. It is very similar to the z-score but with the difference that ''t''-statistic is used when the sample size is small or the population standard deviation is unknown. For example, the ''t''-statistic is used in estimating the population mean from a sampling distribution of sample means if the population standard deviation is unknown. It is also used along with p-value when running hypothesis tests where the p-value tells us what the odds are of the results to have happened. Definition and features Let \hat\beta be an estimator of parameter ''β'' in some statistical model. Then a ''t''-statistic for this parameter is any quantity of the form : t_ = \frac, where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Distribution
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f(x) = \frac e^\,. The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter \sigma^2 is the variance. The standard deviation of the distribution is (sigma). A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable—whose distribution c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normalization (statistics)
In statistics and applications of statistics, normalization can have a range of meanings. In the simplest cases, normalization of ratings means adjusting values measured on different scales to a notionally common scale, often prior to averaging. In more complicated cases, normalization may refer to more sophisticated adjustments where the intention is to bring the entire probability distributions of adjusted values into alignment. In the case of normalization of scores in educational assessment, there may be an intention to align distributions to a normal distribution. A different approach to normalization of probability distributions is quantile normalization, where the quantiles of the different measures are brought into alignment. In another usage in statistics, normalization refers to the creation of shifted and scaled versions of statistics, where the intention is that these normalized values allow the comparison of corresponding normalized values for different datasets in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Normal Distribution
''The'' is a grammatical article in English, denoting nouns that are already or about to be mentioned, under discussion, implied or otherwise presumed familiar to listeners, readers, or speakers. It is the definite article in English. ''The'' is the most frequently used word in the English language; studies and analyses of texts have found it to account for seven percent of all printed English-language words. It is derived from gendered articles in Old English which combined in Middle English and now has a single form used with nouns of any gender. The word can be used with both singular and plural nouns, and with a noun that starts with any letter. This is different from many other languages, which have different forms of the definite article for different genders or numbers. Pronunciation In most dialects, "the" is pronounced as (with the voiced dental fricative followed by a schwa) when followed by a consonant sound, and as (homophone of the archaic pronoun ''thee' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Normal Deviate
Standard may refer to: Symbols * Colours, standards and guidons, kinds of military signs * Standard (emblem), a type of a large symbol or emblem used for identification Norms, conventions or requirements * Standard (metrology), an object that bears a defined relationship to a unit of measure used for calibration of measuring devices * Standard (timber unit), an obsolete measure of timber used in trade * Breed standard (also called bench standard), in animal fancy and animal husbandry * BioCompute Standard, a standard for next generation sequencing * ''De facto'' standard, product or system with market dominance * Gold standard, a monetary system based on gold; also used metaphorically for the best of several options, against which the others are measured * Internet Standard, a specification ratified as an open standard by the Internet Engineering Task Force * Learning standards, standards applied to education content * Standard displacement, a naval term describing the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Omega Ratio
The Omega ratio is a risk-return performance measure of an investment asset, portfolio, or strategy. It was devised by Con Keating and William F. Shadwick in 2002 and is defined as the probability weighted ratio of gains versus losses for some threshold return target. The ratio is an alternative for the widely used Sharpe ratio and is based on information the Sharpe ratio discards. Omega is calculated by creating a partition in the cumulative return distribution in order to create an area of losses and an area for gains relative to this threshold. The ratio is calculated as: : \Omega(\theta) = \frac, where F is the cumulative probability distribution function of the returns and \theta is the target return threshold defining what is considered a gain versus a loss. A larger ratio indicates that the asset provides more gains relative to losses for some threshold \theta and so would be preferred by an investor. When \theta is set to zero the gain-loss-ratio by Bernardo and Led ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mahalanobis Distance
The Mahalanobis distance is a distance measure, measure of the distance between a point P and a probability distribution D, introduced by Prasanta Chandra Mahalanobis, P. C. Mahalanobis in 1936. The mathematical details of Mahalanobis distance first appeared in the ''Journal of The Asiatic Society of Bengal'' in 1936. Mahalanobis's definition was prompted by the problem of similarity measure, identifying the similarities of skulls based on measurements (the earliest work related to similarities of skulls are from 1922 and another later work is from 1927). Raj Chandra Bose, R.C. Bose later obtained the sampling distribution of Mahalanobis distance, under the assumption of equal dispersion. It is a multivariate generalization of the square of the standard score z=(x- \mu)/\sigma: how many standard deviations away P is from the mean of D. This distance is zero for P at the mean of D and grows as P moves away from the mean along each principal component axis. If each of these axes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error Function
In mathematics, the error function (also called the Gauss error function), often denoted by , is a function \mathrm: \mathbb \to \mathbb defined as: \operatorname z = \frac\int_0^z e^\,\mathrm dt. The integral here is a complex Contour integration, contour integral which is path-independent because \exp(-t^2) is Holomorphic function, holomorphic on the whole complex plane \mathbb. In many applications, the function argument is a real number, in which case the function value is also real. In some old texts, the error function is defined without the factor of \frac. This nonelementary integral is a sigmoid function, sigmoid function that occurs often in probability, statistics, and partial differential equations. In statistics, for non-negative real values of , the error function has the following interpretation: for a real random variable that is normal distribution, normally distributed with mean 0 and standard deviation \frac, is the probability that falls in the range . ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coefficient Of Variation
In probability theory and statistics, the coefficient of variation (CV), also known as normalized root-mean-square deviation (NRMSD), percent RMS, and relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is defined as the ratio of the standard deviation \sigma to the mean \mu (or its absolute value, , and often expressed as a percentage ("%RSD"). The CV or RSD is widely used in analytical chemistry to express the precision and repeatability of an assay. It is also commonly used in fields such as engineering or physics when doing quality assurance studies and ANOVA gauge R&R, by economists and investors in economic models, in epidemiology, and in psychology/neuroscience. Definition The coefficient of variation (CV) is defined as the ratio of the standard deviation \sigma to the mean \mu, CV = \frac. It shows the extent of variability in relation to the mean of the population. The coefficien ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sample Mean
The sample mean (sample average) or empirical mean (empirical average), and the sample covariance or empirical covariance are statistics computed from a sample of data on one or more random variables. The sample mean is the average value (or mean value) of a sample of numbers taken from a larger population of numbers, where "population" indicates not number of people but the entirety of relevant data, whether collected or not. A sample of 40 companies' sales from the Fortune 500 might be used for convenience instead of looking at the population, all 500 companies' sales. The sample mean is used as an estimator for the population mean, the average value in the entire population, where the estimate is more likely to be close to the population mean if the sample is large and representative. The reliability of the sample mean is estimated using the standard error, which in turn is calculated using the variance of the sample. If the sample is random, the standard error falls with th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
