|
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] |
Probability Theory
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms of probability, axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure (mathematics), measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event (probability theory), event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of determinism, non-deterministic or uncertain processes or measured Quantity, quantities that may either be single occurrences or evolve over time in a random fashion). Although it is no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Psychology
Psychology is the scientific study of mind and behavior. Its subject matter includes the behavior of humans and nonhumans, both consciousness, conscious and Unconscious mind, unconscious phenomena, and mental processes such as thoughts, feelings, and motivation, motives. Psychology is an academic discipline of immense scope, crossing the boundaries between the Natural science, natural and social sciences. Biological psychologists seek an understanding of the Emergence, emergent properties of brains, linking the discipline to neuroscience. As social scientists, psychologists aim to understand the behavior of individuals and groups.Hockenbury & Hockenbury. Psychology. Worth Publishers, 2010. A professional practitioner or researcher involved in the discipline is called a psychologist. Some psychologists can also be classified as Behavioural sciences, behavioral or Cognitive science, cognitive scientists. Some psychologists attempt to understand the role of mental functions in i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normally Distributed
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real number, real-valued random variable. The general form of its probability density function is f(x) = \frac e^\,. The parameter is the Mean#Mean of a probability distribution, mean or expected value, expectation of the distribution (and also its median and mode (statistics), 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 science, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biased Estimator
In statistics, the bias of an estimator (or bias function) is the difference between this estimator's expected value and the true value of the parameter being estimated. An estimator or decision rule with zero bias is called ''unbiased''. In statistics, "bias" is an property of an estimator. Bias is a distinct concept from consistency: consistent estimators converge in probability to the true value of the parameter, but may be biased or unbiased (see bias versus consistency for more). All else being equal, an unbiased estimator is preferable to a biased estimator, although in practice, biased estimators (with generally small bias) are frequently used. When a biased estimator is used, bounds of the bias are calculated. A biased estimator may be used for various reasons: because an unbiased estimator does not exist without further assumptions about a population; because an estimator is difficult to compute (as in unbiased estimation of standard deviation); because a biased estima ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Deviation
In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its Expected value, mean. A low standard Deviation (statistics), deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. The standard deviation is commonly used in the determination of what constitutes an outlier and what does not. Standard deviation may be abbreviated SD or std dev, and is most commonly represented in mathematical texts and equations by the lowercase Greek alphabet, Greek letter Sigma, σ (sigma), for the population standard deviation, or the Latin script, Latin letter ''s'', for the sample standard deviation. The standard deviation of a random variable, Sample (statistics), sample, statistical population, data set, or probability distribution is the square root of its variance. (For a finite population, v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Population Standard Deviation
In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its mean. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. The standard deviation is commonly used in the determination of what constitutes an outlier and what does not. Standard deviation may be abbreviated SD or std dev, and is most commonly represented in mathematical texts and equations by the lowercase Greek letter σ (sigma), for the population standard deviation, or the Latin letter '' s'', for the sample standard deviation. The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance. (For a finite population, variance is the average of the squared deviations from the mean.) A useful property of the stan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Likelihood Estimation
In statistics, maximum likelihood estimation (MLE) is a method of estimation theory, estimating the Statistical parameter, parameters of an assumed probability distribution, given some observed data. This is achieved by Mathematical optimization, maximizing a likelihood function so that, under the assumed statistical model, the Realization (probability), observed data is most probable. The point estimate, point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference. If the likelihood function is Differentiable function, differentiable, the derivative test for finding maxima can be applied. In some cases, the first-order conditions of the likelihood function can be solved analytically; for instance, the ordinary least squares estimator for a linear regression model maximizes the likelihood when ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Midhinge
In statistics, the midhinge () is the average of the first and third quartiles and is thus a measure of location. Equivalently, it is the 25% trimmed mid-range or 25% midsummary; it is an L-estimator. The midhinge is defined as \begin \operatorname(X) &= \overline \\ &= \frac \\ &= \frac \\ &= M_(X). \end The midhinge is related to the interquartile range (), the difference of the third and first quartiles (i.e. ), which is a measure of statistical dispersion. The two are complementary in sense that if one knows the midhinge and the , one can find the first and third quartiles. The use of the term ''hinge'' for the lower or upper quartiles derives from John Tukey's work on exploratory data analysis in the late 1970s,Tukey, J. W. (1977) ''Exploratory Data Analysis'', Addison-Wesley. and ''midhinge'' is a fairly modern term dating from around that time. The midhinge is slightly simpler to calculate than the trimean (), which originated in the same context and equals the avera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interquartile Range
In descriptive statistics, the interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the data. The IQR may also be called the midspread, middle 50%, fourth spread, or H‑spread. It is defined as the difference between the 75th and 25th percentiles of the data. To calculate the IQR, the data set is divided into quartiles, or four rank-ordered even parts via linear interpolation. These quartiles are denoted by ''Q''1 (also called the lower quartile), ''Q''2 (the median), and ''Q''3 (also called the upper quartile). The lower quartile corresponds with the 25th percentile and the upper quartile corresponds with the 75th percentile, so IQR = ''Q''3 − ''Q''1. The IQR is an example of a trimmed estimator, defined as the 25% trimmed range, which enhances the accuracy of dataset statistics by dropping lower contribution, outlying points. It is also used as a robust measure of scale It can be clearly visualized by the box on a box plot. Use ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quartile Coefficient Of Dispersion
In statistics, the quartile coefficient of dispersion () is a descriptive statistic which measures dispersion and is used to make comparisons within and between data sets. Since it is based on quantile information, it is less sensitive to outliers than measures such as the coefficient of variation. As such, it is one of several robust measures of scale. The statistic is easily computed using the first and third quartiles, and , respectively) for each data set. The quartile coefficient of dispersion is the ratio of half of the interquartile range () to the average of the quartiles (the midhinge):\begin \mathrm &= \frac \\ &= . \end Example Consider the following two data sets: : ''A'' = :: ''n'' = 7, range = 12, mean = 8, median = 8, ''Q''1 = 4, ''Q''3 = 12, quartile coefficient of dispersion = 0.5 : ''B'' = :: ''n'' = 7, range = 1.2, mean = 2.4, median = 2.4, ''Q''1 = 2, ''Q''3 = 2.9, quartile coefficient of dispersion = 0.18 The quartile coefficient of dispersion of da ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Log-normal
In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normal distribution, normally distributed. Thus, if the random variable is log-normally distributed, then has a normal distribution. Equivalently, if has a normal distribution, then the exponential function of , , has a log-normal distribution. A random variable which is log-normally distributed takes only positive real values. It is a convenient and useful model for measurements in exact and engineering sciences, as well as medicine, economics and other topics (e.g., energies, concentrations, lengths, prices of financial instruments, and other metrics). The distribution is occasionally referred to as the Galton distribution or Galton's distribution, after Francis Galton. The log-normal distribution has also been associated with other names, such as Donald MacAlister#log-normal, McAlister, Gibrat's law, Gibrat and Cobb–Douglas. A l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kelvin
The kelvin (symbol: K) is the base unit for temperature in the International System of Units (SI). The Kelvin scale is an absolute temperature scale that starts at the lowest possible temperature (absolute zero), taken to be 0 K. By definition, the Celsius scale (symbol °C) and the Kelvin scale have the exact same magnitude; that is, a rise of 1 K is equal to a rise of 1 °C and vice versa, and any temperature in degrees Celsius can be converted to kelvin by adding 273.15. The 19th century British scientist Lord Kelvin first developed and proposed the scale. It was often called the "absolute Celsius" scale in the early 20th century. The kelvin was formally added to the International System of Units in 1954, defining 273.16 K to be the triple point of water. The Celsius, Fahrenheit, and Rankine scales were redefined in terms of the Kelvin scale using this definition. The 2019 revision of the SI now defines the kelvin in terms of energy by setting the Bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
