Search results
Results from the WOW.Com Content Network
In statistics, a sequence of random variables is homoscedastic (/ ˌ h oʊ m oʊ s k ə ˈ d æ s t ɪ k /) if all its random variables have the same finite variance; this is also known as homogeneity of variance. The complementary notion is called heteroscedasticity, also known as heterogeneity of variance.
The positive predictive value (PPV), or precision, is defined as = + = where a "true positive" is the event that the test makes a positive prediction, and the subject has a positive result under the gold standard, and a "false positive" is the event that the test makes a positive prediction, and the subject has a negative result under the gold standard.
An equivalent definition of entropy is the expected value of the self-information of a variable. [1] Two bits of entropy: In the case of two fair coin tosses, the information entropy in bits is the base-2 logarithm of the number of possible outcomes — with two coins there are four possible outcomes, and two bits of entropy. Generally ...
Simpson's paradox has been used to illustrate the kind of misleading results that the misuse of statistics can generate. [7] [8] Edward H. Simpson first described this phenomenon in a technical paper in 1951, [9] but the statisticians Karl Pearson (in 1899 [10]) and Udny Yule (in 1903 [11]) had mentioned similar effects
Confidence bands can be constructed around estimates of the empirical distribution function.Simple theory allows the construction of point-wise confidence intervals, but it is also possible to construct a simultaneous confidence band for the cumulative distribution function as a whole by inverting the Kolmogorov-Smirnov test, or by using non-parametric likelihood methods.
Predictive modelling uses statistics to predict outcomes. [1] Most often the event one wants to predict is in the future, but predictive modelling can be applied to any type of unknown event, regardless of when it occurred. For example, predictive models are often used to detect crimes and identify suspects, after the crime has taken place. [2]
The fields of mathematics, probability, and statistics use formal definitions of randomness, typically assuming that there is some 'objective' probability distribution. In statistics, a random variable is an assignment of a numerical value to each possible outcome of an event space. This association facilitates the identification and the ...
In frequentist statistics, the likelihood function is itself a statistic that summarizes a single sample from a population, whose calculated value depends on a choice of several parameters θ 1... θ p, where p is the count of parameters in some already-selected statistical model. The value of the likelihood serves as a figure of merit for the ...