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On the other hand, the internally studentized residuals are in the range , where ν = n − m is the number of residual degrees of freedom. If t i represents the internally studentized residual, and again assuming that the errors are independent identically distributed Gaussian variables, then: [2]
In statistics and applications of statistics, normalization can have a range of meanings. [1] In the simplest cases, ... Studentized residual
In statistics, Studentization, named after William Sealy Gosset, who wrote under the pseudonym Student, is the adjustment consisting of division of a first-degree statistic derived from a sample, by a sample-based estimate of a population standard deviation.
In statistics, Grubbs's test or the Grubbs test (named after Frank E. Grubbs, who published the test in 1950 [1]), also known as the maximum normalized residual test or extreme studentized deviate test, is a test used to detect outliers in a univariate data set assumed to come from a normally distributed population.
In regression analysis, the distinction between errors and residuals is subtle and important, and leads to the concept of studentized residuals. Given an unobservable function that relates the independent variable to the dependent variable – say, a line – the deviations of the dependent variable observations from this function are the ...
The studentized bootstrap, also called bootstrap-t, is computed analogously to the standard confidence interval, but replaces the quantiles from the normal or student approximation by the quantiles from the bootstrap distribution of the Student's t-test (see Davison and Hinkley 1997, equ. 5.7 p. 194 and Efron and Tibshirani 1993 equ 12.22, p. 160):
Diagram showing the cumulative distribution function for the normal distribution with mean (μ) 0 and variance (σ 2) 1. These numerical values "68%, 95%, 99.7%" come from the cumulative distribution function of the normal distribution. The prediction interval for any standard score z corresponds numerically to (1 − (1 − Φ μ,σ 2 (z)) · 2).
In order to create the studentized range distribution for normal data, we first switch from the generic f X and F X to the distribution functions φ and Φ for the standard normal distribution, and change the variable r to s·q, where q is a fixed factor that re-scales r by scaling factor s: