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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]
An f-test pdf with d1 and d2 = 10, at a significance level of 0.05. (Red shaded region indicates the critical region) An F-test is a statistical test that compares variances. It's used to determine if the variances of two samples, or if the ratios of variances among multiple samples, are significantly different.
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 ...
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.
For example, Tukey's range test and Duncan's new multiple range test (MRT), in which the sample x 1, ..., x n is a sample of means and q is the basic test-statistic, can be used as post-hoc analysis to test between which two groups means there is a significant difference (pairwise comparisons) after rejecting the null hypothesis that all groups ...
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.
The concept of F-statistics was developed during the 1920s by the American geneticist Sewall Wright, [1] [2] who was interested in inbreeding in cattle. However, because complete dominance causes the phenotypes of homozygote dominants and heterozygotes to be the same, it was not until the advent of molecular genetics from the 1960s onwards that ...
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):