Externally studentized residual

Upper bounds for externally studentized residuals have not been developed. Externally studentized residuals are distributed as a Student s t-distribution with n—p—1 degrees of freedom. Thus in the case of a single outlier observation, a quick test would be to compare the value of the external studentized residual to the appropriate t-distribution value, although as Cook and Weisberg (1999) point out, because of issues with multiplicity a more appropriate comparison would be Student s t-distribution with a/n critical value and n—p—1 degrees of freedom. In general, however, a yardstick of 2 or 2.5 is usually used as a critical value to flag suspect observations. 

Classical statistical tests can be applied mainly to validate regression models that are linear with respect to the model parameters. The most common empirical models used in EXDE are linear models (main effect models), linear plus interactions models, and quadratic models. They all are linear with respect to the p>arameters. The most useful of these (in DOE context) are 1) t-tests for testing the significance of the individual terms of the model, 2) the lack-of-fit test for testing the model adequacy, and 3) outlier tests based on so-called externally studentized residuals, see e.g. (Neter et. al., 1996). 

The externally studentized residual is also termed jackknifed residual. 

The externally studentized residual is scale invariant. Com-monly, an outlier is detected if tj- > 2. 

Hence, raw residuals are often standardized by some quantity, usually its standard deviation, to account for the unequal variance of the residuals. If the estimate of the standard deviation is based on the observation in question the method is called internal studentization, but if the observation is not included in the estimate of the standard deviation, then the method is called external studentization. Studentized residuals can be estimated... 

Other analysts prefer the second of the four, the studentized residual (the externalized t ratio ). 

The mechanism can only be retained if a base very much better than water is present at the enzyme active site to deprotonate the Zn(OH2)2+ species. In fact, the structure determination reveals a histidine residue with its side chain positioned approximately halfway down the -15 A-deep cleft in the protein structure within which the Zn site is located. This arrangement could act as a proton shuttle between the Zn(OH2)2+ and external solvent water, possibly via another two water molecules also found within the cleft. As a consequence, the enhancement of ligand acidity by Zn11 is more important in the kinetic than the equilibrium sense (taken from http //www.chem.uwa.edu.aU/enrolled students/BIC sect4/sect4.2.htmll. 

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