Pseudo standard error

Lenth (1989) referred to this estimator 67. as the pseudo standard error of the estimators Pi. He recommended using the test statistic P, / i to test the null hypothesis Pi = 0 and recommended using the quantity (Pi — Pi)/aL to construct a confidence interval for p,. 

We now discuss what it means for a method of analysis to be robust or adaptive . Lenth s method is adaptive because of the two-stage procedure used to obtain the pseudo standard error. The pseudo standard error i is computed from... 

Consider now robustness. If the estimators A are computed from independent response variables then, as noted in Section 1, the estimators have equal variances and are usually at least approximately normal. Thus the usual assumptions, that estimators are normally distributed with equal variances, are approximately valid and we say that there is inherent robustness to these assumptions. However, the notion of robust methods of analysis for orthogonal saturated designs refers to something more. When making inferences about any effect A, all of the other effects At (k i) are regarded as nuisance parameters and robust means that the inference procedures work well, even when several of the effects ft are large in absolute value. Lenth s method is robust because the pseudo standard error is based on the median absolute estimate and hence is not affected by a few large absolute effect estimates. The method would still be robust even if one used the initial estimate 6 of op, rather than the adaptive estimator 6L, for the same reason. 

In summary, Lenth s method is robust in the sense that it maintains good power as long as there is effect sparsity and it is adaptive to the degree of effect sparsity, using a pseudo standard error that attempts to involve only the estimates of negligible effects. 

Pseudo First-Order Hydrolysis Rate Constants with Standard Errors [(k + SE) x 10-2] in Aqueous Buffer Solutions for 12 Sulfonylurea Herbicides at Different pHs and Temperatures. 

It has been suggested that the number of degrees of freedom used in the calculation of RMSEC and t i l/i is determined by the approach of pseudo degrees of freedom proposed by Van der Voet. Other estimates of the standard error of prediction have been proposed. A quite popular and user-friendly one, although with limited value for some data, is eontained in the Unscrambler software (CAMO ASA, Norway). 

When the sin / method (Sec. 16-4) is used, some specimens that have been plastically deformed in the region examined yield values of df that vary with sin in an oscillatory manner, rather than linearly [16.33, 16.34, 16.26]. These oscillations in di are not fully understood. They must be caused by a system of micro-stresses more complex than pseudo-macrostress, because pseudo-macrostress, like true macrostress, yields a linear variation of di with sin ij/. When oscillations occur, the standard two-exposure method of stress measurement (Sec. 16.4) can be seriously in error.)... 

First, using a DVM, check the potential difference between the WE and the RE. An unexpected potential shift in the current response is likely due to the reference electrode. If a problem with the RE is suspected, run a voltammogram with a pseudo-reference (e.g. Ag or Pt wire). To test the faulty RE, place it in an electrolyte and measure its potential against a commercial RE of the same type. The potential difference between them should be less than 5 mV and stable. Major sources of error in a RE can come from either the electrode being stored in the wrong solution or the presence of a bubble in the electrode. If in doubt, empty the solution from the electrode and replace with fresh solution. A freshly made RE needs time to equilibrate, so store it in the same solution as the internal one and check its potential against a commercial RE. After 24 h, the difference should be less than 5 mV and stable. If it is not, then dismantle the electrode and recondition it (e.g. for an SCE ensure that the internal solution is saturated in KCl). With non-aqueous solvents, it is not advised to use a RE with an aqueous internal solution instead, use a quasi-RE with an internal redox standard, such as ferrocene. 

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