Subset pivotality

Another condition, similar to conditions SI to S3, which also guarantees that a stepdown method strongly controls the family wise error rate is the subset pivotality condition proposed by Westfall and Young (1993, page 42). Their original subset pivotality condition is given in terms of adjusted -values. For comparability with S1 to S3, we have paraphrased that condition here in terms of test statistics ... 

One should verify either conditions SI to S3 are satisfied, or subset pivotality is satisfied, before implementing a stepdown test for, otherwise, the stepdown test may not strongly control the familywise error rate. Such conditions are easier to check with a model that connects the observations with the parameters, but harder to check with a model (such as the randomization model) that only describes the distribution of the observations under the null hypotheses. Indeed, Westfall and Young (1993, page 91) cautioned that the randomization model does not guarantee that the subset pivotality condition holds. Outside the context of bioinformatics, there are in fact examples of methods that were in use at one time that violate... 

WHO/IPCS (1994, 1999) stated that a minimum data set considered adequate for an assessment will vary according to the purpose of the assessment. The major deficiencies in a toxicity database, other than those related to the pivotal study, which increase the uncertainty of the extrapolation should be recognized by the use of an additional UF. Since the quality and/or completeness of different databases vary, the additional UF will also vary. For example, a value of 1 would be applied to a database that was considered complete for the evaluation of the compound under consideration, but a factor of 1-100 might be necessary for limited databases. If minor deficiencies in the data exist with respect to quality, quantity, or omission, then an extra factor of 3 or 5 would be appropriate. An extra factor of 10 would be appropriate where major deficiencies in the data exist, e.g., a lack of chronic toxicity studies and reproductive toxicity studies. It was pointed out that inadequacies of the pivotal study could also be considered as a subset of inadequacies of the database and that the total factor for limitations of the pivotal study plus adequacy of the overall database should not exceed 100 since such a database is generally not acceptable for development of a TDI. 

The new subset is selected by first computing the SVD of the least squares matrix A. A rank estimate, f, is obtained by first determining the condition number of the matrix from the singular values and then deciding upon the number of parameters that must be eliminated to reduce k to an acceptable value. The QR scheme with column pivoting is then applied to... 

The lariat ethers comprise a subset of the polyether macrocycles, and are identified by their pendant chainsT They can be categorized as either N-pivot (19) or C-pivot (20), depending on which type of atom the chain is attached. As for their polyether parents, much of the focus on these macrocycles has been on complexation of alkali and alkaline earth metal ions. 

One of the milestone references for EDA is the comprehensive book by Tukey [1]. Tukey, in his work, aimed to create a data analysis framework where the visual examination of data sets, by means of statistically significant representations, plays the pivotal role to aid the analyst to formulate hypotheses that could be tested on new data sets. The stress on two concepts such as dynamic experimenting on data (e.g. evaluating the results on different subsets of a same data set, under different data-preprocessing conditions) and exhaustive visualization capabilities offers researchers the possibility to identify outliers, trends and patterns in data, upon which new theories and hypothesis can be built. Tukey s first view on EDA was based on robust and nonparametric statistical concepts such as the assessment of data by means of empirical distributions, hence the use of the so-called five-number summary of data (range extremes, median and quartiles), which led to one of his most known graphical tools for EDA, the box plot. 

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