Variation, statistical selection

Gaylor, D. W, R. L. Suber, G. L. Wolff, and J. A. Crowell. 1987. Statistical variation of selected clinical pathological and biochemical measurements in rodents. Proceedings of the Society for Experimental Biology and Medicine 185 361-367. 

Ulusay, R., Turrell, K. and Ider, M.H. 1994. Prediction of engineering properties of a selected litharenite sandstone from its petrographic characteristics using correlation and multi-variate statistical techniques. Engineering Geology, 38, 135-157. 

Selection of appropriate time intei vals for increment extractions relates to property variation (inhomogeneity) within material flow streams. Ten minute extraction intei vals are generally adequate to obtain suitably representative samples from material flows under practical circumstances. Precise determination of extraction intei vals consistent with individual apphcations can be calculatedthrough autocorrelation of historical sampling data, a statistical method described in references (Gy, Pitard). 

Because X-ray counting rates are relatively low, it typically requires 100 seconds or more to accumulate adequate counting statistics for a quantitative analysis. As a result, the usual strategy in applying electron probe microanalysis is to make quantitative measurements at a limited collection of points. Specific analysis locations are selected with the aid of a rapid imaging technique, such as an SEM image prepared with backscattered electrons, which are sensitive to compositional variations, or with the associated optical microscope. 

Attention must be paid to the specific technical problems posed by measuring flow in industrial ventilating systems, such as high turbulence level and long time-variation of mean velocity. The LDA measurement conditions (statistically sufficient number of LDA data, suitably long duration of LDA measurements for recognition of long-term phenomena) must be carefully selected for an appropriate treatment of these problems. 

Figure 21.3 Modeling and simulation in the general context of the study of xenobiot-ics. The network of signals and regulatory pathways, sources of variability, and multistep regulation that are involved in this problem is shown together with its main components. It is important to realize how between-subject and between-event variation must be addressed in a model of the system that is not purely structural, but also statistical. The power of model-based data analysis is to elucidate the (main) subsystems and their putative role in overall regulation, at a variety of life stages, species, and functional (cell to organismal) levels. Images have been selected for illustrative purposes only. See color plate.

The homologues of the methylated non-ionic EO/PO surfactant blend were ionised as [M + NH4]+ ions. A mixture of these isomeric compounds, which could not be defined by their structure because separation was impossible, was ionised with its [M + NH4]+ ion at m/z 568. The mixture of different ions hidden behind this defined m/z ratio was submitted to fragmentation by the application of APCI—FIA—MS— MS(+). The product ion spectrum of the selected isomer as shown with its structure in Fig. 2.9.23 is presented together with the interpretation of the fragmentation behaviour of the isomer. One of the main difficulties that complicated the determination of the structure was that one EO unit in the ethoxylate chain in combination with an additional methylene group in the alkyl chain is equivalent to one PO unit in the ethoxylate chain (cf. table of structural combinations). The overview spectrum of the blend was complex because of this variation in homologues and isomers. The product ion spectrum was also complex, because product ions obtained by FIA from isomers with different EO/PO sequences could be observed complicating the spectrum. The statistical variations of the EO and PO units in the ethoxylate chain of the parent ions of isomers with m/z 568 under CID... 

In the problem of selecting a distribution for a ID model of variation, there are 2 kinds of variables, namely, 1) the data, which we know and 2) distribution parameters, which will be assigned values based on the data. Here we will often follow statistical terminology by using the term estimation (of parameters) instead of fitting. In statistical terminology, the values assigned to distribution parameters are termed estimates the expressions used to compute estimates are estimators. ... 

Data used to describe variation are ideally representative of some population of risk assessment interest. Representativeness was a focus of an earlier workshop on selection of distributions (USEPA 1998). The role of problem formulation is emphasized. In case of representativeness issues, some adjustment of the data may be possible, perhaps based on a mechanistic or statistical model. Statistical random-effects models may be useful in situations where the model includes distributions among as well as within populations. However, simple approaches may be adequate, depending on the assessment tier, such as an attempt to characterize quantitatively the consequences of assuming the data to be representative. 

There is a tendency among control and statistics theorists to refer to trial and error as one-variable-at-a-time (OVAT). The results are often treated as if only one variable were controlled at a time. The usual trial, however, involves variation in more than one controlled variable and almost always includes uncontrolled variations. The trial-and-error method is fortunately seldom a random process. The starting cycle is usually based on manufacturers specifications or experience with a similar process and/or material. Trial variations on the starting cycle are then made, sequentially or in parallel, until an acceptable cycle is found or until funds and/or time run out. The best cycle found, in terms of one or a combination of product qualities, is then selected. Because no process can be repeated exactly in all cases, good cure cycles include some flexibility, called a process window, based on equipment limitations and/or experience. 

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