Sources of variability

Variability in toxicity measurements is recognised at every level of biological organisation, from the subcellular (Ratner and Fairbrother, 1991) to the community level (Taub el al., 1989). Differences in the response of individuals to pollutants may be due to environmental or genetic factors or a combination of the two (Hoffmann and Parsons, 1991). The total variability in the response of an organism to a chemical (Vp) can be represented by the equation  

Forbes and DePledge (1992) add a third consideration, that of experimental error. Our experience of ring-testing would tend to support this as an important consideration there is evidence to indicate that greater precision is achieved by the more experienced laboratories and that closely defined protocols, such as the Microtox example mentioned earlier, are associated with greater precision than those where there is a high degree of latitude in the test protocol (Whitehouse et al., 1996). 

Clearly there can come a point when estimates of toxicity are so imprecise or subject to bias that any conclusions drawn from them are meaningless. At the same time, it would be inappropriate to devote resources to constraining variability unless it was going to benefit decision-making in risk assessment. 

A complete absence of any constraint on variability would seem to be irresponsible. The development of test protocols is an important contribution to constraining variability because it limits the latitude for systematic variation between operators. However, the resulting variability within or between laboratories 

This is illustrated in Table 6.1. Note that the expected value, which is a measure of central tendency or population mean, of a linear model is the sum of the expectations, so that for Eq. (6.1) 

Assuming the S s across subjects sum to zero and sy s within a subject sum to zero, then 

Notice the difference between E(Y), the expected value for an individual randomly sampled from Y, and E(Y Si), the expected value for a particular individual. If the expected value of individuals in their most general sense is of interest, then E(Y) is of interest. But as soon as the discussion moves to particular subjects, then E(Y Si) becomes of interest. 

The generic equation for the variance of a linear combination of random variables is 

Since the variance of p is zero, i.e., the population mean is a constant, then the variability of Y is 

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The precision for an analysis in which the only source of variability is the analysis of replicate samples. 

Precision is a measure of the spread of data about a central value and may be expressed as the range, the standard deviation, or the variance. Precision is commonly divided into two categories repeatability and reproducibility. Repeatability is the precision obtained when all measurements are made by the same analyst during a single period of laboratory work, using the same solutions and equipment. Reproducibility, on the other hand, is the precision obtained under any other set of conditions, including that between analysts, or between laboratory sessions for a single analyst. Since reproducibility includes additional sources of variability, the reproducibility of an analysis can be no better than its repeatability. 

Proofing materials have many of the same sources of variability as film, plus the added problem of registering, ie, accurately overlaying, the different colored layers. The printing plate must be exposed precisely to hold all that is discernible in the films. The accuracy of the exposure is critical because the plate must retain all the information contained in the films for faithful reproduction on the press. 

Repetitive, irregular or non-symmetrical features require greater process control and complex set-up or tooling requirements. This can be an added source of variability. 

Post-processing, e.g. machining (for dimensional restoration) or shot peening (remove residual stresses), can be an added source of variability. 

Electrical Stability of Emuisions. The electrical stability test indicates the stability of emulsions of water in oil. The emulsion tester consists of a reliable circuit using a source of variable AC current (or DC current in portable units) connected to strip electrodes. The voltage imposed across the electrodes can be increased until a predetermined amount of current flows through the mud emulsion-breakdown point. Relative stability is indicated as the voltage at the breakdown point. 

Dealkalization/softening by SAC(H)/BX/blend/Degassing This process is very suitable for water sources of variable hardness and alkalinity levels and ratios. It passes a portion of the RW through the SAC (H) and the balance through a BX (the process is called split-stream dealkalization and softening). The first vessel removes all cations, producing mineral acidity, while the BX replaces all... 

Larkin, P.J. Skowcroft, W.R. (1981). Somaclonal variation - a novel source of variability from cell cultures for plant improvement. Theoretical and Applied Genetics, 60, 197-214. 

In addition to the Ford field-retrieval study, NHTSA has carried out further studies of aging from tires retrieved from Phoenix [8]. Analysis in this chapter will be Umited to tires SUV/Minivan-A, -B, and -C and Large Car-C from the Ford study. Tire sizes and maximum inflation pressures for these tires are reported in Table 34.2. The analysis will focus on extracting accurate rate data from the field data. Of key importance is developing an understanding regarding the sources of variability in field aging. 

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.

Unlike non-radiometric methods of analysis, uncertainty modelling in NAA is facilitated by the existence of counting statistics, although in principle an additional source of uncertainty, because this parameter is instantly available from each measurement. If the method is in a state of statistical control, and the counting statistics are small, the major source of variability additional to analytical uncertainty can be attributed to sample inhomogeneity (Becker 1993). In other words, in Equation (2.1) ... 

The objective of sediment and water sampling is to obtain reliable information about the behavior of agrochemicals applied to paddy fields. Errors or variability of results can occur randomly or be due to bias. The two major sources of variability are sediment body or water body variability and measurement variability . For the former, a statistical approach is required the latter can be divided into sampling variability, handling, shipping and preparation variability, subsampling variability, laboratory analysis variability, and between-batch variability. ... 

PK synthases, alternatively, have significantly more regulated biosyntheses with regard to monomer choice. In most cases, elongation monomers are restricted to malonate and methylmalonate starter units. The major source of variability within these synthases lies in... 

Heterogeneous conditions both in terms of hydrodynamics and composition prevails in the GI tract. Parameters such as D, Cs, V, and h are influenced by the conditions in the GI tract which change with time. Thus, time dependent rate coefficients govern the dissolution process under in vivo conditions. One of the major sources of variability for poorly soluble drugs can be associated with the time dependent character of the rate coefficient, which governs drug dissolution under in vivo conditions. 

It must be noted that although the calibration cell is very different from the adsorption cell [Fig. 18, cells (1) and (2)3, the heat capacity of both cells is not very different, as the similar values of the time constant of the calorimeter containing one cell or the other indeed show (350 sec in the case of the calibration cell and 400 sec in the case of the adsorption cell) (55). This is explained by the fact that in both eases, the calorimeter cell is almost completely filled with a metal. However, the glass tube which is immersed in the calorimeter cell and the pressure changes which occur in the course of the adsorption experiments may be the sources of variable thermal leaks. The importance of these leaks was appreciated by means of the following control experiments. 

Removal of the extraneous source of variability did indeed reduce the between-flasks variance to a level that is now explainable (in the statistical sense) by the underlying random variations attributable to the within-flask variability. 

Another source of variability, which can have still different characteristics, is comprised of the interaction of any of the above factors with a nonlinearity anywhere in the system. These nonlinearities could consist of nonlinearity in the detector, in the spectrometer s electronics, optical effects such as changes in the field of view, and so on. Many of these nonlinearities are likely to be idiosyncratic to the cause, and would have to be characterized individually and also analyzed on a case-by-case basis. 

All those discussions, however, were based on considerations of the effects of multiple sources of variability, but on only a single variable. In order to compare Statistics with Chemometrics, we need to enter the multivariate domain, and so we ask the question Can ANOVA be calculated on multivariate data The answer to this question, as our long-time readers will undoubtedly guess, is of course, otherwise we wouldn t have brought it up ... 

Use could be made of aerodynamic effects such as Bernouille or Magnus effects to generate quite high forces. Water could also be used as a source of variable mass, filling containers which can change the balance of various hinged parts of a sculpture. 

F. Both the age of the test animal and the application site (saddle of the back versus flank) can markedly alter test outcome. Both of these factors are also operative in humans, of course (Mathias, 1983), but in dermal irritation tests, the objective is to remove all such sources of variability. In general, as an animal ages, sensitivity to irritation decreases. For the dermal test, the skin middle of the back (other than directly over the spine) tends to be thicker (and therefore less sensitive to irritations) than that on the flanks. 

NMR-assay of meclizine (I) and methaqualone (II), besides a number of other potent hypnotics and their corresponding mixtures have been successfully carried out using an external standardization procedure reported. It is, however, interesting to observe that additional sources of variability are usually incorporated into an assay employing external standardization, and the same has been duly shown in the results thus obtained i.e., a large coefficient of variation to the extent of 4% achieved. 

Early optimism about the possibility of in vitro-in vivo correlation was tempered by the need for a performance test that would yield reproducible results (10). Even though not necessarily correlated to bioavailability, dissolution requirements were seen as useful in controlling variables in formulation or processing. Thus, from the start, sources of variability in the results were seen as factors to be minimized in any proposed compendial method. 

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