Validity statistics

It should be recognized that the total volume of wastewater as well as the chemical analyses iadicating the organic and inorganic components are requited, backed by statistical validity, before the conceptualizing of the overall treatment plant design can begia. The basic parameters ia wastewater characterization are summarized ia Table 2. 

Suppose we have two methods of preparing some product and we wish to see which treatment is best. When there are only two treatments, then the sampling analysis discussed in the section Two-Population Test of Hypothesis for Means can be used to deduce if the means of the two treatments differ significantly. When there are more treatments, the analysis is more detailed. Suppose the experimental results are arranged as shown in the table several measurements for each treatment. The goal is to see if the treatments differ significantly from each other that is, whether their means are different when the samples have the same variance. The hypothesis is that the treatments are all the same, and the null hypothesis is that they are different. The statistical validity of the hypothesis is determined by an analysis of variance. 

Pitot-static traverse The set positions of a Prandtl tube m a duct run required to provide a statistically valid set of readings, A series of measurements of the torn 1 and static pressure taken across an area of a duct to determine the air veloc-it> at that point. The sampling distance should be at least 7.5 times the diameter of the duct away from any disturbances of air flow. 

An appropriate sampling program is critical in the conduct of a hcaltli risk assessment. This topic could arguably be part of the exposure assessment, but it has been placed within hazard identification because, if the degree of contamination is small, no further work may be necessary. Not only is it important that samples be collected in a random or representative manner, but the number of samples must be sufficient to conduct a statistically valid analysis. The number needed to insure statistical validity will be dictated by the variability between the results. The larger the variance, tlic greater the number of samples needed to define tire problem, ... 

This value is identified in F tables for the corresponding dfc and dfs. For example, for the data in Figure 11.13, F = 7.26 for df=6, 10. To be significant at the 95% level of confidence (5% chance that this F actually is not significant), the value of F for df = 6, 10 needs to be > 4.06. In this case, since F is greater than this value there is statistical validation for usage of the most complex model. The data should then be fit to a four-parameter logistic function to yield a dose-response curve. 

The data in the training set are used to derive the calibration which we use on the spectra of unknown samples (i.e. samples of unknown composition) to predict the concentrations in those samples. In order for the calibration to be valid, the data in the training set which is used to find the calibration must meet certain requirements. Basically, the training set must contain data which, as a group, are representative, in all ways, of the unknown samples on which the analysis will be used. A statistician would express this requirement by saying, "The training set must be a statistically valid sample of the population... 

The second factor is the temporal variation in concentrations in different ecosystem compartments. For example, sediments and prey fish exhibit less temporal variation in mercuiy concentration than do air or water, and thus statistically valid estimates of their status can be collected with less frequent monitoring (e.g., annual sampling for prey fish vs. daily or hourly sampling for atmospheric concentrations of mercury). 

To obtain a value for the dimensions of an irregular particle, several measurement approaches can be used Martin s diameter (defined as the length of a line that bisects the particle image), Feret s diameter (or end-to-end measurement, defined as the distance between two tangents on opposite sides of the particle parallel to some fixed direction), and the projected area diameter (defined as the diameter of a circle having the same area as that of the particle observed perpendicular to the surface on which the particle rests). With any technique, a sufficiently large number of particles is required in order to obtain a statistically valid conclusion. This is best accomplished by using a... 

In assessing animal data, careful attention must be paid to the quality of the data, the incidence of spontaneous tumors in the control population, consistency if more than one study is available, and statistical validity. If the exposure route and experimental regimen employed do not agree with the most likely mode(s) of human exposure (e.g., intramuscular injection), the data must be interpreted cautiously. Consideration should be given to data on metabolism of the compound by the animal species tested, as compared with metabolism in humans if this information is known. If only in vitro data are available, only qualitative estimates may be possible because of uncertainties regarding the association between in vitro results and human or animal effects. The availability of associated pharmacokinetic data, however, may allow development of a rough quantitative estimate. 

Stereological methods have often been used without the advantage of a computer or video screen. Such an approach superimposes a grid of dots, lines or areas on the specimen image and counts the inclusions and intersections this grid format shows with the feature of interest within the specimen field. Such a procedure, without automation, is most laborious requiring much effort to establish statistical validity for the measurements. 

Since A is roughly proportional to vTz according to the Gaussian statistics valid approximately before the quench, we expect... 

The acceptance criterion for recovery data is 98-102% or 95-105% for drug preparations. In biological samples, the recovery should be 10%, and the range of the investigated concentrations is 20% of the target concentrations. For trace level analysis, the acceptance criteria are 70-120% (for below 1 ppm), 80-120% (for above 100 ppb), and 60-100% (for below 100 ppb) [2]. For impurities, the acceptance criteria are 20% (for impurity levels <0.5%) and 10% (for impurity levels >0.5%) [30], The AOAC (cited in Ref. [11]) described the recovery acceptance criteria at different concentrations, as detailed in Table 2. A statistically valid test, such as a /-test, the Doerffel-test, or the Wilcoxon-test, can be used to prove whether there is no significant difference between the result of accuracy study with the true value [29],... 

As noted above, the variations in the data representing the error must meet the usual conditions for statistical validity they must be random and statistically independent, and it is highly desirable that they be homoscedastic and Normally distributed. The data should be a representative sampling of the populations that the experiment is supposed... 

In equation 3.4-18, the right side is linear with respect to both the parameters and the variables, j/the variables are interpreted as 1/T, In cA, In cB,.. . . However, the transformation of the function from a nonlinear to a linear form may result in a poorer fit. For example, in the Arrhenius equation, it is usually better to estimate A and EA by nonlinear regression applied to k = A exp( —EJRT), equation 3.1-8, than by linear regression applied to Ini = In A — EJRT, equation 3.1-7. This is because the linearization is statistically valid only if the experimental data are subject to constant relative errors (i.e., measurements are subject to fixed percentage errors) if, as is more often the case, constant absolute errors are observed, linearization misrepresents the error distribution, and leads to incorrect parameter estimates. 

For reproducible expression analysis and protein quantification MS methods based on isotopic labeling are available. They were designed in conjunction with two or more dimensional chromatographic peptide separation coupled online to MS and require advanced bioinformatics input to analyze the complex data sets in a reasonable time frame. This is also true for the alternative fluorescence-based technology of differential gel electrophoresis (DIGE Fig. 10.6) with tailor-made software which allows statistical validation of multiple data sets. 

Figure 10.6. Principle of DIGE analysis separation of control and treated sample on one gel and statistical validation using more than three repeated experiments. Printed by kind permission of GE Healthcare (formerly Amersham Biosciences). (See color insert.)...

Sampling procedures are extremely important in the analysis of soils, sediments and sludges. It is essential to ensure that the composition of the portion of the sample being analysed is representative of the material being analysed. This fact is even more evident when it is conceded that the size of the portion of sample being analysed is in many modern methods of analysis extremely small. It is therefore essential to ensure before the analysis is commenced that correct statistically validated sampling procedures are used to ensure as far as is possible that the portion of the sample being analysed is representative of the bulk of material from which the sample was taken. 

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