Sampling statistical validation

Few populations, however, meet the conditions for a true binomial distribution. Real populations normally contain more than two types of particles, with the analyte present at several levels of concentration. Nevertheless, many well-mixed populations, in which the population s composition is homogeneous on the scale at which we sample, approximate binomial sampling statistics. Under these conditions the following relationship between the mass of a randomly collected grab sample, m, and the percent relative standard deviation for sampling, R, is often valid. ... 

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, ... 

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). 

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... 

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.)...

The useful equations (4.3.6) and (4.3.7), which are valid only for smooth monotonous functions, can be translated into relationships between the corresponding sample statistics... 

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. 

Part—I has three chapters that exclusively deal with General Aspects of pharmaceutical analysis. Chapter 1 focuses on the pharmaceutical chemicals and their respective purity and management. Critical information with regard to description of the finished product, sampling procedures, bioavailability, identification tests, physical constants and miscellaneous characteristics, such as ash values, loss on drying, clarity and color of solution, specific tests, limit tests of metallic and non-metallic impurities, limits of moisture content, volatile and non-volatile matter and lastly residue on ignition have also been dealt with. Each section provides adequate procedural details supported by ample typical examples from the Official Compendia. Chapter 2 embraces the theory and technique of quantitative analysis with specific emphasis on volumetric analysis, volumetric apparatus, their specifications, standardization and utility. It also includes biomedical analytical chemistry, colorimetric assays, theory and assay of biochemicals, such as urea, bilirubin, cholesterol and enzymatic assays, such as alkaline phosphatase, lactate dehydrogenase, salient features of radioimmunoassay and automated methods of chemical analysis. Chapter 3 provides special emphasis on errors in pharmaceutical analysis and their statistical validation. The first aspect is related to errors in pharmaceutical analysis and embodies classification of errors, accuracy, precision and makes... 

Independent of existing intra-lot variability, a sample size of six dosage units is generally recognized to suffice the needs of quality control (QC). In very early development less than six specimens may be used to create data, but as soon as possible tests should be run with at least n = 6. It is advisable to create statistically valid and sound data for manufacturing prototypes even at very early phases of development, in order to be able to identify formulations/batches with unwanted dissolution behavior. In the early phases of a drug product s development, formulations may not be of acceptable stability. This means that stability phenomena may mask... 

A statistically valid sampling plan requires careful design emd execution so that generalizations based on mathematical probability can be drawn from a small number of test portions. Guidelines are given for estimation of the minimum number and size of sample increments needed to achieve a given level of confidence in chemical analyses. 

Francl et al. (1996) examined the conditioning of the least squares matrix in the fitting procedure, and conclude that the method cannot be used to assign statistically valid charges to all atoms in a given molecule. This problem cannot be alleviated by the selection of more sampling points, and thus may require the introduction of chemical constraints to reduce the number of charges to be determined. 

The average concentration of PBBs (on an adipose basis and as hexabromobiphenyl) in pooled extracts of several hundred individual tissue samples collected in a statistically valid manner from all nine regions of the continental United States was 1-2 ppb (Lewis and Sovocool 1982). Chemical workers involved in the PBB manufacturing process had a median adipose PBB concentration of 6,000 ppb (range... 

Wilson et al. (2003, 2005) demonstrate the stochastic nature of the SCP, and that many measurements should be performed on a single sample in order to obtain statistically valid measurements of the SCP. However, a particularly... 

For chemical measurements with a linear calibration function, traceability of results can be formally established without great expenditure if the calibration is based on suitable reference standards and the linear regression is performed as shown above and (statistically) validated. The use of reference materials as samples make it possible to establish the traceability of a new analysis protocol by using an existing analysis method. 

When the analytical laboratory is not responsible for sampling, the quality management system often does not even take these weak links in the analytical process into account. Furthermore, if sample preparation (extraction, cleanup, etc.) has not been carried out carefully, even the most advanced, quality-controlled analytical instruments and sophisticated computer techniques cannot prevent the results of the analysis from being called into question. Finally, unless the interpretation and evaluation of results are underpinned by solid statistical data, the significance of these results is unclear, which in turn greatly undermines their merit. We therefore believe that quality control and quality assurance should involve all the steps of chemical analysis as an integral process, of which the validation of the analytical methods is merely one step, albeit an important one. In laboratory practice, quality criteria should address the rationality of the sampling plan, validation of methods, instruments and laboratory procedures, the reliability of identifications, the accuracy and precision of measured concentrations, and the comparability of laboratory results with relevant information produced earlier or elsewhere. 

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