Sample size selection, environmental sampling

The steps of the analytical process are illustrated in Fig. 1-1. It is well known that in each step of this process experimental errors are possible. Furthermore, each analytical result contains at least some experimental error the relative size of this error increases considerably as the analyte concentration in the sample decreases. This general relationship is demonstrated in Fig. 1-6 for some selected environmentally relevant compounds. Because the majority of studies concerning the environment deals with trace or ultratrace analysis, this fact is very evident and important. 

Therefore, the challenge in sampling solids for environmental analysis is to collect a relatively small portion of the sample that accurately represents the composition of the whole. This requires that sample increments be collected such that no piece, regardless of position (or size) relative to the sampling position and implement, is selectively collected or rejected. Optimization of solids sampling is a function of the many variable constituents of coal and is reflected in the methods by which an unbiased sample can be obtained, as is required by coal sampling (ASTM D197). 

Problem of Verification. Much of the data used in this study were gathered by interviews with R D personnel from the sample firms. These individuals provided both subjective and objective information about their companies and the manner in which environmental protection regulations impact their R D activities. Given the size and complexity of these sample firms, this data were difficult to verify. However, to help substantiate the validity of the data provided, the researchers analyzed the responses for consistencies or possible contradictions. Comparisons were made between individual responses and data gathered from trade journals, annual reports, and other secondary data sources. Further, in selected instances, the researchers made plant tours to personally observe the manner in which the companies had been affected. 

Based on the sample data, we may reject the null hypothesis when in fact it is true, and consequently accept the alternative hypothesis. By failing to recognize a true state and rejecting it in favor of a false state, we will make a decision error called a false rejection decision error. It is also called a false positive error, or in statistical terms, Type I decision error. The measure of the size of this error or the probability is named alpha (a). The probability of making a correct decision (accepting the null hypothesis when it is true) is then equal to 1—a. For environmental projects, a is usually selected in the range of 0.05-0.20. 

The AA analyses were used as a guide for selecting the elements to be analyzed with the Philips XRF system (Table II). Major elements not usually of environmental concern were analyzed as well as trace elements because of their effect on the X-ray absorption of the heavier elements. Elements below the XRF analysis detection limits, such as Hg and Cd, were not analyzed. Samples prefixed with the letter F were mechanically separated so as to bias the fine-particle size. This procedure indicated to what degree the shipboard centrifugal cone separator, used to select the finer sediment particles, influenced the elemental composition. 

Care must also be taken to ensure that particle size distributions are adequate as selected particle size distributions will achieve greater homogeneity in reference materials especially when very low sample intakes are used for measurements. This is extremely important for environmental reference materials such as soils, sediments, etc., and is optimally achieved by jet-milling with ultra-fine classification of particles. With this technique, which is non-contaminating, fast and well-controlled, the sieved fraction below 2 mm of the material is ground by... 

The second-order calibration example shown next is from the field of environmental analytical chemistry. A sensor was constructed to measure heavy metal ions in tap and lake water [Lin et al. 1994], The two heavy metal ions Pb2+ and Cd2+ are of special interest (the analytes) and there may be interferents from other metals, such as Co2+, Mn2+, Ni2+ and Zn2+. The principle of the sensor is described in detail in the original publication but repeated here briefly for illustration. The metal ions diffuse through a membrane and enter the sensor chamber upon which they form a colored complex with the metal indicator (4-(2-pyridylazo) resorcinol PAR) present in that chamber. Hence, the two modes (instrumental directions) of the sensor are the temporal mode related to the diffusion through the membrane, and the spectroscopic mode (visible spectroscopy from 380 to 700 nm). Selectivity in the temporal mode is obtained by differences in diffusion behavior of the metal ions (see Figure 10.22) and in the spectroscopic mode by spectral differences of the complexes formed. In the spectroscopic mode, second-derivative spectra are taken to enhance the selectivity (see Figure 10.23). The spectra were measured every 30 s with a resolution of 1 nm from 420 to 630 nm for a period of 37 min. This results in a data matrix of size 74 (times) x 210 (wavelengths) for each sample. 

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