Target populations

Selecting a sample introduces a source of determinate error that cannot be corrected during the analysis. If a sample does not accurately represent the population from which it is drawn, then an analysis that is otherwise carefully conducted will yield inaccurate results. Sampling errors are introduced whenever we extrapolate from a sample to its target population. To minimize sampling errors we must collect the right sample. 

From where within the target population should samples be collected ... 

A sample collected at random from the target population. 

A randomly collected sample makes no assumptions about the target population, making it the least biased approach to sampling. On the other hand, random sampling requires more time and expense than other sampling methods since a greater number of samples are needed to characterize the target population. 

Samples collected from the target population using available information about the analyte s distribution within the population. 

As a starting point, let s assume that our target population consists of two types of particles. Particles of type A contain analyte at a fixed concentration, and type B particles contain no analyte. If the two types of particles are randomly distributed, then a sample drawn from the population will follow the binomial distribution. If we collect a sample containing n particles, the expected number of particles containing analyte, ti, is... 

When the target population is segregated, or stratified, equation 7.5 provides a poor estimate of the amount of sample needed to achieve a desired relative standard deviation for sampling. A more appropriate relationship, which can be applied to both segregated and nonsegregated samples, has been proposed. ... 

In the previous section we considered the amount of sample needed to minimize the sampling variance. Another important consideration is the number of samples required to achieve a desired maximum sampling error. If samples drawn from the target population are normally distributed, then the following equation describes the confidence interval for the sampling error... 

This is not an uncommon problem. For a target population with a relative sampling variance of 50 and a desired relative sampling error of 5%, equation 7.7 predicts that ten samples are sufficient. In a simulation in which 1000 samples of size 10 were collected, however, only 57% of the samples resulted in sampling errors of less than 5% By increasing the number of samples to 17 it was possible to ensure that the desired sampling error was achieved 95% of the time. 

Once a sample is withdrawn from a target population, there is a danger that it may undergo a chemical or physical change. This is a serious problem since the properties of the sample will no longer be representative of the target population. For this reason, samples are often preserved before transporting them to the laboratory for analysis. Even when samples are analyzed in the field, preservation may still be necessary. 

The initial sample is called the primary, or gross sample and may be a single increment drawn from the target population, or a composite of several increments. In many cases the gross sample cannot be analyzed without further treatment. Processing the gross sample may be used to reduce the sample s particle size, to transfer the sample into a more readily analyzable form, or to improve its homogeneity. 

The initial sample, collected from the target population without any processing. 

Sample Preservation Once removed from its target population, a liquid sample s chemical composition may change as a result of chemical, biological, or physical processes. Following its collection, samples are preserved by controlling the solu-... 

Sample Collection Solids are usually heterogeneous, and samples must be collected carefully if they are to be representative of the target population. As noted earlier, solids come in a variety of forms, each of which is sampled differently. 

An analysis requires a sample, and how we acquire the sample is critical. To be useful, the samples we collect must accurately represent their target population. Just as important, our sampling plan must provide a sufficient number of samples of appropriate size so that the variance due to sampling does not limit the precision of our analysis. 

The results from the consequence analysis step are estimates of the statistically expected exposure of the target population to the hazard of interest and the safety/health effects related to that level of exposure. For example ... 

Variability arises from true heterogeneity in characteristics such as dose-response differences within a population, or differences in contaminant levels in tlie enviromiient The values of some variables used in an assessment change witli time and space, or across tlie population whose exposure is being estimated. Assessments should address tlie resulting variability in doses received by members of the target population. Individual exposure, dose, and risk can vary widely in a large population. The central tendency and high end individual risk descriptors are intended to capture tlie variability in exposure, lifestyles, and other factors tliat lead to a distribution of risk across a population. 

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