Sampling uncertainties

In order to determine how many samples we require, it is necessary to consider the sources of uncertainty in the final result. Uncertainty is dealt with in more detail in Chapter 6. In this section, we are mainly concerned with the uncertainty arising from sampling. It is necessary to use a few statistical terms namely, sample standard deviation (s) and variance (.v2). These terms are defined in Chapter 6, Section 6.1.3. 

The total variance in the final result (,v2ita ) is made up of two contributions. One is from variation in the composition of the laboratory samples due to the nature of the bulk material and the sampling procedures used ( ample). The other (Tanalysis) is from the analysis of the sample carried out in the laboratory  

The analytical variance can be determined by carrying out replicate analysis of samples that are known to be homogeneous. You can then determine the total variance. To do this, take a minimum of seven laboratory samples and analyse each of them (note that Sample characterizes the uncertainty associated with producing the laboratory sample, whereas sanalysis w h take into account any sample treatment required in the laboratory to obtain the test sample). Calculate the variance of the results obtained. This represents stQtal as it includes the variation in results due to the analytical process, plus any additional variation due to the sampling procedures used to produce the laboratory samples and the distribution of the analyte in the bulk material. 

The variance of the sample (Sample) s also made up of two components, i.e. that due to the population,. y20p (i.e. the variation of the distribution of the analyte throughout the material) and that due to the sampling process ( ). You should always try to make sure the variance due to sampling is negligible. The variance due to the population is the one that is of most concern to the analyst  

The magnitude of each of these components will influence the number of samples you need to take so as to achieve a given overall uncertainty. 

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The analytical uncertainty should be reduced to one-third or less of sampling uncertainty (16). Poor results obtained because of reagent contamination, operator errors ia procedure or data handling, biased methods, and so on, can be controlled by proper use of blanks, standards, and reference samples. 

If, in the above example, the analytical error was 0.2 per cent then the total error sT would be equal to 3.006 per cent. Hence the contribution of the analytical error to the total error is virtually insignificant. Youden7 has stated that once the analytical uncertainty is reduced to one-third of the sampling uncertainty, further reduction of the former is not necessary. It is most important to realise that if the sampling error is large, then a rapid analytical method with relatively low precision may suffice. 

Ks is expressed in the units of mass and is numerically equal to the sample mass necessary to limit the error due to sample heterogeneity (sampling uncertainty) to I % (with 68 % confidence). 

As before, our simulation data are subject to statistical (sampling) uncertainties, which are particularly pronounced near the extremes of particle numbers and energies visited during a run. When data from multiple runs are combined, as shown in Fig. 10.3, the question arises of how to determine the optimal amount by which to shift the raw data in order to obtain a global free energy function. As reviewed in... 

Table II Calculation by Visman Equation of Number of Samples Required for Determination of Dieldrin with a Sampling Uncertainty of 50% Relative Standard Deviation in Test Data of Table I, Using Pairs of Large Cores Taken Perpendicular to Spray-Track Direction.

It can be concluded that for a system as heterogeneous as this example the number and size of the samples must be large if a significant reduction in the sampling uncertainty is to be achieved. The data also reveal the extent of the variability in spray application. An additional conclusion is that reduction in costs and time in the analytical operations may be possible without sacrificing information, since a less precise procedure would suffice under these circumstances. 

Extrapolation from field studies with other pesticides, and/or sampling uncertainty due to limited numbers of field sites... 

FIGURE 6.11 Kolmogorov-Smirnov confidence limits (black) acconnting for both mea-snrement uncertainty and sampling uncertainty about the p-box (gray) from Figure 6.9. 

The results of these measurements are also given in Figure 9.8. Unfortunately, the technique utilizing equation (9.26) cannot provide an estimate of sampling uncertainty. 

Interlaboratory studies usually provide the test material in a homogeneous form that can be subsampled without additional uncertainty. In the field, if the result is attributed to a bulk material from which the sample was drawn, then sampling uncertainty needs to be estimated. Again, proper definition of the measurand is important in understanding where to start adding in uncertainty components. 

Suppose that much finer particles of 80/120 mesh size (average diameter = 152 pm, average volume = 1.84 nL) were used instead. Now the mass containing 104 particles is reduced from 11.0 to 0.038 8 g. We could analyze a larger sample to reduce the sampling uncertainty for chloride. 

Example Reducing Sample Uncertainty with a Larger Test Portion... 

How many grams of 80/120 mesh sample are required to reduce the chloride sampling uncertainty to 1% ... 

Even with an average particle diameter of 152 pm, we must analyze 3.84 g to reduce the sampling uncertainty to 1 %. There is no point using an expensive analytical method with a precision of 0.1%, because the overall uncertainty will still be 1% from sampling uncertainty. 

There is no advantage to reducing the analytical uncertainty if the sampling uncertainty is high, and vice versa. 

We just saw that a single 0.7-g sample is expected to give a sampling standard deviation of 7%. How many 0.7-g samples must be analyzed to give 95% confidence that the mean is known to within 4% The meaning of 95% confidence is that there is only a 5% chance that the true mean lies more than 4% away from the measured mean. The question we just asked refers only to sampling uncertainty and assumes that analytical uncertainty is much smaller than sampling uncertainty. 

IMEP certified test samples uncertainty contributions... 

Replicate samples are used to indicate sample uncertainty, which shows the contribution of sampling and sample handling to the overall uncertainty. 

Field intercomparisons are another important quality assurance step for quantifying the uncertainty of methods they also include the sampling uncertainty and not just the analytical uncertainty... 

A critical examination of the analytical procedures used prior to 1977 showed these to be inadequate for the determination of organic compounds in combustion effluents of special concern were the short-comings in sample collection methods. These short-comings are delineated in a review published recently (2). Because of these sampling uncertainties, the continuous development and validation of new procedures and sampling systems was an essential element of this study. 

Sample uncertainty is also referred to as statistical random sampling error. This type of uncertainty is often estimated assuming that data are sampled randomly and without replacement and that the data are random samples from an unknown population distribution. For example, when measuring body weights of different individuals, one might randomly sample a particular number of individuals and use the data to make an estimate of the interindividual variability in body weight for the entire population of similar individuals (e.g. for a similar age and sex cohort). 

In order to assess the precision of the chemical analysis relative to the variation due to sample preparation and sampling, duplicate samples and repeat measurements should be carried out. The duplicate samples, prepared independendy of each other and analyzed randomly along with all other samples, with each duplicate sample also analyzed in duplicate, allows estimation of sampling uncertainty by the analysis of variance (ANOVA) statistical interpretation method. 

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