The principle of correct sampling

The error incurred when the boundary of the sample to be taken is not defined according to the principle of correct sampling. 

The principle of correct sampling for bulk solids, liquids, and gases... 

Later in this chapter, we will examine these three steps in detail to understand how the principle of correct sampling can be followed or violated. 

To take a random sample of 2 blocks, we could number the blocks in the cluster from 1 to 27. Then we could generate 2 random numbers from a computer, or, alternatively, number 27 pieces of paper, mix them, and draw 2 at random. We select the 2 blocks with those numbers as our sample. Since all the blocks are easily accessible, this procedure is fairly straightforward, and we have followed the principle of correct sampling. 

Gy refers to this sampling situation as zero-dimensional. As we saw in Chapter 2, he develops a model for the variance of the FE and bases it on statistical sampling theory, where all the sampling units are discrete and well defined. As long as all units are accessible., we can easily define and extract the units for the sample. Adhering to the principle of correct sampling is thus straightforward. 

Gy concludes that except in the case of nonviscous liquids, the principle of correct sampling cannot be followed in three-dimensional sampling situations. Thus, three-dimensional sampling situations should be avoided if possible, and we discuss next a way to do this that can be applied in many instances. 

We are fully aware that one-dimensional cross-stream sampling is not always possible in practice, especially for liquids and gases. However, it is important to look for alternative sampling points in the process that will allow reduction of the sampling dimension. We will then be better able to follow the principle of correct sampling and thus improve our chances of getting good, representative samples. 

For liquids, there are several ways to apply the principle of correct sampling across the vertical dimension. A tool that uses the same idea as the thief is the coliwasa (Composite Liquid WAste SAmpler), shown in Figure 3.9. They come in various lengths and diameters, depending on the depth and size of the container lot. This hollow column is lowered slowly through the liquid until the desired depth is reached. Then the top and bottom are plugged to retain a core. 

Solids moving along a conveyor belt provide the opportunity for correct, one-dimensional, cross-stream sampling before the material collects as a three-dimensional lot where the principle of correct sampling cannot be followed. In both of these cases, we also have the fourth dimension, time, where sampling frequency and process variation add complicating elements. These will be explored in detail in Chapter 4. 

Choose the right sampling tool. Examine the tool and look for violations of the principle of correct sampling. The tool must be capable of taking the sample that is defined and taking it correctly. 

Error 5 Delimitation error (DE) (including the principle of correct sampling)... 

Therefore, sampling correctness has a special meaning in Gy s theory. When we talk about a correct sample, we mean that the principle of correct sampling has been followed. Note that correctness is a process, which we have some control over. We do not have control, however, over the accuracy of a sample value, which is a result. This is no different than SRS, where we can control the method by which we obtain a subset of the population of individual units using a random technique. But we are stuck with the resulting sample and its value of the characteristic of interest. 

While defining a correct sample is straightforward in theory, sample extraction is difficult to carry out in practice because of the sampling dimension, the tools used, and how they are used. The sampling tool must be compatible with the boundaries defined, and the tool must be used correctly. When the sample defined is not the same as the sample extracted, we incur an EE, another of the three errors arising from violating the principle of correct sampling. 

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