Subsampling

A subsample is a portion of a sample, prepared in such a way (hat there is some confidence that it has the same concentration of analyte as that in the original sample. The laboratory sample may be a subsample of a bulk sample and a test sample may be a subsample of the laboratory sample. Because of inhomogeneity, differences may occur between samples but there should not be any significant inhomogeneity between subsamples. 

Although the error associated with subsampling carried out in the laboratory to obtain the test portion is sometimes insignificant, it can be much greater than intuition would predict. It becomes more important as the concentration of the analyte 

An indication of the minimum size of a subsample can be obtained by using the concept of a sampling constant. For example, in the laboratory, the sampling constant can be used to estimate the minimum size of the test portion. However, the suitability of the chosen test portion size must be confirmed as part of method validation. The sampling constant Ks has units of mass. This is the mass of the test portion necessary to ensure a relative subsampling error of 1% (at the 68% confidence level) in a single determination. The value of /Ks is numerically equal to the coefficient of variation, CV (see Chapter 6, Section 6.1.3) for results obtained on 1 g subsamples in a procedure with insignificant analytical error. 

If the laboratory sample has been prepared in a particular way to pass a specific mesh size, the coefficient of variation of the result for one component varies inversely with m, where m is the mass of the test portion. A sampling constant (Ks) can be defined by the following  

This relationship presumes that the test portion corresponds to at least a certain minimum number of particles and that the sample is well-mixed . The combined results from two test portions, each of mass m, has the same subsampling variability as a single test portion of mass 2m. 

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Illustration showing the method of coning and quartering as a means of reducing a gross sample for subsampling, (a) The gross sample is first piled into a cone and... 

Practical considerations enter into the experimental plan in various other ways. In many programs, variables are introduced at different operational levels. For example, in evaluating the effect of alloy composition, oven temperature, and varnish coat on tensile strength, it may be convenient to make a number of master alloys with each composition, spHt the alloys into separate parts to be subjected to different heat treatments, and then cut the treated samples into subsamples to which different coatings are appHed. Tensile strength measurements are then obtained on all coated subsamples. 

The standard way to proceed would be to fit the model to the data relative to each experimental unit, one at a time, thus obtaining a sample of parameter estimates, one for each experimental tumor observed. The sample mean and dispersion of these estimates would then constitute our estimate of the population mean and dispersion. By the same token, we could find the mean and dispersion in the Control and Treated subsamples. 

Preparation of Emulsions. The entire aqueous phase was stirred until all solids were dissolved. Sufficient water was withheld from the formulation so small volumes of experimental and control components could be added to emulsion subsamples. Sulfuric acid (1 N) was added to the aqueous phase to decrease the pH to 5.7. The two phases in separate containers were blanketed with nitrogen, sealed, and heated to 75 in an 80 water bath (about 30 minutes). The hot oil phase was stirred slowly and blanketed with nitrogen, then the hot aqueous phase was quickly added while stirring. The emulsion was blanketed with nitrogen and slowly stirred (about 2 hours) in the stoppered container until ambient temperature ( 25 ) was reached. Subsamples of the master batch were removed for the addition of experimental components and stored in 1-oz containers. The containers had been washed with hot tap water, deionized water, and methanol, then dried at 120 . 

In experiments with water-soluble inhibitors, the subsample was stirred under nitrogen during post-addition of an aqueous solution of the inhibitor followed by an aqueous sodium nitrite solution. Aliquots were weighed into 1-oz ointment jars, covered with nitrogen, sealed, and stored at 37 for later replicate analyses. Preparation of the positive control subsample was identical except that water was added in place of inhibitor. 

Lin, H.C. and Sheen, G.J., An approximation approach for making decisions in assessing the capability index C-pk from the subsamples. Comm. Stat. Sim. Comp., 34, 191, 2005. 

Three- Stage Sampling (Strata, Samples, Subsamples)... 

The literature on sampling bulk materials is more specific and more quantitative than the general discussion presented above. Nevertheless, experiments on the sampling and subsampling procedures... 

The test presented in the previous section is useful when a smaller probability of false detection is needed than is provided by the distribution-free test. However, the test in the previous section is no panacea. Reduction of the skewness through proper choice of sampling and subsampling procedures is an alternative that may have much more potential for improving the study. 

Due to combination of several analytical steps often sigiuficant errors Small methodological error, small subsamples, but only applicable to elements... 

It is recommended to use a borer of diameter greater than 5 cm to avoid column compaction. The sediment columns are mixed and homogenized and a subsample is taken for laboratory analysis. To investigate the vertical distribution of a chemical for... 

The objective of sediment and water sampling is to obtain reliable information about the behavior of agrochemicals applied to paddy fields. Errors or variability of results can occur randomly or be due to bias. The two major sources of variability are sediment body or water body variability and measurement variability . For the former, a statistical approach is required the latter can be divided into sampling variability, handling, shipping and preparation variability, subsampling variability, laboratory analysis variability, and between-batch variability. ... 

Water subsamples for analysis are prepared for cleanup by filling 200-inL volumetric flasks to volume and adding 10 mL of MeOH and 0.10 mL of concentrated phosphoric acid to adjust to approximately 5% MeOH and 0.01% H3PO4 by volume. All samples are stored at 4 2 °C until cleanup. 

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