During this initial step of analysis, a portion of a bulk material is removed in order to be assayed. The portion should be chosen so that it is representative of the bulk material. To assist in this, statistics is used as a guide to determine the sample size and the number of samples. When selecting a sampling program, it is important that the analyst has a detailed description of the information required from the analysis, an estimate of the accuracy to be achieved, and an estimate of the amount of time and money that can be spent on sampling. It is worthwhile to discuss with the users of the analytical results the type of data that is desired. Results may provide needless or insufficient information if the
sampling procedure is either excessive or inadequate.
Generally the accuracy of an analysis is increased by obtaining multiple samples at varying locations (and times) within the bulk material. As an example, analysis of a lake for a chemical pollutant will likely yield inaccurate results if the lake is sampled only in the centre and at the surface. It is preferable to sample the lake at several locations around its periphery as well as at several depths near its centre. The homogeneity of the bulk material influences the number of samples needed. If the
material is homogeneous, only a single sample is required. More samples are needed to obtain an accurate analytical result when the bulk material is heterogeneous. The disadvantages of taking a larger number of samples are the added time and expense. Few laboratories can afford massive sampling programs.
After the sample has been collected, it may be necessary to chemically or physically treat it at the sampling site. Normally this treatment is done immediately after the sample has been collected. The nature of the treatment is dependent on the sample and the substances for which it is being analyzed. For example, natural water samples that are assayed for dissolved oxygen generally are placed in containers that are sealed, stored, and transported in a refrigerated compartment. Sealing prevents a change in oxygen concentration owing to exposure to the atmosphere, and refrigeration slows changes in oxygen levels caused by microscopic organisms within the sample. Similarly, samples that are to be assayed for trace levels of metallic pollutants are pretreated in order to prevent a decrease in the concentration of the pollutant that is caused by adsorption on the walls of the sample vessel. Metallic adsorption can be minimized by adding nitric acid to the sample and by washing the walls of
the vessel with the acid.
After the samples arrive at the laboratory, additional operations might be required prior to performing the assay. In some cases, multiple samples simply are combined into a composite sample which is made homogeneous and then assayed. This process eliminates the need to assay each of the individual specimens. In other instances, the sample must be chemically or physically treated in order to place it in a form that can be assayed. For example, ore samples normally must be first dissolved in acidic solutions. Sometimes it is necessary to change the concentration of the analyte prior to performing the assay so that it will fall within the range of the analytical method. Once the specimen is
prepared, enough laboratory assays are completed to allow the analyst to estimate the amount of random error. Typically a minimum of three assays are performed on each sample.
After the assays have been completed, quantitative results are mathematically manipulated, and both qualitative and quantitative results are presented in a meaningful manner. In most cases, two values are reported for quantitative analyses. The first value is an estimate of the correct value for the analysis, and the second value indicates the amount of random error in the analysis. The most common way of reporting the best value is to give the mean (average) of the results of the laboratory
assays. In specific cases, however, it is better to report either the median (central value when the results are arranged in order of size) or the mode (the value obtained most often).
Accuracy is the degree of agreement between the experimental result and the true value. Precision is the degree of agreement among a series of measurements of the same quantity; it is a measure of the
reproducibility of results rather than their correctness. Errors may be either systematic (determinant) or random (indeterminant). Systematic errors cause the results to vary from the correct value in a predictable manner and can often be identified and corrected. An example of a systematic error is improper calibration of an instrument. Random errors are the small fluctuations introduced in nearly all analyses. These errors can be minimized but not eliminated. They can be treated, however,
using statistical methods. Statistics is used to estimate the random error that occurs during each step random error. The units of standard deviation are identical to those of the individual analytical results.
The variance (V) is the square of the standard deviation and is useful because, in many cases, it is probability level are values greater than and less than the average, between which the results are statistically expected to fall a given percentage of the time.