Number of Individual Samples Required

A normally distributed parent population X is characterized by its expected mean value / and standard deviation a. If the samples taken from this population are representative, the sample average x is an unbiased estimate of /c 

For a small sample size and a particular confidence level other than GAUSSian distribution, the STUDENT /-distribution has to be assumed. Furthermore, the confidence range for the estimate x is  

If the maximum allowed uncertainty is U and the variance of the population is s2, which includes the variances of all steps of the analytical process from sampling to analysis, the sample size n is given very simply and pragmatically by  

The total weight w/0/a/ of the composite sample can be calculated according to  

An estimate of x and s1 can be obtained from past experience or preliminary sampling. The application of this equation is described in detail by KRAFT [1978 1994] and HOLSTEIN [1980], 

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The description of an object in the sense of environmental investigation may be the determination of the gross composition of an environmental compartment, for example the mean state of a polluted area or particular location. If this is the purpose, the number of individual samples required and the required mass or size of these increments have to be determined. The relationship between the variance of sampling and that of analysis must be known and both have to be optimized. The origin of the variance of the samples can be investigated by the study of variance contribution of the different steps of the analytical process by means of the law of error propagation (Eq. 4-21) according to Section 4.3.4. 

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