Minimizing the Overall Variance

If Sm is significantly greater than Sj, then we only need to collect and analyze a single sample. The number of replicate analyses, r, needed to minimize the error due to the method is given by an equation similar to equation 7.7 

Unfortunately, the simple situations just described are often the exception. In many cases, both the sampling variance and method variance are significant, and both multiple samples and replicate analyses of each sample are required. The overall error in this circumstance is given by 

Equation 7.8 does not have a unique solution because different combinations of and give the same overall error. The choice of how many samples to collect and how many times each sample should be analyzed is determined by other concerns, such as the cost of collecting and analyzing samples, and the amount of available sample. 

A certain analytical method has a relative sampling variance of 0.40% and a relative method variance of 0.070%. Evaluate the relative error (a = 0.05) if (a) you collect five samples, analyzing each twice and, (b) you collect two samples, analyzing each five times. 

Both sampling strategies require a total of ten determinations. Using Appendix IB, we find that the value of t is 2.26. Substituting into equation 7.8, we find that the relative error for the first sampling strategy is 

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More attention to selecting and obtaining a representative sample. The design of a statistically based sampling plan and its implementation are discussed earlier, and in more detail than in other textbooks. Topics that are covered include how to obtain a representative sample, how much sample to collect, how many samples to collect, how to minimize the overall variance for an analytical method, tools for collecting samples, and sample preservation. 

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