How Much Sample to Collect

As a starting point, let s assume that our target population consists of two types of particles. Particles of type A contain analyte at a fixed concentration, and type B particles contain no analyte. If the two types of particles are randomly distributed, then a sample drawn from the population will follow the binomial distribution. If we collect a sample containing n particles, the expected number of particles containing analyte, ti, is 

The relative standard deviation for sampling, Sj r, is obtained by dividing equation 

Solving for n allows us to calculate the number of particles that must be sampled to obtain a desired sampling variance. 

Note that the relative sampling variance is inversely proportional to the number of particles sampled. Increasing the number of particles in a sample, therefore, improves the sampling variance. 

Suppose you are to analyze a solid where the particles containing analyte represent only 1 X 10 % of the population. How many particles must be collected to give a relative sampling variance of 1%  

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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. 

Sampling is one of the most important operations in a chemical analysis. Chemical analyses use only a small fraction of the available sample. The fractions of the sandy and loam soil samples shown in the photo that are collected for analyses must be representative of the bulk materials. Knowing how much sample to collect and how to further subdivide the collected sample to obtain a laboratory sample is vital in the analytical process. Sampling, standardization, and calibration are the focal points of this chapter. All three steps require a knowledge of statistics. 

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