Obtaining and Preparing Samples for Analysis

Percent of overall variance (So) due to the method as a function of the relative magnitudes of the standard deviation of the method and the standard deviation of sampling (Sm/Ss). The dotted lines show that the variance due to the method accounts for 10% of the overall variance when Ss= 3 xs . 

Selecting a sample introduces a source of determinate error that cannot be corrected during the analysis. If a sample does not accurately represent the population from which it is drawn, then an analysis that is otherwise carefully conducted will yield inaccurate results. Sampling errors are introduced whenever we extrapolate from a sample to its target population. To minimize sampling errors we must collect the right sample. 

A quantitative analysis for an analyte gives a mean concentration of 12.6 ppm. The standard deviation for the method is found to be 1.1 ppm, and that due to sampling is 2.1 ppm. (a) What is the overall variance for the analysis (b) By how much does the overall variance change if is improved by 10% to 0.99 ppm (c) By how much does the overall variance change if Sj is improved by 10% to 1.9 ppm  

a 10% improvement in the method s standard deviation changes the overall variance by approximately 4%. 

To determine which step has the greatest effect on the overall variance, both si, and si must be known. The analysis of replicate samples can be used to estimate the overall variance. The variance due to the method is determined by analyzing a standard sample, for which we may assume a negligible sampling variance. The variance due to sampling is then determined by difference. 

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